Maths Perplexors: Ages 10-11

RIC-6068 2.85/1162

Maths perplexors (Ages 10–11) Published by R.I.C. Publications® 2009 under licence to MindWare Holdings Inc. Copyright © 2007 MindWare Holdings Inc. This version copyright © R.I.C. Publications® 2009

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Introduction

Contents

Maths perplexors are deductive logic puzzles. They are specifically designed to challenge and extend mainstream or more able maths students. It is strongly recommended that the teacher models the process of deductive reasoning once or twice with the students, if necessary, before allowing them to work independently (or in pairs or small groups).

Introduction .................................... iii Contents ......................................... iii Instructions ...................................... iv

When you are faced with a number of options, logic is often used to make a choice. Logic uses reasoning and proof to help you analyse information and come to a conclusion.

Cheeky chipmunks .......................... 1 Chicken pieces ................................ 2 Marriage counts ............................... 3 Trees a crowd .................................. 4 Farmer’s market ............................... 5 Nuts to you ...................................... 6 Grocery pokers ................................ 7 Don’t dry this at home ..................... 8 Money in the bank .......................... 9 Flower power ................................ 10 Pig eaters ....................................... 11 Race memories .............................. 12 Beans to you .................................. 13 Let’s all do the monkey hop ........... 14 Garden bounty .............................. 15 Farmer’s markup ............................ 16 Stand by me .................................. 17 School picnics ............................... 18 Baker’s dozen ................................ 19 That’s just ducky ............................ 20 Gone fishing .................................. 21 Running backs ............................... 22 Are you a loser? ............................. 23 Pig town pride ............................... 24 When pigs fly ................................ 25 It’s a hit .......................................... 26 How low can you get? ................... 27 Family bike trip .............................. 28 Thanksgiving plays ........................ 29 That’s mice to know ....................... 30 Nuts to count ................................. 31 The hole thing ............................... 32 Shape up kids ................................ 33 Winter holiday fun ......................... 34 Camelot? ....................................... 35 Bug zappers ................................... 36 Cactuses factuses? ......................... 37 All abeard! .................................... 38 An eggsact count ........................... 39 Tripping out ................................... 40 Climb every mountain ................... 41 Great Caesar’s goats ...................... 42 Pirate figures .................................. 43 High life ........................................ 44 Bakery goods ................................. 45 Flying frogs? .................................. 46 Lumberjacks are OK! ..................... 47 Smore the merrier .......................... 48 Racing woes .................................. 49 Fruit tree bounty ............................ 50 Answers .................................... 51–53

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Perhaps the easiest way to understand this technique is to look at the sample puzzle on page iv and follow along as the reasons for crossing off and circling an answer are given.

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All the information needed to solve a Maths perplexors logic problem is given in the puzzle story and its following clues. In the beginning, all the possibilities are listed for each category. As they are eliminated by information given in the clues, these possibilities should be crossed off. In a vertical column, if all the answers in a column are eliminated except for one, then that one remaining possibility must be the answer and it should be circled. The same is true in horizontal rows. If all the possibilities are eliminated in a row except for one, then that one remaining possibility must be the answer and it should be circled.

Puzzles

Maths perplexors are not designed as easy, done-in-a-minute activities. Rather, they are challenges that require a reasoned, logical response over time. They will both challenge and extend students.

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There are many ways in which these puzzles can be used in a classroom. The following are examples only, not an exhaustive list.

Homework This is not a ‘more of the same’ activity; it is an opportunity for students to consolidate and expand on what they have learnt in the classroom.

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Extension activities This is self-explanatory. The extension could be in terms of content or process.

Small-group problem-solving Thinking and talking mathematically are two vital skills. By working on the logic puzzles in pairs or small groups, thinking and talking about the problem, students can share and strengthen these skills.

Whole-class challenges Teacher assistance may be required with some students; modelling is an effective strategy.

‘Extras’ This is mainly a fun activity/challenge for the more mathematically able or advanced students.

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Instructions The story

The clues

Three geckos named Greg, Gail, and Gordon lived together in the desert. They were 8, 4 and 2 years old.

One recent day they ate 40, 20, and 10 flies for dinner.

Based on the clues, match the geckos with their ages and fly ‘consumptions’.

1. Multiply Greg’s age by 10 and the answer is the number of flies he ate for dinner.

2. Gail ate twice as many flies as the oldest gecko.

Greg 8 years old 4 years old 2 years old

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Gordon

8 years old 4 years old 2 years old

8 years old 4 years old 2 years old

40 flies 20 flies 10 flies

40 flies 20 flies 10 flies

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40 flies 20 flies 10 flies

r o e t s Bo r e p ok u S Gail

Clue 1 allows you to cross out ‘8 years old’ under Greg because 10 x 8 = 80 and 80 is not a choice. Clue 1 also allows you to cross out ‘10 flies’ under Greg because multiplying 10 by any age number cannot result in 10.

Greg

Gail

Gordon

8 years old 4 years old 2 years old

8 years old 4 years old 2 years old

8 years old 4 years old 2 years old

40 flies 20 flies 10 flies

40 flies 20 flies 10 flies

40 flies 20 flies 10 flies

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Clue 2 allows you to cross out ‘8 years old’ under Gail as she ate twice as many flies as the 8-year-old gecko. This means Gordon must be the 8 year old gecko and that number should be circled under Gordon, and ‘4 years old’ and ‘2 years old’ under Gordon should be crossed off the list. Clue 2 also allows you to cross out ‘10 flies’ under Gail as 10 is not twice as much as anything on the list. Crossing off 10 under Gail means that Gordon had to be the gecko that ate 10 flies. ‘10 flies’ under Gordon should be circled, and ‘40 flies’ and ‘20 flies’ under Gordon should be crossed off.

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Greg 8 years old 4 years old 2 years old 40 flies 20 flies 10 flies

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8 years old 4 years old 2 years old

40 flies 20 flies 10 flies

40 flies 20 flies 10 flies

Now that we know Gordon is the oldest gecko and he ate 10 flies, and we know that Gail ate 20 flies because she ate twice as many flies as Gordon, circle 20 flies under Gail and complete the crossing out; we know that Greg ate 40 flies.

Clue 1 says multiplying Greg’s age by 10 reveals the number of flies he ate. Since we now know he ate 40 flies, we must conclude he is 4 years old because 4 x 10 = 40.

iv | Maths perplexors

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1

Cheeky chipmunks The clues

Binky, Alvin and Patrick were three squirrels living in the same area of the Glenview Forest. They lived in burrows that were 60, 50 and 35 metres long. Once they held a contest to see who could stuff the most sunflower seeds in their cheeks. They stuffed 120, 100 and 90 seeds in their cheeks for the contest. It’s a well-known fact that owls like to chase squirrels, and these three squirrels kept track of how many times they had been chased by owls. They had been chased 180, 150 and 125 times.

Based on the clues, match the squirrels with their burrow lengths, their sunflower seed-stuffing totals and the number of times they had been chased by owls.

1. Patrick’s seed-stuffing total was twice the size of Alvin’s burrow length.

2. Patrick’s owl number divided by 3 would be Binky’s burrow length.

3. Alvin’s burrow was longer than Binky’s burrow.

4. Alvin and Patrick’s seed-stuffing total combined would be 220.

5. Alvin was not chased by as many owls as Patrick.

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Binky

Alvin

Patrick

60 m 50 m 35 m

60 m 50 m 35 m

120 seeds 100 seeds 90 seeds

120 seeds 100 seeds 90 seeds

120 seeds 100 seeds 90 seeds

180 owls 150 owls 125 owls

180 owls 150 owls 125 owls

180 owls 150 owls 125 owls

60 m 50 m 35 m

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Chicken pieces The clues

Tom, Teresa and Terry all went into a fried chicken restaurant together. They loved chicken legs and coleslaw, and they ordered 6, 5 and 3 chicken legs for their three meals and 6, 5 and 3 orders of coleslaw. All three ordered just one order of chips. But when they got their orders of chips and counted each one, they discovered they had received 79, 70 and 61 individual chips in their orders. Based on the clues, match the names with their chicken leg orders, their coleslaw orders and their chip numbers.

1. Nobody ordered the same number of leg pieces and the same number of orders of coleslaw.

2. Tom received 9 fewer chips than Teresa received.

3. Teresa did not receive the most chips with her order.

4. One of the three ordered twice as many orders of coleslaw as chicken legs.

5. Terry did not order the fewest chicken legs.

6. Tom’s coleslaw order number was smaller than his chicken leg number, but it was not the smallest coleslaw number.

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Tom

Teresa

6 legs 5 legs 3 legs

6 legs 5 legs 3 legs

6 legs 5 legs 3 legs

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79 chips 70 chips 61 chips

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Terry

6 coleslaw 5 coleslaw 3 coleslaw

6 coleslaw 5 coleslaw 3 coleslaw

79 chips 70 chips 61 chips

79 chips 70 chips 61 chips

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6 coleslaw 5 coleslaw 3 coleslaw

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Marriage counts The clues

Nancy, Naomi and Nellie were three married women.

They had been married for 15, 13 and 11 years. They were the proud mothers of 4, 3 and 2 sons, and the equally as proud mothers of 4, 3 and 2 daughters.

Based on the clues, match the women with the length of time they had been married, their number of sons and their number of daughters.

1. No woman had an equal number of sons and daughters.

2. If you subtracted Nancy’s years of marriage from Naomi’s years of marriage, the answer would be the number of daughters Nellie had.

3. If you subtracted Naomi’s marriage years from Nellie’s marriage years, the answer would be the number of sons Naomi had.

4. To find the number for Naomi’s daughters, subtract one woman’s marriage years from another woman’s marriage years.

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Nancy

Naomi

Nellie

15 years 13 years 11 years

15 years 13 years 11 years

4 sons 3 sons 2 sons

4 sons 3 sons 2 sons

4 sons 3 sons 2 sons

4 daughters 3 daughters 2 daughters

4 daughters 3 daughters 2 daughters

4 daughters 3 daughters 2 daughters

15 years 13 years 11 years

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Trees a crowd The clues

Rosie, Ruth and Rita were three robins who all had nests in the same tree. The nests were at different heights in the tree; they were 40, 35 and 30 metres high. The robins all laid eggs in their nests; they laid 13, 10 and 7 eggs. One day, while waiting for their eggs to hatch, they held a worm-eating contest. They ate 33, 27 and 21 worms in an hour. Based on the clues, match the robins with their nest heights, the number of eggs they laid and the number of worms they ate in an hour.

1. Rosie’s nest was 5 metres lower than Ruth’s nest.

2. Ruth laid 3 fewer eggs than Rosie.

3. Rita ate 6 fewer worms than Ruth, but she laid more eggs than at least one other robin.

4. Rosie ate fewer worms than Rita, and Rita did not have the lowest nest.

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Rosie

Ruth

40 m 35 m 30 m

40 m 35 m 30 m

13 eggs 10 eggs 7 eggs

13 eggs 10 eggs 7 eggs

40 m 35 m 30 m

13 eggs 10 eggs 7 eggs

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Rita

33 worms 27 worms 21 worms

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33 worms 27 worms 21 worms

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5

Farmer’s market The clues

Victor, Vinnie, Vera and Vivian were four farmers who each brought 2000 pieces of produce to sell at the local farmer’s market. They brought 800, 600, 400 and 200 apples to sell that day. They brought 800, 600, 400 and 200 tomatoes to sell. They also brought 800, 600, 400 and 200 beetroot, and 800, 600, 400 and 200 potatoes to sell that day. Of course, no farmer brought the same number of any item of produce as another farmer brought to market that day. If one farmer brought 200 apples then no other farmer brought exactly 200 apples, and so on. Based on the clues, match the farmers with the exact amount of produce they brought to market that day.

1. Victor brought more apples to market than Vinnie, and their combined total of apples brought to market that day was 1000.

2. Vera brought more apples to market than Vivian or Victor.

3. Victor and Vera only brought a combined total of 600 tomatoes to market that day.

4. Vinnie did not bring as many tomatoes to market as Vivian, and Vera brought fewer tomatoes to market than Victor brought that day.

5. Vivian brought more potatoes to market than either Vinnie and Vera, but she didn’t bring the most.

6. Vinnie brought more beetroot than Vera.

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Victor

Vinnie

Vera

800 apples 600 apples 400 apples 200 apple

800 apples 600 apples 400 apples 200 apples

800 apples 600 apples 400 apples 200 apples

800 tomatoes 600 tomatoes 400 tomatoes 200 tomatoes

800 tomatoes 600 tomatoes 400 tomatoes 200 tomatoes

800 tomatoes 600 tomatoes 400 tomatoes 200 tomatoes

800 beetroot 600 beetroot 400 beetroot 200 beetroot

800 beetroot 600 beetroot 400 beetroot 200 beetroot

800 beetroot 600 beetroot 400 beetroot 200 beetroot

800 potatoes 600 potatoes 400 potatoes 200 potatoes

800 potatoes 600 potatoes 400 potatoes 200 potatoes

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Vivian

800 apples 600 apples 400 apples 200 apples

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800 potatoes 600 potatoes 400 potatoes 200 potatoes

800 tomatoes 600 tomatoes 400 tomatoes 200 tomatoes

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800 beetroot 600 beetroot 400 beetroot 200 beetroot

800 potatoes 600 potatoes 400 potatoes 200 potatoes

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Nuts to you The clues

Sara, Sam, Seth and Sheena were four squirrels who collected four kinds of nuts and stored them away for the winter. They collected 700, 650, 600 and 500 acorns. They collected 375, 355, 350 and 335 pecans.

They also collected 911, 900, 899 and 888 walnuts, and 900, 700, 350 and 200 almonds. Based on the clues, match the squirrels with the exact number of acorns, pecans, walnuts and almonds they collected.

1. Sara, Sam and Seth each managed to collect exactly equal numbers of two different kinds of nuts in their collections.

2. Sam and Sheena’s combined acorn collection equalled 1200 acorns and, of course, Sara collected more acorns than Seth.

3. Seth collected more almonds than Sara.

4. Sheena collected exactly 11 fewer walnuts than Sam and exactly 20 fewer pecans than Sam as well.

5. Sam, of course, did not collect the most pecans.

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Sara

Sam

Seth

700 acorns 650 acorns 600 acorns 500 acorns

700 acorns 650 acorns 600 acorns 500 acorns

700 acorns 650 acorns 600 acorns 500 acorns

375 pecans 355 pecans 350 pecans 335 pecans

375 pecans 355 pecans 350 pecans 335 pecans

911 walnuts 900 walnuts 899 walnuts 888 walnuts

911 walnuts 900 walnuts 899 walnuts 888 walnuts

911 walnuts 900 walnuts 899 walnuts 888 walnuts

900 almonds 700 almonds 350 almonds 200 almonds

900 almonds 700 almonds 350 almonds 200 almonds

900 almonds 700 almonds 350 almonds 200 almonds

700 acorns 650 acorns 600 acorns 500 acorns

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Sheena

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375 pecans 355 pecans 350 pecans 335 pecans

911 walnuts 900 walnuts 899 walnuts 888 walnuts

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375 pecans 355 pecans 350 pecans 335 pecans

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The story

900 almonds 700 almonds 350 almonds 200 almonds

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7

Grocery pokers The clues

Greta, George, Greg and Gail were all standing in line at the checkout counter in a grocery shop. Naturally enough, they were 1st, 2nd, 3rd and 4th in line. They all had exactly the same three items in their grocery carts but nobody had the same number of items as anybody else. They had 22, 18, 16 and 12 potatoes in their carts. They had 44, 40, 32, and 24 bananas in their carts. They had 17, 15, 13 and 11 apples in their carts. Based on the clues, match the names with their place in line, and the number of potatoes, bananas and apples in their carts.

1. Gail poked George in the back with her cart, and George poked somebody else in the back with his cart.

2. Greta poked Greg in the back with her cart.

3. Greg had exactly 2 more potatoes in his cart than George.

4. Greg’s banana number was twice as large as Gail’s potato number, Gail’s banana number was twice the size of Greta’s potato number, and Gail’s apple number was half the size of her potato number.

5. George had exactly 8 more bananas in his cart than the person with the most apples, and George had exactly 2 more apples in his cart than Greg.

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Greta

George

Greg

1st in line 2nd in line 3rd in line 4th in line

1st in line 2nd in line 3rd in line 4th in line

1st in line 2nd in line 3rd in line 4th in line

22 potatoes 18 potatoes 16 potatoes 12 potatoes

22 potatoes 18 potatoes 16 potatoes 12 potatoes

22 potatoes 18 potatoes 16 potatoes 12 potatoes

44 bananas 40 bananas 32 bananas 24 bananas

44 bananas 40 bananas 32 bananas 24 bananas

44 bananas 40 bananas 32 bananas 24 bananas

17 apples 15 apples 13 apples 11 apples

17 apples 15 apples 13 apples 11 apples

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Gail

1st in line 2nd in line 3rd in line 4th in line

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22 potatoes 18 potatoes 16 potatoes 12 potatoes

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44 bananas 40 bananas 32 bananas 24 bananas 17 apples 15 apples 13 apples 11 apples

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Don’t dry this at home The clues

Alvin, Alice, Albert and Ava were sitting in a laundromat waiting for the clothes they had just washed to dry. They had all washed exactly the same four items of clothing but, of course, nobody washed the same number of any item of clothing as anyone else. They had washed 22, 18, 16 and 14 individual socks. They had washed 31, 29, 24 and 22 shirts. They had also washed 17, 15, 14 and 13 pairs of pants, and 11, 9, 8 and 7 scarves. Based on the clues, match the names with the number of socks, shirts, pants and scarves they had washed that day.

1. Each of the four people washed the most of exactly one of the four items of clothing.

2. Ava washed exactly 4 more socks than Albert, and Alice washed exactly 2 more socks than Alvin.

3. Albert and Ava washed a combined total of 60 shirts.

4. Alice washed exactly 2 more shirts than somebody else, and Albert also washed exactly 2 more shirts than somebody else.

5. Alice washed exactly 2 more pants than somebody else, but Alvin also washed exactly 2 more pants than somebody else.

6. Albert washed exactly 2 fewer pants than somebody else.

7. Alvin and Alice’s combined scarf-washing total was 20, and Ava washed exactly 2 fewer scarves than Alice.

22 socks 18 socks 16 socks 14 socks

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11 scarves 9 scarves 8 scarves 7 scarves

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Albert

22 socks 18 socks 16 socks 14 socks

22 socks 18 socks 16 socks 14 socks

31 shirts 29 shirts 24 shirts 22 shirts

31 shirts 29 shirts 24 shirts 22 shirts

17 pants 15 pants 14 pants 13 pants

17 pants 15 pants 14 pants 13 pants

11 scarves 9 scarves 8 scarves 7 scarves

11 scarves 9 scarves 8 scarves 7 scarves

Ava

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31 shirts 29 shirts 24 shirts 22 shirts 17 pants 15 pants 14 pants 13 pants

Alice

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22 socks 18 socks 16 socks 14 socks 31 shirts 29 shirts 24 shirts 22 shirts

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Alvin

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17 pants 15 pants 14 pants 13 pants

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11 scarves 9 scarves 8 scarves 7 scarves

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Money in the bank

The story

Four American students, Carl, Connie, Cliff and Coral all had lots and lots of coins in their piggy banks. They had 250, 225, 200 and 190 quarters.

They had 1200, 1100, 1000 and 900 dimes in their banks. They had 2000, 1800, 1750 and 1600 nickels. They had 9000, 8700, 8300 and 8000 pennies in their banks. Based on the clues, match the names with the amount of quarters, dimes, nickels and pennies they had in their piggy banks.

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In American currency: 1 quarter = 25 cents 1 dime = 10 cents 1 nickel = 5 cents 1 penny = 1 cent

Teac he r Carl

Connie

Cliff

250 quarters 225 quarters 200 quarters 190 quarters

250 quarters 225 quarters 200 quarters 190 quarters

250 quarters 225 quarters 200 quarters 190 quarters

1200 dimes 1100 dimes 1000 dimes 900 dimes

1200 dimes 1100 dimes 1000 dimes 900 dimes

1200 dimes 1100 dimes 1000 dimes 900 dimes

2000 nickels 1800 nickels 1750 nickels 1600 nickels

2000 nickels 1800 nickels 1750 nickels 1600 nickels

2000 nickels 1800 nickels 1750 nickels 1600 nickels

9000 pennies 8700 pennies 8300 pennies 8000 pennies

9000 pennies 8700 pennies 8300 pennies 8000 pennies

9000 pennies 8700 pennies 8300 pennies 8000 pennies

Carol

250 quarters 225 quarters 200 quarters 190 quarters

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1200 dimes 1100 dimes 1000 dimes 900 dimes

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1. Each of the four had the most of one of the four types of coins.

2. Cliff and Coral had a combined total of $97.50 worth of quarters in their banks.

3. Carl and Connie had a combined total of $230.00 worth of dimes in their banks.

4. Connie and Cliff had a combined total of $190.00 worth of nickels in their banks.

5. If you added Connie’s nickels and Cliff’s pennies together you would have $170.00.

6. Carl had both more dimes and more pennies in his bank than Connie had in her piggy bank.

7. If you added together Cliff’s quarters and dimes he would have $150.00 and, of course, Carl did not have the fewest nickels.

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*Note:

The clues

2000 nickels 1800 nickels 1750 nickels 1600 nickels

9000 pennies 8700 pennies 8300 pennies 8000 pennies

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Flower power The clues

Helga, Harry, Henry and Hilda all had flower gardens running across the fronts of their houses. The gardens were all in a narrow strip exactly 30 metres long. All the 30-metre long strips of garden were divided into exact sections of 3, 6, 9 and 12 metres. Of course, none of the gardeners organised their strips exactly the same as another gardener. All four gardeners planted exactly the same flowers; they planted roses, violets, daisies and petunias. But, of course, each gardener had a different favourite flower and devoted their largest section of garden to that particular flower. Based on the clues, match the gardeners with the different lengths they gave to the roses, violets, daisies and petunias in their garden strips.

1. Each gardener devoted the most metres of garden space to his or her favourite flower.

2. No gardener planted the same flower in the same sized strip as another gardener.

3. Henry and Hilda planted the shortest strips of roses and violets.

4. Harry and Hilda planted a combined total of 12 metres of roses.

5. Helga and Henry planted a combined total of 12 metres of daisies.

6. Harry and Henry planted the longest strips of petunias and violets.

7. Hilda planted more petunias than Helga did.

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Helga

Harry

Henry

3 m roses 6 m roses 9 m roses 12 m roses

3 m roses 6 m roses 9 m roses 12 m roses

3 m roses 6 m roses 9 m roses 12 m roses

3 m violets 6 m violets 9 m violets 12 m violets

3 m violets 6 m violets 9 m violets 12 m violets

3 m daisies 6 m daisies 9 m daisies 12 m daisies

3 m daisies 6 m daisies 9 m daisies 12 m daisies

3 m petunias 6 m petunias 9 m petunias 12 m petunias

3 m petunias 6 m petunias 9 m petunias 12 m petunias

Hilda

3 m roses 6 m roses 9 m roses 12 m roses

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3 m daisies 6 m daisies 9 m daisies 12 m daisies

3 m petunias 6 m petunias 9 m petunias 12 m petunias

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3 m violets 6 m violets 9 m violets 12 m violets

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3 m violets 6 m violets 9 m violets 12 m violets

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3 m daisies 6 m daisies 9 m daisies 12 m daisies

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3 m petunias 6 m petunias 9 m petunias 12 m petunias

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Pig eaters The clues

Peter, Paula, Penny, Porky and Patty were five pigs who were invited to Farmer Brown’s birthday party. At the party, all five were just swine until the sweets were served, and then they got a little carried away. They ate 450, 425, 400, 375 and 350 cupcakes. They also gobbled 75, 70, 65, 60 and 50 slices of birthday cake.

They went hog wild when the ice-cream was served and ate 900, 850, 800, 750 and 700 scoops of icecream. Based on the clues, match the pigs with the number of cupcakes, the slices of cake and the number of ice-cream scoops they ate at the birthday party.

1. One pig managed to eat both the most cupcakes and the most scoops of ice-cream, but that same pig did not eat the fewest slices of cake.

2. Peter and Paula’s combined cake slice-eating total was 145.

3. Penny ate exactly 5 fewer cake slices than Peter, and Patty ate exactly 5 fewer cakes slices than Penny.

4. Patty did not eat the most cupcakes but she ate exactly 50 more cupcakes than Peter, and Peter did eat more cupcakes than Paula.

5. Peter, Paula and Porky each ate more than 700 scoops of ice-cream with Peter eating exactly 100 more scoops of ice-cream than Patty.

6. Of course, Paula also ate exactly 100 more scoops of ice-cream than another pig.

r o e t s Bo r e p ok u S

Peter

Paula

Penny

ew i ev Pr

Teac he r

The story

Porky

Patty

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y• 450 cupcakes 425 cupcakes 400 cupcakes 375 cupcakes 350 cupcakes

450 cupcakes 425 cupcakes 400 cupcakes 375 cupcakes 350 cupcakes

450 cupcakes 425 cupcakes 400 cupcakes 375 cupcakes 350 cupcakes

75 slices 70 slices 65 slices 60 slices 50 slices

75 slices 70 slices 65 slices 60 slices 50 slices

75 slices 70 slices 65 slices 60 slices 50 slices

75 slices 70 slices 65 slices 60 slices 50 slices

75 slices 70 slices 65 slices 60 slices 50 slices

900 scoops 850 scoops 800 scoops 750 scoops 700 scoops

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450 cupcakes 425 cupcakes 400 cupcakes 375 cupcakes 350 cupcakes

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450 cupcakes 425 cupcakes 400 cupcakes 375 cupcakes 350 cupcakes

o c . che e r o t r s super

900 scoops 850 scoops 800 scoops 750 scoops 700 scoops

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900 scoops 850 scoops 800 scoops 750 scoops 700 scoops

900 scoops 850 scoops 800 scoops 750 scoops 700 scoops

900 scoops 850 scoops 800 scoops 750 scoops 700 scoops

Maths perplexors

| 11

12

Race memories The clues

Champ, Scout, Peggy, Rex and Belle were five retired racehorses living on a retirement farm. One day, they were standing around in a pasture discussing their racing careers. They had raced in 400, 390, 380, 350 and 200 races. They had won 150, 125, 100, 90 and 80 times. They had been ridden by 75, 70, 60, 45 and 40 different jockeys. Based on the clues, match the racehorses with their total races run, their total races won and their number of jockeys.

1. Peggy, Rex and Belle ran in a combined total of 1170 races.

2. The horse that ran in the most races had the fewest wins and the fewest jockeys.

3. Peggy had exactly 5 more jockeys than Scout.

4. Rex ran in exactly 10 fewer races than Belle, but Rex had exactly 5 more jockeys than Belle.

5. Champ ran in more races than Scout, Peggy won exactly 10 more races than Rex, and Scout did not win the most races.

r o e t s Bo r e p ok u S

Champ

Scout

Peggy

Rex

400 race 390 races 380 races 350 races 200 races

400 races 390 races 380 races 350 races 200 races

400 races 390 races 380 races 350 races 200 races

400 races 390 races 380 races 350 races 200 races

150 wins 125 wins 100 wins 90 wins 80 wins

150 wins 125 wins 100 wins 90 wins 80 wins

150 wins 125 wins 100 wins 90 wins 80 wins

75 jockeys 70 jockeys 60 jockeys 45 jockeys 40 jockeys

75 jockeys 70 jockeys 60 jockeys 45 jockeys 40 jockeys

75 jockey 70 jockeys 60 jockeys 45 jockeys 40 jockeys

Belle

400 races 390 races 380 races 350 races 200 races

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

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75 jockeys 70 jockeys 60 jockeys 45 jockeys 40 jockeys

12 | Maths perplexors

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150 wins 125 wins 100 wins 90 wins 80 wins

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150 wins 125 wins 100 wins 90 wins 80 wins

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Teac he r

The story

o c . che e r o t r s super

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75 jockeys 70 jockeys 60 jockeys 45 jockeys 40 jockeys

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13

Beans to you The clues

Kirk, Kendra, Kathy, Kenny and Kevin went on a tour of a jellybean factory. During the tour, they were invited to eat all the jellybeans they wanted. The five tourists only liked red, green and yellow jellybeans, but they certainly ate a lot of them. They ate 900, 850, 800, 795 and 745 red jellybeans. They ate 1250, 1200, 1100, 1000 and 900 green jellybeans. They ate 875, 865, 855, 840 and 820 yellow jellybeans. Based on the clues, match the names with the number of red, green and yellow jellybeans they ate.

1. Kirk, Kendra and Kathy each ate the most of one colour of jellybeans and none of them ate the fewest of any colour of jellybeans.

2. Kenny ate more red, green and yellow jellybeans than Kevin.

3. Kendra ate exactly 50 more red jellybeans than Kathy, but Kirk ate more red jellybeans than Kendra.

4. Kirk ate more green jellybeans than Kathy.

5. Kenny ate exactly 100 fewer green jellybeans than Kathy.

6. Kenny ate exactly 20 more yellow jellybeans than another tourist, and Kendra ate more yellow jellybeans than Kirk.

r o e t s Bo r e p ok u S

ew i ev Pr

Teac he r

The story

Kirk

Kendra

Kathy

Kenny

Kevin

900 red 850 red 800 red 795 red 745 red

900 red 850 red 800 red 795 red 745 red

900 red 850 red 800 red 795 red 745 red

900 red 850 red 800 red 795 red 745 red

900 red 850 red 800 red 795 red 745 red

1250 green 1200 green 1100 green 1000 green 900 green

1250 green 1200 green 1100 green 1000 green 900 green

1250 green 1200 green 1100 green 1000 green 900 green

1250 green 1200 green 1100 green 1000 green 900 green

1250 green 1200 green 1100 green 1000 green 900 green

875 yellow 865 yellow 855 yellow 840 yellow 820 yellow

875 yellow 865 yellow 855 yellow 840 yellow 820 yellow

875 yellow 865 yellow 855 yellow 840 yellow 820 yellow

875 yellow 865 yellow 855 yellow 840 yellow 820 yellow

w ww 875 yellow 865 yellow 855 yellow 840 yellow 820 yellow

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© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

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Maths perplexors

| 13

14

Let’s all do the monkey hop The clues

Bonzo, Binko, Gummo, Harpo and Marlo were five competitive monkeys living together in the Rainiere rainforest. For no apparent reason, they decided to hold a series of contests. Their first contest was to see who could bounce a ball the most times without making a mistake. They bounced a ball 1300, 1250, 1100, 1000 and 750 times. The second contest was a ropejumping contest. They jumped 950, 925, 920, 915 and 900 times before making a mistake. Their final contest was a hopping-on-one-foot contest. They hopped 730, 720, 700, 680 and 650 times before making a mistake.

Based on the clues, match the monkeys with their ball bouncing, rope jumping and hopping totals.

1. Binko, Gummo and Marlo each managed to win one of the three contests, but each also managed to finish last in one of the three contests.

2. Harpo bounced better than Bonzo, Bonzo jumped better than Harpo, and Harpo hopped better than Bonzo.

3. Gummo and Harpo’s combined bouncing total was 2550 bounces, and Bonzo bounced the ball exactly 250 more times than Binko.

4. Binko was not the best hopper, and Gummo was not the worst rope jumper.

5. Harpo jumped exactly 5 more times than Gummo, and Binko hopped exactly 30 more times than Gummo.

Bonzo

Binko

Gummo

Harpo

Marlo

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y• 1300 bounces 1250 bounces 1100 bounces 1000 bounces 750 bounces

1300 bounces 1250 bounces 1100 bounces 1000 bounces 750 bounces

950 jumps 925 jumps 920 jumps 915 jumps 900 jumps

950 jumps 925 jumps 920 jumps 915 jumps 900 jumps

950 jumps 925 jumps 920 jumps 915 jumps 900 jumps

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950 jumps 925 jumps 920 jumps 915 jumps 900 jumps

1300 bounces 1250 bounces 1100 bounces 1000 bounces 750 bounces

730 hops 720 hops 700 hops 680 hops 650 hops

14 | Maths perplexors

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1300 bounces 1250 bounces 1100 bounces 1000 bounces 750 bounces 950 jumps 925 jumps 920 jumps 915 jumps 900 jumps

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1300 bounces 1250 bounces 1100 bounces 1000 bounces 750 bounce

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Teac he r

The story

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730 hops 720 hops 700 hops 680 hops 650 hops

730 hops 720 hops 700 hops 680 hops 650 hops

730 hops 720 hops 700 hops 680 hops 650 hops

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730 hops 720 hops 700 hops 680 hops 650 hops

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15

Garden bounty The clues

Stella, Sylvia, Simon, Shane and Sophie all had the same types of fruit trees in their gardens. They each had a lemon tree, an orange tree and an apple tree. One year, they decided to keep a record of the number of fruit their trees produced and compare the results. Their lemon trees produced 1150, 1125, 1000, 975 and 950 lemons. Their orange trees produced 807, 800, 793, 790 and 683 oranges. Their apple trees produced 735, 700, 665, 630 and 600 apples. Based on the clues, match the names with the number of lemons, oranges and apples their trees produced.

1. Stella, Sylvia and Simon each had a different type of tree that produced the most fruit.

2. Shane and Sophie’s combined lemon production was 1925 lemons.

3. Stella’s lemon tree produced more lemons than Sylvia’s lemon tree but not the most and, of course, Sophie’s lemon tree was not the worst in lemon production.

4. Sylvia and Sophie’s combined apple production was only 1230 apples.

5. The person with the best producing apple tree also had the worst producing orange tree.

6. Sophie’s orange tree produced exactly 7 fewer oranges than Sylvia’s orange tree.

7. The person with the best producing orange tree also had the worst producing apple tree.

8. Simon’s apple tree produced more apples than Shane’s apple tree, but Shane’s orange tree produced more oranges than Simon’s orange tree.

r o e t s Bo r e p ok u S

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Teac he r

The story

© R. I .

C.Publ i cat i ons Stella Sylvia Simon Shane Sophie •f orr evi ew pur posesonl y• 1150 lemons 1125 lemons 1000 lemons 975 lemons 950 lemons

1150 lemons 1125 lemons 1000 lemons 975 lemons 950 lemons

1150 lemons 1125 lemons 1000 lemons 975 lemons 950 lemons

807 oranges 800 oranges 793 oranges 790 oranges 683 oranges

807 oranges 800 oranges 793 oranges 790 oranges 683 oranges

807 oranges 800 oranges 793 oranges 790 oranges 683 oranges

807 oranges 800 oranges 793 oranges 790 oranges 683 oranges

807 oranges 800 oranges 793 oranges 790 oranges 683 oranges

735 apples 700 apples 665 apples 630 apples 600 apples

735 apples 700 apples 665 apples 630 apples 600 apples

735 apples 700 apples 665 apples 630 apples 600 apples

735 apples 700 apples 665 apples 630 apples 600 apples

735 apples 700 apples 665 apples 630 apples 600 apples

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1150 lemons 1125 lemons 1000 lemons 975 lemons 950 lemons

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1150 lemons 1125 lemons 1000 lemons 975 lemons 950 lemons

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Maths perplexors

| 15

16

Farmer’s markup The clues

Tom, Toula, Terry, Tina and Tex were farmers whose last names were, Smith, Jones, Brown, Black and Noble.

They all had their best day ever selling produce at the local farmer’s market. They sold 468, 444, 420, 384 and 312 fresh eggs. They sold 800, 768, 704, 640 and 608 grams of honey. They sold 110, 100, 90, 85 and 80 kilograms of green beans. Based on the clues, match first names with last names, and the amount of eggs, honey and green beans they sold that day.

1. Tina and Tex were not named Smith, Jones or Brown, and between the two of them they sold 76 dozen eggs, 1.568 kg of honey, and 210 kg of green beans.

2. Smith sold the fewest eggs and Toula sold exactly 3 dozen more eggs than Tom (whose last name was not Jones).

3. Tina sold 2 dozen more eggs than Noble.

4. Terry and Tex sold a combined total of 1.504 kg of honey, and Toula and Tina sold a combined total of 200 kg of beans.

5. Brown sold more honey than Jones, and Smith sold more green beans than Brown.

r o e t s Bo r e p ok u S

Tom

Toula

Terry

Tina

Smith Jones Brown Black Noble

Smith Jones Brown Black Noble

Smith Jones Brown Black Noble

Smith Jones Brown Black Noble

468 eggs 444 eggs 420 eggs 384 eggs 312 eggs

468 eggs 444 eggs 420 eggs 384 eggs 312 eggs

468 eggs 444 eggs 420 eggs 384 eggs 312 eggs

468 eggs 444 eggs 420 eggs 384 eggs 312 eggs

800 g 768 g 704 g 640 g 608 g

800 g 768 g 704 g 640 g 608 g

800 g 768 g 704 g 640 g 608 g

800 g 768 g 704 g 640 g 608 g

110 kg 100 kg 90 kg 85 kg 80 kg

110 kg 100 kg 90 kg 85 kg 80 kg

110 kg 100 kg 90 kg 85 kg 80 kg

ew i ev Pr

Teac he r

The story

Tex

Smith Jones Brown Black Noble

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

16 | Maths perplexors

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w ww

110 kg 100 kg 90 kg 85 kg 80 kg

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468 eggs 444 eggs 420 eggs 384 eggs 312 eggs

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800 g 768 g 704 g 640 g 608 g

110 kg 100 kg 90 kg 85 kg 80 kg

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17

Stand by me The clues

Gino, Reggie, Ruth, Gail and Greg worked at food stalls A, B, C, D and E at a football stadium. After a recent game, their sales were 5000, 4800, 4300, 3800 and 3300 hot dogs. They sold 4700, 4600, 4300, 3700 and 3300 burgers. They sold 8000, 7600, 6600, 6500 and 6200 soft drinks. Based on the clues, match the names with their food stalls and their sales of hot dogs, burgers and drinks.

1. Stall A sold the most hot dogs, Stall C sold the most burgers, and Stall B sold the most drinks.

2. Stall C sold the fewest hot dogs and drinks, and Stall B sold the fewest burgers.

3. Gino, Reggie and Greg did not work at Stalls A or B. 4. Ruth and Greg sold a combined total of 9100 hot dogs.

5. Reggie sold exactly 500 fewer hot dogs than Ruth.

6. Reggie and Greg sold a combined total of 8900 burgers and, of course, Stall E sold more burgers than Stall D. 7. Greg did not work at Stall D. 8. Stall D sold exactly 100 fewer drinks than Stall E.

r o e t s Bo r e p ok u S

ew i ev Pr

Teac he r

The story

Gino

Reggie

Ruth

Gail

Greg

Stall A Stall B Stall C Stall D Stall E

Stall A Stall B Stall C Stall D Stall E

Stall A Stall B Stall C Stall D Stall E

Stall A Stall B Stall C Stall D Stall E

Stall A Stall B Stall C Stall D Stall E

5000 hot dogs 4800 hot dogs 4300 hot dogs 3800 hot dogs 3300 hot dogs

5000 hot dogs 4800 hot dogs 4300 hot dogs 3800 hot dogs 3300 hot dogs

5000 hot dogs 4800 hot dogs 4300 hot dogs 3800 hot dogs 3300 hot dogs

5000 hot dogs 4800 hot dogs 4300 hot dogs 3800 hot dogs 3300 hot dogs

5000 hot dogs 4800 hot dogs 4300 hot dogs 3800 hot dogs 3300 hot dogs

4700 burgers 4600 burgers 4300 burgers 3700 burgers 3300 burgers

4700 burgers 4600 burgers 4300 burgers 3700 burgers 3300 burgers

4700 burgers 4600 burgers 4300 burgers 3700 burgers 3300 burgers

4700 burgers 4600 burgers 4300 burgers 3700 burgers 3300 burgers

4700 burgers 4600 burgers 4300 burgers 3700 burgers 3300 burgers

8000 drinks 7600 drinks 6600 drinks 6500 drinks 6200 drinks

8000 drinks 7600 drinks 6600 drinks 6500 drinks 6200 drinks

8000 drinks 7600 drinks 6600 drinks 6500 drinks 6200 drinks

8000 drinks 7600 drinks 6600 drinks 6500 drinks 6200 drinks

8000 drinks 7600 drinks 6600 drinks 6500 drinks 6200 drinks

w ww

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© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

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R.I.C. Publications®

Maths perplexors

| 17

18

School picnics The clues

The Taft, Knox, Twain, Wilson and Adams schools recently held their annual school picnics. The school enrolments were 1650, 1450, 1250, 825 and 650 students. At the picnic grounds they grilled and ate 2900, 2500, 2300, 2000 and 1300 hot dogs. The schools also handed out 4600, 4000, 2600, 2400 and 2300 bags of potato chips. Based on the clues, match the schools with their enrolments, and their grilled hot dog and bags of potato chips totals.

1. The Twain School had twice as many students as the Knox School.

2. The school with the smallest enrolment ate the most hot dogs and the most bags of chips.

3. The Taft School ate fewer bags of chips than the Adams School.

4. The Wilson School had more pupils than the Taft School.

5. The Twain School ate exactly 200 fewer hot dogs than the Wilson School.

6. The Knox School did not eat the fewest hot dogs.

7. The Twain School and the Wilson School ate a combined total of 4700 bags of potato chips.

8. The combined chip total of the Knox and Wilson schools was 4900 bags of chips.

1650 students 1450 students 1250 students 825 students 650 students

Knox

Twain

Wilson

Adams

1650 students 1450 students 1250 students 825 students 650 students

1650 students 1450 students 1250 students 825 students 650 students

1650 students 1450 students 1250 students 825 students 650 students

2900 hot dogs 2500 hot dogs 2300 hot dogs 2000 hot dogs 1300 hot dogs

2900 hot dogs 2500 hot dogs 2300 hot dogs 2000 hot dogs 1300 hot dogs

2900 hot dogs 2500 hot dogs 2300 hot dogs 2000 hot dogs 1300 hot dogs

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

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2900 hot dogs 2500 hot dogs 2300 hot dogs 2000 hot dogs 1300 hot dogs 4600 chips 4000 chips 2600 chips 2400 chips 2300 chips

18 | Maths perplexors

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1650 students 1450 students 1250 students 825 students 650 students

2900 hot dogs 2500 hot dogs 2300 hot dogs 2000 hot dogs 1300 hot dogs

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Taft

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Teac he r

The story

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4600 chips 4000 chips 2600 chips 2400 chips 2300 chips

4600 chips 4000 chips 2600 chips 2400 chips 2300 chips

4600 chips 4000 chips 2600 chips 2400 chips 2300 chips

R.I.C. Publications®

4600 chips 4000 chips 2600 chips 2400 chips 2300 chips

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19

Baker’s dozen The clues

Betty, Benny, Bonnie, Barry and Beth all owned bakeries in the same town. After they had closed for the day, they liked to get together and compare sales. This particular evening they discovered they had sold 420, 408, 384, 372 and 312 pies. They had also sold 720, 696, 672, 600 and 528 doughnuts, and 960, 948, 912, 900 and 852 cookies. Based on the clues, match the bakers with the number of pies, doughnuts and cookies they sold.

1. Benny, Bonnie and Barry each sold the most of one of the three items but each sold the fewest of one of the three bakery items as well.

2. Betty and Benny sold a combined total of 57 dozen pies, and Barry and Beth sold a combined total of 69 dozen pies.

3. Betty and Barry sold a combined total of 94 dozen doughnuts, and Bonnie and Beth sold a combined total of 118 dozen doughnuts.

4. Bonnie and Beth’s combined cookie total was 146 dozen cookies and, of course, Barry sold more cookies than Betty.

r o e t s Bo r e p ok u S

ew i ev Pr

Teac he r

The story

Betty

Benny

Bonnie

Barry

Beth

420 pies 408 pies 384 pies 372 pies 312 pies

420 pies 408 pies 384 pies 372 pies 312 pies

420 pies 408 pies 384 pies 372 pies 312 pies

420 pies 408 pies 384 pies 372 pies 312 pies

420 pies 408 pies 384 pies 372 pies 312 pies

720 doughnuts 696 doughnuts 672 doughnuts 600 doughnuts 528 doughnuts

720 doughnuts 696 doughnuts 672 doughnuts 600 doughnuts 528 doughnuts

720 doughnuts 696 doughnuts 672 doughnuts 600 doughnuts 528 doughnuts

720 doughnuts 696 doughnuts 672 doughnuts 600 doughnuts 528 doughnuts

720 doughnuts 696 doughnuts 672 doughnuts 600 doughnuts 528 doughnuts

960 cookies 948 cookies 912 cookies 900 cookies 852 cookies

960 cookies 948 cookies 912 cookies 900 cookies 852 cookies

960 cookies 948 cookies 912 cookies 900 cookies 852 cookies

w ww

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960 cookies 948 cookies 912 cookies 900 cookies 852 cookies

www.ricpublications.com.au

960 cookies 948 cookies 912 cookies 900 cookies 852 cookies

m . u

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

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Maths perplexors

| 19

20

That’s just ducky The clues

Duke, Donnie, Daisy, Daphne and Devon were five young American ducks living together in Lake Tahoe in California. Getting bored with ordinary duck doings, they decided to hold two contests. But first, before the contests began, they all painted their favourite numbers on their backs. Their favourite numbers were 83, 72, 60, 48 and 40. The first contest was to see which duck could fly backwards the farthest before quacking up. They flew 930, 900, 780, 690 and 600 metres backwards. The second contest was an underwater breath-holding contest. The ducks held their breath for 600, 540, 420, 300 and 240 seconds. Based on the clues, match the ducks with their favourite numbers, the distances they flew backwards and their underwater times.

1. Duke and Donnie’s favourite numbers would add up to 100, and they flew backwards a combined total of 1.29 kilometres.

2. Daphne and Devon held their breath underwater for a combined total of only 9 minutes.

3. Multiply Duke’s favourite number by 10 to find the number of feet he was able to fly backwards.

4. Donnie and Daphne’s combined breath-holding total was 15 minutes.

5. The duck with the highest favourite number flew backwards 930 metres but was the worst at breathholding.

6. Daisy’s favourite number subtracted from Duke’s favourite number would result in the number 12.

7. Daphne and Devon’s combined backwards flying total was 1.83 km, and Duke was not as good at holding his breath as Daisy.

83 favourite 72 favourite 60 favourite 48 favourite 40 favourite

Donnie Daisy Daphne © R. I .

C.P ubl i cat i ons Devon •f orr evi ew pur posesonl y•

w ww

930 metres 900 metres 780 metres 690 metres 600 metres

600 seconds 540 seconds 420 seconds 300 seconds 240 seconds

20 | Maths perplexors

83 favourite 72 favourite 60 favourite 48 favourite 40 favourite

83 favourite 72 favourite 60 favourite 48 favourite 40 favourite

83 favourite 72 favourite 60 favourite 48 favourite 40 favourite

930 metres 900 metres 780 metres 690 metres 600 metres

930 metres 900 metres 780 metres 690 metres 600 metres

930 metres 900 metres 780 metres 690 metres 600 metres

600 seconds 540 seconds 420 seconds 300 seconds 240 seconds

600 seconds 540 seconds 420 seconds 300 seconds 240 seconds

600 seconds 540 seconds 420 seconds 300 seconds 240 seconds

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83 favourite 72 favourite 60 favourite 48 favourite 40 favourite

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Duke

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The story

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930 metres 900 metres 780 metres 690 metres 600 metres

600 seconds 540 seconds 420 seconds 300 seconds 240 seconds

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21

Gone fishing The clues

Jack, Jill, Joie, Jim and Joy recently went on a fishing trip to Lake Glenview. They had a very good day even if it was not such a good day for the fish involved. They caught 25, 24, 20, 17 and 6 perch. They caught 28, 26, 25, 19 and 17 bass. They also caught 13, 12, 10, 9 and 8 catfish. Based on the clues, match the names with the number of perch, bass and catfish they caught.

1. Joie, Jim and Joy each caught the most of one species of fish but one of them also caught the fewest catfish and, of course, Jack and Jill each caught the fewest of one of the two remaining species of fish.

2. Multiply Jill’s catfish total by 2 to discover Joie’s perch total.

3. Joy caught more catfish than Jill.

4. Jill caught exactly 2 fewer bass than Jack and, of course, Joy caught more bass than Jim. 5. Jill caught fewer perch than Joie, Joy did not catch the most perch but she caught more perch than Joie.

6. Joie did not catch the most catfish but she caught more catfish than Jill.

r o e t s Bo r e p ok u S

ew i ev Pr

Teac he r

The story

Jack

Jill

Joie

Jim

Joy

25 perch 24 perch 20 perch 17 perch 6 perch

25 perch 24 perch 20 perch 17 perch 6 perch

25 perch 24 perch 20 perch 17 perch 6 perch

25 perch 24 perch 20 perch 17 perch 6 perch

25 perch 24 perch 20 perch 17 perch 6 perch

28 bass 26 bass 25 bass 19 bass 17 bass

28 bass 26 bass 25 bass 19 bass 17 bass

28 bass 26 bass 25 bass 19 bass 17 bass

28 bass 26 bass 25 bass 19 bass 17 bass

28 bass 26 bass 25 bass 19 bass 17 bass

13 catfish 12 catfish 10 catfish 9 catfish 8 catfish

13 catfish 12 catfish 10 catfish 9 catfish 8 catfish

13 catfish 12 catfish 10 catfish 9 catfish 8 catfish

13 catfish 12 catfish 10 catfish 9 catfish 8 catfish

w ww 13 catfish 12 catfish 10 catfish 9 catfish 8 catfish

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© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

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Maths perplexors

| 21

22

Running backs

The story

The clues

Dean, Diane, Daryl, Dana and Donny were five running backs in the Hamilton Gridiron Football League. They wore the numbers 48, 45, 40, 37 and 35 on their uniforms. During the season they gained 960, 930, 900, 860 and 850 yards. They caught 77, 74, 70, 63 and 60 passes. Based on the clues, match the running backs with their uniform numbers, their yards gained and the number of passes they caught during the season.

1. If you added Dean’s uniform number to Donny’s uniform number, the answer would be the number of passes Dean caught that season.

2. If you subtracted Dana’s uniform number from Dean’s uniform number, the answer would be 5, but if you subtracted Dean’s uniform number from Diane’s uniform number, the answer would also be 5.

3. Donny gained 90 more feet than Dana, but Dana gained 90 more feet than Daryl.

4. If you subtracted Donny’s passing number from Dana’s passing number, the answer would be 3, but if you subtracted Diane’s passing number from Dean’s passing number, the answer would also be 3.

5. Diane gained more yards than Dean.

Dean

Daryl

Dana

Donny

© R. I .

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960 yards 930 yards 900 yards 860 yards 850 yards

77 passes 74 passes 70 passes 63 passes 60 passes

22 | Maths perplexors

48 uniform 45 uniform 40 uniform 37 uniform 35 uniform

48 uniform 45 uniform 40 uniform 37 uniform 35 uniform

48 uniform 45 uniform 40 uniform 37 uniform 35 uniform

960 yards 930 yards 900 yards 860 yards 850 yards

960 yards 930 yards 900 yards 860 yards 850 yards

960 yards 930 yards 900 yards 860 yards 850 yards

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48 uniform 45 uniform 40 uniform 37 uniform 35 uniform 960 yards 930 yards 900 yards 860 yards 850 yards

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48 uniform 45 uniform 40 uniform 37 uniform 35 uniform

Diane

ew i ev Pr

Measurements are imperial, not metric.

1 yard = 3 feet

Teac he r

Note:

r o e t s Bo r e p ok u S

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77 passes 74 passes 70 passes 63 passes 60 passes

77 passes 74 passes 70 passes 63 passes 60 passes

77 passes 74 passes 70 passes 63 passes 60 passes

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77 passes 74 passes 70 passes 63 passes 60 passes

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23

Are you a loser?

The clues

Sharon, Sandy, Sammy, Sara and Sally were always losing things. These five had the most trouble keeping track of their school supplies. In one school year, they lost 220, 215, 200, 195 and 175 pencils. In that same school year, they lost 45, 40, 30, 25 and 20 pens. They had the most trouble keeping track of their crayons, and in that year they lost 440, 430, 400, 350 and 325 crayons. Based on the clues, match the names with the number of pencils, pens and crayons they lost that school year.

1. Sara lost twice as many pens as Sharon.

2. Multiply the number of pens Sandy lost by 8 to determine the number of pencils Sharon lost.

3. Sally did not lose the most pens.

4. Multiply the number of pens Sara lost by 10 to reveal the number of crayons Sammy lost.

5. Both Sharon and Sandy lost more crayons than Sammy, and Sara lost more crayons than Sally.

6. The two students who lost a combined total of 675 crayons also lost a combined total of 435 pencils.

7. Sandy lost more pencils than Sammy, and Sandy lost more crayons than Sharon.

8. The student who lost the fewest crayons lost the most pencils.

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Sharon

Sandy

Sammy

Sara

Sally

220 pencils 215 pencils 200 pencils 195 pencils 175 pencils

220 pencils 215 pencils 200 pencils 195 pencils 175 pencils

220 pencils 215 pencils 200 pencils 195 pencils 175 pencils

220 pencils 215 pencils 200 pencils 195 pencils 175 pencils

220 pencils 215 pencils 200 pencils 195 pencils 175 pencils

45 pens 40 pens 30 pens 25 pens 20 pens

45 pens 40 pens 30 pens 25 pens 20 pens

45 pens 40 pens 30 pens 25 pens 20 pens

45 pens 40 pens 30 pens 25 pens 20 pens

45 pens 40 pens 30 pens 25 pens 20 pens

440 crayons 430 crayons 400 crayons 350 crayons 325 crayons

440 crayons 430 crayons 400 crayons 350 crayons 325 crayons

440 crayons 430 crayons 400 crayons 350 crayons 325 crayons

440 crayons 430 crayons 400 crayons 350 crayons 325 crayons

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440 crayons 430 crayons 400 crayons 350 crayons 325 crayons

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24

Pig town pride The clues

The towns of Alpha, Beta, Crown, Dofuss and Enid were very proud of their town pigs. Each town was sure they had the heaviest pig around. To settle the matter, the pigs were weighed by an independent authority and weighed 1020, 1010, 1000, 900 and 850 kilograms. A majority of the towns decided that weight was not as important as talent, and two contests were held to see whose pig was really the best. The first contest was to see which town’s town pig could oink the most times in a minute. The pigs oinked 500, 450, 425, 420 and 415 oinks in a minute. The second contest was to see which town’s town pig could drink the most swill in a minute.

The pigs gulped down 22, 21, 20, 18 and 15 litres of swill in a minute. Based on the clues, match the towns with their pig’s weights, the number of oinks they made and the litres of swill they drank.

1. The town pigs of Alpha and Beta did not score the highest in any of the three categories, but they did not have the lowest scores in any of the three categories either.

2. The towns of Crown, Dofuss and Enid each had one category where their town pigs scored the lowest, and each had one category where their pigs had the highest scores.

3. If you added the weight of Beta’s town pig to the weight of Enid’s town pig, the result would be 1850 kg.

4. Crown’s town pig was only 10 kg heavier than Alpha’s town pig, and Dofuss’ town pig did not drink the most swill in a minute.

5. Beta’s pig was a better oinker than Alpha’s pig, but Alpha’s pig was a better oinker than Enid’s pig.

6. Crown’s town pig drank exactly 1 more litre of swill than Beta’s pig.

1020 kg 1010 kg 1000 kg 900 kg 850 kg

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C.Crown Publ i cat i ons Enid Beta R. Dofuss •f orr evi ew pur posesonl y•

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500 oinks 450 oinks 425 oinks 420 oinks 415 oinks 22 L 21 L 20 L 18 L 15 L

24 | Maths perplexors

1020 kg 1010 kg 1000 kg 900 kg 850 kg

1020 kg 1010 kg 1000 kg 900 kg 850 kg

1020 kg 1010 kg 1000 kg 900 kg 850 kg

500 oinks 450 oinks 425 oinks 420 oinks 415 oinks

500 oinks 450 oinks 425 oinks 420 oinks 415 oinks

500 oinks 450 oinks 425 oinks 420 oinks 415 oinks

22 L 21 L 20 L 18 L 15 L

22 L 21 L 20 L 18 L 15 L

22 L 21 L 20 L 18 L 15 L

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1020 kg 1010 kg 1000 kg 900 kg 850 kg

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500 oinks 450 oinks 425 oinks 420 oinks 415 oinks 22 L 21 L 20 L 18 L 15 L

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25

When pigs fly The clues

Ever-competitive about their pigs, the towns of Alpha, Beta, Crown, Dofuss and Enid decided to try once again to see which town had the best pig in the land.

The pigs were named Porkly, Snorts, Spamy, Grunto and Trotter. The pigs were trained in hang gliding, and they flew 3000, 2700, 2610, 2520 and 2400 metres. Then the pigs were timed to see who could swim across Lake Glenview in the fastest time. They swam across the lake in 345, 330, 315, 300 and 285 minutes. Finally, the very tired pigs were asked to tap dance and the winner would be the pig that made the most taps in a minute.

They tapped 500, 497, 494, 470 and 467 taps in a minute. Based on the clues, match the towns with their pigs, the distances they flew, their swimming times and their tapping totals.

1. The towns of Crown, Dofuss and Enid held celebrations because each of their pigs won one of the three contests.

2. Porkly and Snorts were downcast because they did not win a single contest, and they were the worst in two out of the three contests.

3. Porkly was the worst at flying, and Dofuss’ Grunto flew 300 metres less than Trotter.

4. Spamy was not Enid’s town pig, Beta’s town pig flew 300 metres less than Grunto, and Snorts flew farther than Spamy.

5. Grunto was the worst tap dancer, and Trotter was not the best tap dancer.

6. Trotter took a quarter hour less than Spamy to swim across the lake and was half an hour faster than Porkly.

7. Trotter was 3 taps faster than Snorts, and do try to remember that the best time is the shortest time.

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©R I .

C.Pu bl i cat i oDofuss ns Beta.

Crown •f orr evi ew pur posesonl y•

Alpha

Porkly Snorts Spamy Grunto Trotter

Porkly Snorts Spamy Grunto Trotter

Porkly Snorts Spamy Grunto Trotter

3000 m 2700 m 2610 m 2520 m 2400 m

3000 m 2700 m 2610 m 2520 m 2400 m

3000 m 2700 m 2610 m 2520 m 2400 m

3000 m 2700 m 2610 m 2520 m 2400 m

345 minutes 330 minutes 315 minutes 300 minutes 285 minutes

345 minutes 330 minutes 315 minutes 300 minutes 285 minutes

345 minutes 330 minutes 315 minutes 300 minutes 285 minutes

345 minutes 330 minutes 315 minutes 300 minutes 285 minutes

345 minutes 330 minutes 315 minutes 300 minutes 285 minutes

500 taps 497 taps 494 taps 470 taps 467 taps

500 taps 497 taps 494 taps 470 taps 467 taps

500 taps 497 taps 494 taps 470 taps 467 taps

500 taps 497 taps 494 taps 470 taps 467 taps

500 taps 497 taps 494 taps 470 taps 467 taps

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Porkly Snorts Spamy Grunto Trotter

3000 m 2700 m 2610 m 2520 m 2400 m

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Porkly Snorts Spamy Grunto Trotter

Enid

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26

It’s a hit The clues

Biff, Betty, Byron, Bev and Baxter were all baseball players on the same team. At the close of the season they compared hitting totals to see how well each of them had done. None of them hit a home run. They hit 93, 90, 87, 85 and 70 singles. They hit 58, 50, 45, 40 and 35 doubles. They hit 27, 25, 20, 18 and 15 triples.

Based on the clues, match the baseball players with the number of singles, doubles and triples they hit that baseball season.

1. Between Bev and Baxter, one of them hit the most singles, one of them hit the most doubles and one of them hit the most triples, and between Biff and Betty, one of them hit the fewest singles, one of them hit the fewest doubles and one of them hit the fewest triples.

2. Biff and Baxter hit a combined total of 155 singles and, of course, Betty hit more singles than Byron.

3. Bev did not hit the most doubles, and Baxter did not hit the most triples.

4. Betty and Bev hit a combined total of 75 doubles and, of course, Biff hit more doubles than Byron.

5. Bev hit exactly two more triples than Betty and, of course, Byron hit more triples than Baxter.

Biff

Betty

Byron

Bev

Baxter

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58 doubles 50 doubles 45 doubles 40 doubles 35 doubles 27 triples 25 triples 20 triples 18 triples 15 triples

26 | Maths perplexors

93 singles 90 singles 87 singles 85 singles 70 singles

93 singles 90 singles 87 singles 85 singles 70 singles

93 singles 90 singles 87 singles 85 singles 70 singles

58 doubles 50 doubles 45 doubles 40 doubles 35 doubles

58 doubles 50 doubles 45 doubles 40 doubles 35 doubles

58 doubles 50 doubles 45 doubles 40 doubles 35 doubles

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93 singles 90 singles 87 singles 85 singles 70 singles

58 doubles 50 doubles 45 doubles 40 doubles 35 doubles

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93 singles 90 singles 87 singles 85 singles 70 singles

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27 triples 25 triples 20 triples 18 triples 15 triples

27 triples 25 triples 20 triples 18 triples 15 triples

27 triples 25 triples 20 triples 18 triples 15 triples

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27 triples 25 triples 20 triples 18 triples 15 triples

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27

How low can you get?

The clues

Tommy, Connie, Bert, Paula and Tina were a trout, a catfish, a bass, a perch and a tuna living together in Lake George. One recent day they decided to compete against each other in a series of three contests. Their first contest was to see who could eat the most worms in an hour. They ate 112, 110, 100, 56 and 55 worms in an hour. Their second contest was to see who could eat the most leeches in an hour. They ate 224, 200, 168, 165 and 100 leeches in an hour. Their final contest was to see who could dive the deepest. They dived 1000, 995, 950, 925 and 900 metres deep. Based on the clues, match the names with their fish species, the number of worms they ate, the number of leeches they ate and the depths they dived to.

1. Tommy, Connie and Bert were not either a perch or a tuna.

2. Multiply the tuna’s worm-eating total by 2 to find the number of worms the bass ate, and multiply the perch’s worm-eating total by 2 to discover the wormeating total of the catfish.

3. Bert was not a catfish or a bass, Connie was not a bass, and Paula was not a perch.

4. The bass ate twice as many leeches as worms, and the catfish ate twice as many leeches as the perch.

5. Bert ate more leeches than the tuna.

6. The perch dived 5 metres deeper than the tuna, and the catfish dived 25 metres deeper than the bass.

7. The trout dived deeper than the catfish.

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Tommy

Connie

Bert

Paula

trout catfish bass perch tuna

trout catfish bass perch tuna

trout catfish bass perch tuna

trout catfish bass perch tuna

trout catfish bass perch tuna

112 worms 110 worms 100 worms 56 worms 55 worms

112 worms 110 worms 100 worms 56 worms 55 worms

112 worms 110 worms 100 worms 56 worms 55 worms

112 worms 110 worms 100 worms 56 worms 55 worms

224 leeches 200 leeches 168 leeches 165 leeches 100 leeches

o c . che e r o t r s super

112 worms 110 worms 100 worms 56 worms 55 worms

224 leeches 200 leeches 168 leeches 165 leeches 100 leeches

224 leeches 200 leeches 168 leeches 165 leeches 100 leeches

224 leeches 200 leeches 168 leeches 165 leeches 100 leeches

224 leeches 200 leeches 168 leeches 165 leeches 100 leeches

1000 metres 995 metres 950 metres 925 metres 900 metres

1000 metres 995 metres 950 metres 925 metres 900 metres

1000 metres 995 metres 950 metres 925 metres 900 metres

1000 metres 995 metres 950 metres 925 metres 900 metres

1000 metres 995 metres 950 metres 925 metres 900 metres

w ww

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Tina

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28

Family bike trip The clues

Linda, Larry, Lulu, Louis and Lucy were all children in the same family. They were 19, 17, 16, 14 and 8 years old. One recent day, they decided to take a bicycle trip to get ice-cream cones. They rode in single file so, naturally, they were 1st, 2nd, 3rd, 4th and 5th in line.

At the ice-cream shop, they ordered cones with 1, 2, 3, 4 and 5 scoops of ice-cream on them. Based on the clues, match the children with their ages, their places in line and the number of scoops of ice-cream on their cones.

1. As the five rode in line they did not ride in birth order. The first-born did not ride 1st in line, the second-born did not ride 2nd in line, and so on.

2. When the five children ordered ice-cream they followed birth order. The first-born ordered 1 scoop, the second-born ordered 2 scoops, and so on.

3. Louis and Lucy ordered a combined total of 3 scoops of ice-cream.

4. Lulu was older than both Linda and Larry.

5. Linda ordered more scoops of ice-cream than Larry, and Louis ordered more scoops than Lucy.

6. The two oldest children took the last two places in line, and the youngest child did not ride 3rd in line.

7. Lulu was not 1st in line, and Louis was not 5th in line.

Linda

Larry

Lulu

Louis

Lucy

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1st in line 2nd in line 3rd in line 4th in line 5th in line 1 scoop 2 scoops 3 scoops 4 scoops 5 scoops

28 | Maths perplexors

19 years old 17 years old 16 years old 14 years old 8 years old

19 years old 17 years old 16 years old 14 years old 8 years old

19 years old 17 years old 16 years old 14 years old 8 years old

1st in line 2nd in line 3rd in line 4th in line 5th in line

1st in line 2nd in line 3rd in line 4th in line 5th in line

1st in line 2nd in line 3rd in line 4th in line 5th in line

1 scoop 2 scoops 3 scoops 4 scoops 5 scoops

1 scoop 2 scoops 3 scoops 4 scoops 5 scoops

1 scoop 2 scoops 3 scoops 4 scoops 5 scoops

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19 years old 17 years old 16 years old 14 years old 8 years old 1st in line 2nd in line 3rd in line 4th in line 5th in line

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19 years old 17 years old 16 years old 14 years old 8 years old

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1 scoop 2 scoops 3 scoops 4 scoops 5 scoops

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29

Thanksgiving plays The clues

Every year, the Taft, Knox, Twain, Wilson and Adams schools in Oregon, USA, put on their annual Thanksgiving plays. All the plays featured the same three characters, but no school had the same number of students playing these three characters. The schools had 5, 10, 15, 20 and 25 students portraying Pilgrims in the plays. The schools had 5, 10, 15, 20 and 25 students portraying Native Americans in the plays. The schools had 5, 10, 15, 20 and 25 students portraying turkeys in the plays. Based on the clues, match the schools with the number of students they had portraying Pilgrims, Native Americans and turkeys.

1. Each school assigned a different number of students to play each part and no school assigned the same number of students to play more than one part. If a school had 5 Pilgrims it did not have 5 Native Americans or 5 turkeys, and so on.

2. Each school had a different total number of students playing all the parts in the plays. Taft used 35 students, Knox used 30 students, Twain used 45 students, Wilson used 60 students, and Adams used 55 students.

3. Taft School had a combined total of 15 students portraying Pilgrims and Native Americans, but it had more Native Americans than Pilgrims.

4. Wilson and Adams had a combined total of 45 students portraying Native Americans.

5. Knox School had a combined total of 25 students portraying Pilgrims and Native Americans.

6. Twain School had a combined total of 20 students portraying Pilgrims and Native Americans.

7. Wilson School had a combined total of 45 students portraying Pilgrims and Native Americans, but it had more Native Americans than Pilgrims in its play.

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C.Publ i cat i ons •f orr evi ew pur posesonl y• Twain

Wilson

Adams

5 Pilgrims 10 Pilgrims 15 Pilgrims 20 Pilgrims 25 Pilgrims

5 Pilgrims 10 Pilgrims 15 Pilgrims 20 Pilgrims 25 Pilgrims

5 Pilgrims 10 Pilgrims 15 Pilgrims 20 Pilgrims 25 Pilgrims

5 Pilgrims 10 Pilgrims 15 Pilgrims 20 Pilgrims 25 Pilgrims

5 Pilgrims 10 Pilgrims 15 Pilgrims 20 Pilgrims 25 Pilgrims

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Knox

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Taft

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5 Americans 10 Americans 15 Americans 20 Americans 25 Americans

5 Americans 10 Americans 15 Americans 20 Americans 25 Americans

5 Americans 10 Americans 15 Americans 20 Americans 25 Americans

5 Americans 10 Americans 15 Americans 20 Americans 25 Americans

5 Americans 10 Americans 15 Americans 20 Americans 25 Americans

5 turkeys 10 turkeys 15 turkeys 20 turkeys 25 turkeys

5 turkeys 10 turkeys 15 turkeys 20 turkeys 25 turkeys

5 turkeys 10 turkeys 15 turkeys 20 turkeys 25 turkeys

5 turkeys 10 turkeys 15 turkeys 20 turkeys 25 turkeys

5 turkeys 10 turkeys 15 turkeys 20 turkeys 25 turkeys

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30

That’s mice to know The clues

Five mice named Muffy, Fluffy, Hinky, Dinky and Moe sat around a hunk of cheese discussing how dangerous life was for them. They had been chased by cats 150, 125, 100, 75 and 50 times. They had been swooped on by owls 300, 250, 200, 150 and 100 times. They had been chased by broom-wielding farmers’ wives 20, 15, 10, 9 and 5 times. Based on the clues, match the mice with the number of cats, owls and farmers’ wives that had tried to catch them.

1. Between the two of them, Hinky and Dinky accounted for the lowest numbers in the three categories.

2. Between the two of them, Muffy and Fluffy accounted for the highest numbers in the three categories.

3. Hinky was not chased by the fewest cats.

4. If you subtracted Dinky’s cat number from Muffy’s cat number, you would get Hinky’s cat number, which, by the way, would be the same as Hinky’s owl number.

5. Fluffy was chased by more cats than Moe, and Muffy was not chased by the most owls.

6. Muffy was chased by exactly 50 fewer owls than Fluffy, and Moe was chased by fewer owls than Dinky.

7. Hinky was chased by more farmers’ wives than Dinky.

8. Moe was chased by exactly 5 more farmers’ wives than Hinky, and Fluffy was not chased by the most farmers’ wives.

© R. I .

C.Publ i cat i ons •f or r evi ewHinky pur pose sonl y• Fluffy Dinky Moe

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150 cats 125 cats 100 cats 75 cats 50 cats

300 owls 250 owls 200 owls 150 owls 100 owls 20 wives 15 wives 10 wives 9 wives 5 wives

30 | Maths perplexors

150 cats 125 cats 100 cats 75 cats 50 cats

150 cats 125 cats 100 cats 75 cats 50 cats

150 cats 125 cats 100 cats 75 cats 50 cats

300 owls 250 owls 200 owls 150 owls 100 owls

300 owls 250 owls 200 owls 150 owls 100 owls

300 owls 250 owls 200 owls 150 owls 100 owls

20 wives 15 wives 10 wives 9 wives 5 wives

20 wives 15 wives 10 wives 9 wives 5 wives

20 wives 15 wives 10 wives 9 wives 5 wives

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150 cats 125 cats 100 cats 75 cats 50 cats

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300 owls 250 owls 200 owls 150 owls 100 owls 20 wives 15 wives 10 wives 9 wives 5 wives

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31

Nuts to count The clues

Binky, Fido, Rover, Nutly and Squints were five squirrels living in the same area of the Glenview Forest. They had spent most of the summer gathering nuts, and late in the season they got together and compared their nut totals. They had collected 250, 200, 150, 100 and 50 walnuts. They had collected 250, 200, 150, 100 and 50 pecans. They had collected 250, 200, 150, 100 and 50 almonds. Based on the clues, match the squirrels with the number of walnuts, pecans and almonds they had gathered.

1. No squirrel gathered the same number of nuts for more than one type of nut. If a squirrel gathered 50 of one kind of nut he did not collect 50 of another kind of nut, and so on.

2. Binky’s total of all the nuts he gathered was 550, Fido gathered 600 in total, Rover’s total was 450, Nutly’s total was 300, and Squint’s total was 350.

3. Binky and Fido gathered a combined total of 450 walnuts and 450 pecans.

4. Nutly and Squints gathered a combined total of 150 walnuts and 250 pecans.

5. Binky gathered more walnuts than Fido.

6. Squints gathered fewer pecans than Nutly.

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Binky

Fido

Rover

Nutly

Squints

250 walnuts 200 walnuts 150 walnuts 100 walnuts 50 walnuts

250 walnuts 200 walnuts 150 walnuts 100 walnuts 50 walnuts

250 walnuts 200 walnuts 150 walnuts 100 walnuts 50 walnuts

250 walnuts 200 walnuts 150 walnuts 100 walnuts 50 walnuts

250 walnuts 200 walnuts 150 walnuts 100 walnuts 50 walnuts

250 pecans 200 pecans 150 pecans 100 pecans 50 pecans

250 pecans 200 pecans 150 pecans 100 pecans 50 pecans

250 pecans 200 pecans 150 pecans 100 pecans 50 pecans

250 pecans 200 pecans 150 pecans 100 pecans 50 pecans

250 pecans 200 pecans 150 pecans 100 pecans 50 pecans

250 almonds 200 almonds 150 almonds 100 almonds 50 almonds

250 almonds 200 almonds 150 almonds 100 almonds 50 almonds

250 almonds 200 almonds 150 almonds 100 almonds 50 almonds

250 almonds 200 almonds 150 almonds 100 almonds 50 almonds

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250 almonds 200 almonds 150 almonds 100 almonds 50 almonds

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32

The hole thing The clues

Walt, Wilma, Willy, Winnie and Warren were five woodpeckers living in the Glenview Forest. They were extremely proud of their pecking skills and held a contest to see who could peck the biggest hole in a dead tree. They pecked away at that tree and pecked holes that were 18, 14, 12, 9 and 6 cm in diameter.

They did not peck for nothing and they ate while pecking. They ate 300, 275, 250, 225 and 175 bugs.

With all that pecking and eating, they became thirsty and decided to race to the lake for a nice drink of water. Naturally enough, they finished 1st, 2nd, 3rd, 4th and 5th in the race. Based on the clues, match the woodpeckers with their hole sizes, the number of bugs they ate and their order of finish in the race.

1. Warren’s diameter was exactly the same as Walt’s radius, but Willy’s radius was exactly the same as Winnie’s diameter.

2. Walt and Wilma’s combined bug-eating total was 575, and Willy and Winnie’s combined bug-eating total was 400.

3. Wilma did not eat the most bugs, and Walt’s hole was not the biggest hole.

4. The two woodpeckers who made the smallest holes finished in 4th and 5th place in the race, but neither of them was the one who ate the fewest bugs.

5. Walt did not win the race, and Winnie did not finish last in the race.

6. The woodpecker who ate the most bugs finished in 2nd place in the race just behind the woodpecker whose hole had an 7-cm radius.

18 cm 14 cm 12 cm 9 cm 6 cm

Wilma

Willy

Winnie

18 cm 14 cm 12 cm 9 cm 6 cm

18 cm 14 cm 12 cm 9 cm 6 cm

18 cm 14 cm 12 cm 9 cm 6 cm

300 bugs 275 bugs 250 bugs 225 bugs 175 bugs

300 bugs 275 bugs 250 bugs 225 bugs 175 bugs

300 bugs 275 bugs 250 bugs 225 bugs 175 bugs

1st place 2nd place 3rd place 4th place 5th place

1st place 2nd place 3rd place 4th place 5th place

1st place 2nd place 3rd place 4th place 5th place

Warren

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300 bugs 275 bugs 250 bugs 225 bugs 175 bugs

1st place 2nd place 3rd place 4th place 5th place

32 | Maths perplexors

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18 cm 14 cm 12 cm 9 cm 6 cm

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300 bugs 275 bugs 250 bugs 225 bugs 175 bugs

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33

Shape up kids The clues

Alex, Anna, Alice, Andy and Arlene all loved to cut out the same three shapes. They just could not get enough triangles, squares and pentagons to make them happy.

One day in class their teacher gave them plenty of paper and a pair of scissors and told them to get cutting.

They happily cut out 30, 40, 50, 60 and 70 triangles.

They joyfully cut out 30, 40, 50, 60 and 70 squares.

They were thrilled and excited to cut out 30, 40, 50, 60 and 70 pentagons. Based on the clues, match the children with the number of triangles, squares and pentagons they cut out that wonderful day in class.

1. Anna made the most of one shape, and Alex made the most of the two remaining shapes.

2. Andy cut the fewest of one shape, and Arlene cut the fewest of the two remaining shapes.

3. Anna counted the total number of sides in one of the piles of shapes she cut and came out with 210, and Arlene counted the sides in one of her piles of shapes and came out with 90.

4. The total number of sides in Andy’s pentagon pile was 200.

5. Alice cut out exactly the same number of squares and pentagons but not triangles.

6. Alex cut out exactly 10 more triangles than Arlene, and Andy cut out fewer triangles than Alice.

7. Arlene cut out more squares than Anna.

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Andy

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Arlene

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C.Publ i cat i ons •f orr evi ew pur posesonl y• 30 triangles 40 triangles 50 triangles 60 triangles 70 triangles

30 triangles 40 triangles 50 triangles 60 triangles 70 triangles

30 triangles 40 triangles 50 triangles 60 triangles 70 triangles

30 squares 40 squares 50 squares 60 squares 70 squares

30 squares 40 squares 50 squares 60 squares 70 squares

30 squares 40 squares 50 squares 60 squares 70 squares

30 squares 40 squares 50 squares 60 squares 70 squares

30 squares 40 squares 50 squares 60 squares 70 squares

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30 pentagons 40 pentagons 50 pentagons 60 pentagons 70 pentagons

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30 triangles 40 triangles 50 triangles 60 triangles 70 triangles

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30 triangles 40 triangles 50 triangles 60 triangles 70 triangles

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30 pentagons 40 pentagons 50 pentagons 60 pentagons 70 pentagons

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30 pentagons 40 pentagons 50 pentagons 60 pentagons 70 pentagons

30 pentagons 40 pentagons 50 pentagons 60 pentagons 70 pentagons

30 pentagons 40 pentagons 50 pentagons 60 pentagons 70 pentagons

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34

Christmas holiday fun The clues

The towns of Alpha, Beta, Crown, Dofuss and Enid all held Christmas celebrations. They all designated one day in December as a special Christmas holiday day and they asked their citizens to dress in holiday costumes and come to their town squares to sing and eat sticky date pudding. At the last celebration, the towns had 1500, 1400, 1300, 1000 and 900 citizens dressed as Santa Claus. The towns had 750, 725, 700, 650 and 450 citizens dressed as Frosty the Snowman.

The towns had 3000, 2800, 2600, 2200 and 2000 citizens dressed as Rudolph the Red-nosed Reindeer.

Based on the clues, match the towns with the number of citizens they each had dressed as Santa, Frosty and Rudolph.

1. The citizens were filled with the holiday spirit and a record number of citizens dressed in holiday costumes. Alpha had a total of 4625 costumed people, Beta had a total of 3900, Crown had a total of 3650, Dofuss had a total of 5050, and Enid had a total of 4750 citizens in costume that year.

2. Dofuss and Enid’s combined total of citizens dressed as Santa was 2900, and their combined total of citizens dressed as Frosty was 1100.

3. Beta and Crown’s combined total of citizens dressed as Santa was 1900.

4. Neither Alpha nor Beta had the most citizens dressed as Frosty.

5. Multiply Beta’s Frosty number by 2 to find Dofuss’ Santa number.

6. Beta did not have the fewest citizens dressed as Santa.

1500 Santas 1400 Santas 1300 Santas 1000 Santas 900 Santas

Beta R. Dofuss © I .

C.Crown Publ i cat i ons Enid •f orr evi ew pur posesonl y• 1500 Santas 1400 Santas 1300 Santas 1000 Santas 900 Santas

1500 Santas 1400 Santas 1300 Santas 1000 Santas 900 Santas

750 Frostys 725 Frostys 700 Frostys 650 Frostys 450 Frostys

750 Frostys 725 Frostys 700 Frostys 650 Frostys 450 Frostys

750 Frostys 725 Frostys 700 Frostys 650 Frostys 450 Frostys

3000 Rudolphs 2800 Rudolphs 2600 Rudolphs 2200 Rudolphs 2000 Rudolphs

3000 Rudolphs 2800 Rudolphs 2600 Rudolphs 2200 Rudolphs 2000 Rudolphs

3000 Rudolphs 2800 Rudolphs 2600 Rudolphs 2200 Rudolphs 2000 Rudolphs

w ww

750 Frostys 725 Frostys 700 Frostys 650 Frostys 450 Frostys

1500 Santas 1400 Santas 1300 Santas 1000 Santas 900 Santas

3000 Rudolphs 2800 Rudolphs 2600 Rudolphs 2200 Rudolphs 2000 Rudolphs

34 | Maths perplexors

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1500 Santas 1400 Santas 1300 Santas 1000 Santas 900 Santas

m . u

Alpha

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750 Frostys 725 Frostys 700 Frostys 650 Frostys 450 Frostys

3000 Rudolphs 2800 Rudolphs 2600 Rudolphs 2200 Rudolphs 2000 Rudolphs

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35

Camelot?

The clues

Gigi, Winnie, Stan, Burt and Ginger were five camels living together in the desert. One of them had a standard 1 hump, another had a common 2 humps, but the others had 3, 4 and 5 humps. Once, they held a contest to see who could go without water for the longest time; they went 17, 14, 13, 10 and 7 days without water. Another time, they held a yodelling contest to see who could yodel the most times in a minute. They yodelled 85, 75, 60, 50 and 45 yodels in a minute. Based on the clues, match the camels with their number of humps, the days they went without water and their yodels per minute.

1. Ginger went without water exactly 72 hours longer than Burt, Winnie went without water one week longer than Burt, and Gigi went without water one week longer than Ginger.

2. Gigi and Winnie’s combined hump total was 5, but Burt and Ginger’s combined hump total was also 5.

3. Gigi and Winnie’s combined yodelling total was 95.

4. Stan yodelled exactly 10 more yodels than Gigi, and Ginger, who did not have the fewest humps, yodelled more yodels than Burt.

5. Both Gigi and Winnie had more humps than Burt, but Gigi had more humps than Winnie.

r o e t s Bo r e p ok u S

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Teac he r

The story

Gigi

Winnie

Stan

Burt

Ginger

5 humps 4 humps 3 humps 2 humps 1 hump

5 humps 4 humps 3 humps 2 humps 1 hump

5 humps 4 humps 3 humps 2 humps 1 hump

5 humps 4 humps 3 humps 2 humps 1 hump

5 humps 4 humps 3 humps 2 humps 1 hump

17 days 14 days 13 days 10 days 7 days

17 days 14 days 13 days 10 days 7 days

17 days 14 days 13 days 10 days 7 days

17 days 14 days 13 days 10 days 7 days

17 days 14 days 13 days 10 days 7 days

85 yodels 75 yodels 60 yodels 50 yodels 45 yodels

85 yodels 75 yodels 60 yodels 50 yodels 45 yodels

85 yodels 75 yodels 60 yodels 50 yodels 45 yodels

85 yodels 75 yodels 60 yodels 50 yodels 45 yodels

w ww 85 yodels 75 yodels 60 yodels 50 yodels 45 yodels

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36

Bug zappers The clues

Carl, Claude, Cass, Cher and Cora all went out and purchased new bug zappers for their backyards. These new machines not only zapped annoying insects but they also kept track of the number and types of bugs they zapped. One recent day, the machines were checked and it was discovered they had zapped 270, 250, 200, 90 and 50 flies. They had zapped 540, 500, 400, 300 and 180 gnats. They had zapped 1080, 1000, 800, 700 and 600 wasps. Based on the clues, match the names with the number of flies, gnats and wasps their machines zapped.

1. If you multiplied Carl’s fly total by 2, the answer would be his gnat total, and if you multiplied his gnat total by 2, the answer would be his wasp total.

2. If you multiplied Claude’s fly total by 12, the answer would be his wasp total, but if you multiplied Claude’s fly total by 2, the answer would be his gnat total.

3. Cher and Cora zapped a combined total of 520 flies.

4. If you multiplied Cass’ fly total by 10, the answer would be her gnat-zapping total, and if you multiplied her gnat-zapping total by 2, the answer would be her wasp-zapping total.

5. Cora zapped more flies than Cher, Cora zapped more gnats than Cher, and Cora zapped more wasps than Cher.

Carl

Claude

Cass

Cher

Cora

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

w ww

540 gnats 500 gnats 400 gnats 300 gnats 180 gnats

1080 wasps 1000 wasps 800 wasps 700 wasps 600 wasps

36 | Maths perplexors

270 flies 250 flies 200 flies 90 flies 50 flies

270 flies 250 flies 200 flies 90 flies 50 flies

270 flies 250 flies 200 flies 90 flies 50 flies

540 gnats 500 gnats 400 gnats 300 gnats 180 gnats

540 gnats 500 gnats 400 gnats 300 gnats 180 gnats

540 gnats 500 gnats 400 gnats 300 gnats 180 gnats

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270 flies 250 flies 200 flies 90 flies 50 flies

540 gnats 500 gnats 400 gnats 300 gnats 180 gnats

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270 flies 250 flies 200 flies 90 flies 50 flies

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Teac he r

The story

o c . che e r o t r s super

1080 wasps 1000 wasps 800 wasps 700 wasps 600 wasps

1080 wasps 1000 wasps 800 wasps 700 wasps 600 wasps

1080 wasps 1000 wasps 800 wasps 700 wasps 600 wasps

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1080 wasps 1000 wasps 800 wasps 700 wasps 600 wasps

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37

Cactuses factuses?

The clues

Drake, Dean, Dina, Debby and Dian were each fortunate enough to have a giant cactus growing on their land. They kept a watchful eye on their cactuses and got together once a year to make comparisons.

Their cactuses were 95, 85, 75, 70 and 50 years old.

Each year when their cactuses bloomed, they went out and counted the blossoms each plant produced.

The cactuses produced 950, 850, 750, 500 and 475 blossoms. The cactuses all had different diameter trunks and were 30, 28, 20, 15 and 14 cm in diameter. Based on the clues, match the names with the age of their cactus, the number of cactus blossoms and the diameter of their cactus in centimetres.

1. Drake’s diameter was exactly the same as Dean’s radius, and Debby’s radius was exactly the same as Dian’s diameter.

2. If you multiplied the number of Dean’s blossoms by 2, the answer would be the number of Drake’s blossoms.

3. Dean and Dina’s cactus ages combined would be 120 years.

4. Dian’s blossom number divided by Dina’s age would result in the number 10.

5. If you multiplied Dean’s radius number by 5, the result would be Drake’s age.

6. Dian’s age multiplied by 10 would result in Dina’s blossom number.

r o e t s Bo r e p ok u S

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Teac he r

The story

Drake

Dean

Dina

Debby

Dian

95 years old 85 years old 75 years old 70 years old 50 years old

95 years old 85 years old 75 years old 70 years old 50 years old

95 years old 85 years old 75 years old 70 years old 50 years old

95 years old 85 years old 75 years old 70 years old 50 years old

95 years old 85 years old 75 years old 70 years old 50 years old

950 blossoms 850 blossoms 750 blossoms 500 blossoms 475 blossoms

950 blossoms 850 blossoms 750 blossoms 500 blossoms 475 blossoms

950 blossoms 850 blossoms 750 blossoms 500 blossoms 475 blossoms

950 blossoms 850 blossoms 750 blossoms 500 blossoms 475 blossoms

950 blossoms 850 blossoms 750 blossoms 500 blossoms 475 blossoms

30 cm 28 cm 20 cm 15 cm 14 cm

30 cm 28 cm 20 cm 15 cm 14 cm

30 cm 28 cm 20 cm 15 cm 14 cm

30 cm 28 cm 20 cm 15 cm 14 cm

w ww 30 cm 28 cm 20 cm 15 cm 14 cm

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38

All abeard!

The clues

The towns of Alpha, Beta, Crown, Dofuss and Enid decided to have a beard-growing contest. All citizens capable of growing a beard were ordered to do so, and the person who grew the best beard would represent their towns in the contest. The best beard growers were Tim, Tom, Tony, Trevor and Troy. They were 50, 45, 40, 30 and 15 years old. The measured lengths of their beards was 20, 18, 17, 15 and 10 cm long, and the measured widths of their beards was 10, 9, 8, 7 and 5 cm wide. Based on the clues, match the towns with the best beard growers, their ages, their beard lengths and their beard widths.

1. Tim’s beard was 160 square cm, Tom’s beard was 135 square cm, Tony’s beard was 126 square cm, Trevor’s beard was 100 square cm, and Troy’s beard was 85 square cm.

2. Multiply Alpha’s beard champion’s age by 2 to discover the age of Enid’s beard champion.

3. The man from Crown was exactly one decade older than Tony from Dofuss, and Tom from Beta was exactly 5 years younger than Tim. 4. Troy was not the youngest of the town champions.

5. Trevor grew the only square beard.

r o e t s Bo r e p ok u S

Alpha

Beta

Crown

Dofuss

Tim Tom Tony Trevor Troy

Tim Tom Tony Trevor Troy

Tim Tom Tony Trevor Troy

Tim Tom Tony Trevor Troy

50 years old 45 years old 40 years old 30 years old 15 years old

50 years old 45 years old 40 years old 30 years old 15 years old

50 years old 45 years old 40 years old 30 years old 15 years old

20 cm long 18 cm long 17 cm long 15 cm long 10 cm long

20 cm long 18 cm long 17 cm long 15 cm long 10 cm long

20 cm long 18 cm long 17 cm long 15 cm long 10 cm long

10 cm wide 9 cm wide 8 cm wide 7 cm wide 5 cm wide

10 cm wide 9 cm wide 8 cm wide 7 cm wide 5 cm wide

10 cm wide 9 cm wide 8 cm wide 7 cm wide 5 cm wide

ew i ev Pr

Teac he r

The story

Enid

Tim Tom Tony Trevor Troy

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

20 cm long 18 cm long 17 cm long 15 cm long 10 cm long

10 cm wide 9 cm wide 8 cm wide 7 cm wide 5 cm wide

38 | Maths perplexors

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50 years old 45 years old 40 years old 30 years old 15 years old

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50 years old 45 years old 40 years old 30 years old 15 years old

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20 cm long 18 cm long 17 cm long 15 cm long 10 cm long

10 cm wide 9 cm wide 8 cm wide 7 cm wide 5 cm wide

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39

An eggsact count The clues

Jenny, Jonas, Josie, John and Jill went to a giant Easter egg festival where they were invited to gather as many coloured Easter eggs as possible. Taking advantage of this offer, they gathered 300, 250, 200, 180 and 160 red Easter eggs. They gathered 220, 210, 200, 180 and 160 yellow Easter eggs. They gathered 170, 160, 150, 120 and 100 purple Easter eggs. Based on the clues, match the names with the number of red, yellow and purple Easter eggs they gathered.

1. Jenny and Jonas gathered a combined total of 550 red Easter eggs, and Josie and John gathered a combined total of 360 red Easter eggs.

2. Josie gathered exactly 20 more red Easter eggs than Jill and exactly 50 fewer red Easter eggs than Jonas.

3. Jenny and Jonas gathered a combined total of 430 yellow Easter eggs, and John and Jill gathered a combined total of 380 yellow Easter eggs.

4. Jenny and Jonas gathered a combined total of 330 purple Easter eggs.

5. If you combined John’s yellow Easter egg total with his purple Easter egg total, the result would be 300, but if you added Jill’s yellow Easter egg total to her purple Easter egg total, the answer would also be 300.

6. If you subtracted the number in Josie’s purple Easter egg collection from the number of Jonas’s red Easter eggs, the answer would be the number of purple Easter eggs in John’s collection.

7. Jonas collected the most of only one colour of Easter eggs, and he gathered exactly 10 more purple Easter eggs than Josie.

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The story

© R. I .

C.Publ i cat i ons •f orr e vi ew pu r posesJohn onl y• Jenny Jonas Josie

220 yellow 210 yellow 200 yellow 180 yellow 160 yellow

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170 purple 160 purple 150 purple 120 purple 100 purple

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300 red 250 red 200 red 180 red 160 red

300 red 250 red 200 red 180 red 160 red

300 red 250 red 200 red 180 red 160 red

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300 red 250 red 200 red 180 red 160 red

o c . che e r o t r s super

Jill 300 red 250 red 200 red 180 red 160 red

220 yellow 210 yellow 200 yellow 180 yellow 160 yellow

220 yellow 210 yellow 200 yellow 180 yellow 160 yellow

220 yellow 210 yellow 200 yellow 180 yellow 160 yellow

220 yellow 210 yellow 200 yellow 180 yellow 160 yellow

170 purple 160 purple 150 purple 120 purple 100 purple

170 purple 160 purple 150 purple 120 purple 100 purple

170 purple 160 purple 150 purple 120 purple 100 purple

170 purple 160 purple 150 purple 120 purple 100 purple

R.I.C. Publications®

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40

Tripping out The clues

The Jones, Smith, Brown, Black and Barnes families bravely set out on driving holidays with parents in the front seat and children in the back seats. In many ways, they were typical family holidays. They drove 3000, 1900, 1750, 1400 and 1200 km. They made 850, 800, 750, 700 and 600 rest stops along the way.

They all heard the words, ‘Are we there yet?’ 22 000, 21 000, 18 000, 17 000 and 15 000 times. Based on the clues, match the families with the distances driven, the number of rest stops and the number of times they heard the words, ‘Are we there yet?’

1. The Jones family took 1 rest stop every 2 km, but the Smith family also took 1 rest stop for every 2 km driven.

2. The Jones family said, ‘Are we there yet?’ 15 times for every km driven, and the Smith family said ‘Are we there yet?’ 30 times for every rest stop it took.

3. The Brown family travelled exactly 350 more kilometres than the Smith family and made exactly 50 more rest stops than the Smith family.

4. The Black family travelled farther than the Barnes family, and the Black family took fewer rest stops than the Barnes family.

5. The Black family said, ‘Are we there yet?’ more than the Barnes family but less than the Brown family.

r o e t s Bo r e p ok u S

Jones

Smith

Brown

Black

3000 km 1900 km 1750 km 1400 km 1200 km

3000 km 1900 km 1750 km 1400 km 1200 km

3000 km 1900 km 1750 km 1400 km 1200 km

3000 km 1900 km 1750 km 1400 km 1200 km

850 stops 800 stops 750 stops 700 stops 600 stops

850 stops 800 stops 750 stops 700 stops 600 stops

850 stops 800 stops 750 stops 700 stops 600 stops

22 000 yet?

21 000 yet?

18 000 yet?

17 000 yet?

15 000 yet?

22 000 yet?

21 000 yet?

18 000 yet?

17 000 yet?

15 000 yet?

ew i ev Pr

Teac he r

The story

Barnes

3000 km 1900 km 1750 km 1400 km 1200 km

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

22 000 yet?

21 000 yet?

18 000 yet?

17 000 yet?

15 000 yet?

40 | Maths perplexors

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22 000 yet?

21 000 yet?

18 000 yet?

17 000 yet?

15 000 yet?

850 stops 800 stops 750 stops 700 stops 600 stops

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850 stops 800 stops 750 stops 700 stops 600 stops

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22 000 yet?

21 000 yet?

18 000 yet?

17 000 yet?

15 000 yet?

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41

Climb every mountain The clues

Chad, Chet, Carol, Connie and Carl were five very experienced mountain climbers. In their careers they had climbed 88, 70, 62, 44 and 31 mountains. One recent day, they were climbing Mt Elbert when disaster struck and they all fell off the mountain. They all were on different parts of the mountain and they fell 1500, 1300, 1100, 700 and 600 metres. Fortunately, nobody was seriously injured but they all suffered cuts that required stitches. They received 70, 60, 50, 40 and 10 stitches. Based on the clues, match the names with the number of mountains they had climbed, the distances they fell and the number of stitches they received.

1. Chad, Chet and Connie each received exactly 10 fewer stitches than at least one other mountain climber.

2. Carol did not receive the most stitches, and Chet received exactly 20 fewer stitches than Connie.

3. Carol climbed 18 fewer mountains than Chad, but Chet climbed 18 fewer mountains than Connie.

4. Connie did climb more mountains than Chad.

5. Carol fell 200 metres farther than Chad, but Carl fell 200 metres less than Chad.

6. Chet did not fall as far as Connie.

r o e t s Bo r e p ok u S

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Chad

Chet

Carol

Connie

Carl

88 mts 70 mts 62 mts 44 mts 31 mts

88 mts 70 mts 62 mts 44 mts 31 mts

88 mts 70 mts 62 mts 44 mts 31 mts

88 mts 70 mts 62 mts 44 mts 31 mts

88 mts 70 mts 62 mts 44 mts 31 mts

1500 m 1300 m 1100 m 700 m 600 m

1500 m 1300 m 1100 m 700 m 600 m

1500 m 1300 m 1100 m 700 m 600 m

1500 m 1300 m 1100 m 700 m 600 m

1500 m 1300 m 1100 m 700 m 600 m

70 stitches 60 stitches 50 stitches 40 stitches 10 stitches

70 stitches 60 stitches 50 stitches 40 stitches 10 stitches

70 stitches 60 stitches 50 stitches 40 stitches 10 stitches

70 stitches 60 stitches 50 stitches 40 stitches 10 stitches

w ww 70 stitches 60 stitches 50 stitches 40 stitches 10 stitches

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42

Great Caesar’s goats The clues

Tom, Tina, Tara, Timmy and Taylor were five goats living on Caesar Smith’s farm. One day, they went to town and wandered into a laundromat and proceeded to eat various items of clothing. They ate 5, 4, 3, 2 and 1 shirts. They also ate 5, 4, 3, 2 and 1 singlets. Finally, they ate 5, 4, 3, 2 and 1 pairs of pants. Of course, no goat ate the same number for any item of clothing as any other goat, and no goat ate the same number for any item of clothing twice. In other words, if a goat ate 1 shirt, he did not eat 1 of anything else. Based on the clues, match the goats with the number of shirts, singlets and pants they ate.

1. Remember, if a goat ate 1 shirt he did not eat 1 of anything else, and if another goat ate 2 shirts he did not eat 2 of anything else, and so on.

2. Tom, Tara and Timmy ate a combined total of 6 shirts.

3. Tom and Tina ate a combined total of 8 shirts and, of course, Timmy ate more shirts than Tara.

4. Tom and Timmy ate a combined total of 6 singlets, but Timmy ate fewer singlets than Tom. 5. Taylor and Tara ate a combined total of 5 singlets but, of course, Taylor ate more singlets than Tara.

6. Two goats ate more pants than Tara, Tina did not eat the fewest pants, but then Taylor did not eat the fewest pants either.

r o e t s Bo r e p ok u S

Tom

Tina

Tara

Timmy

5 shirts 4 shirts 3 shirts 2 shirts 1 shirt

5 shirts 4 shirts 3 shirts 2 shirts 1 shirt

5 shirts 4 shirts 3 shirts 2 shirts 1 shirt

5 shirts 4 shirts 3 shirts 2 shirts 1 shirt

5 singlets 4 singlets 3 singlets 2 singlets 1 singlet

5 singlets 4 singlets 3 singlets 2 singlets 1 singlet

5 singlets 4 singlets 3 singlets 2 singlets 1 singlet

5 pants 4 pants 3 pants 2 pants 1 pants

5 pants 4 pants 3 pants 2 pants 1 pants

ew i ev Pr

Teac he r

The story

Taylor

5 shirts 4 shirts 3 shirts 2 shirts 1 shirt

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

5 pants 4 pants 3 pants 2 pants 1 pants

42 | Maths perplexors

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5 pants 4 pants 3 pants 2 pants 1 pants

5 singlets 4 singlets 3 singlets 2 singlets 1 singlet

m . u

w ww

5 singlets 4 singlets 3 singlets 2 singlets 1 singlet

o c . che e r o t r s super

R.I.C. Publications®

5 pants 4 pants 3 pants 2 pants 1 pants

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43

Pirate figures The clues

Jack, Jessie, Jenny, Jerome and Jodi were five former pirates living together at the Buccaneer Retirement Home. They had kept careful records during their careers and liked to compare notes. It was discovered that they had captured 27, 23, 19, 14 and 10 ships and robbed them of their booty. They had amassed fortunes of 3700, 3400, 3100, 2600 and 2000 gold coins. They had buried their treasures at different depths; they were 100, 90, 80, 60 and 20 metres deep. Based on the clues, match the pirates with the number of ships they captured, the gold coins they had collected and the depth their treasures were buried.

1. Jerome captured 4 fewer ships than Jenny, Jodi captured 4 fewer ships than Jerome and 8 fewer ships than Jenny.

2. Jack captured fewer ships than Jessie.

3. The two pirates who buried their gold a combined total of 190 metres buried a combined total of 4600 gold coins.

4. Jack, Jessie and Jenny each had more than 3000 gold coins.

5. Jerome buried his treasure 10 metres deeper than Jack buried his treasure.

6. The pirate with the fewest gold coins did not bury his or her treasure the deepest.

7. Jenny had 600 fewer gold coins than Jessie.

8. Jack’s treasure was 60 metres deeper than Jenny’s treasure.

r o e t s Bo r e p ok u S

Jack

Jessie

Jenny

ew i ev Pr

Teac he r

The story

Jerome

Jodi

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y• 27 ships 23 ships 19 ships 14 ships 10 ships

27 ships 23 ships 19 ships 14 ships 10 ships

27 ships 23 ships 19 ships 14 ships 10 ships

3700 coins 3400 coins 3100 coins 2600 coins 2000 coins

3700 coins 3400 coins 3100 coins 2600 coins 2000 coins

3700 coins 3400 coins 3100 coins 2600 coins 2000 coins

3700 coins 3400 coins 3100 coins 2600 coins 2000 coins

3700 coins 3400 coins 3100 coins 2600 coins 2000 coins

100 m 90 m 80 m 60 m 20 m

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27 ships 23 ships 19 ships 14 ships 10 ships

w ww

27 ships 23 ships 19 ships 14 ships 10 ships

o c . che e r o t r s super 100 m 90 m 80 m 60 m 20 m

R.I.C. Publications®

100 m 90 m 80 m 60 m 20 m

100 m 90 m 80 m 60 m 20 m

100 m 90 m 80 m 60 m 20 m

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44

High life The clues

Ken, Kyle, Karen, Kathy and Kirk all lived on different floors of the same high-rise apartment building. They lived on the 82nd, 75th, 68th, 61st and 41st floors.

None of them was the same age; they were 55, 50, 45, 30 and 25 years old. They all had jobs that they had to travel to each day. The distances they travelled were 28, 24, 20, 10 and 8 kilometres. Based on the clues, match the names with their apartment floors, their ages and the kilometres they had to travel to work each day.

1. The youngest travelled the shortest distance and lived on the highest floor.

2. The oldest travelled twice as far as the youngest and lived on the lowest floor.

3. Ken, Karen and Kathy were each exactly 5 years younger than at least one other person, but Kyle was older than only one other person.

4. Karen and Kathy had thus far lived a combined total of 75 years.

5. Karen travelled 4 km less than Ken. 6. One morning, as Karen was travelling down on the lift from her floor, she met Kyle when he got on the lift at his floor, and 7 floors further down they both met Ken as he got on at his floor.

7. Kyle had to travel 4 km farther than Kirk.

Ken

Kyle

Karen

Kathy

Kirk

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w ww

age 55 age 50 age 45 age 30 age 25 28 km 24 km 20 km 16 km 8 km

44 | Maths perplexors

82nd floor 75th floor 68th floor 61st floor 41st floor

82nd floor 75th floor 68th floor 61st floor 41st floor

82nd floor 75th floor 68th floor 61st floor 41st floor

age 55 age 50 age 45 age 30 age 25

age 55 age 50 age 45 age 30 age 25

age 55 age 50 age 45 age 30 age 25

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82nd floor 75th floor 68th floor 61st floor 41st floor age 55 age 50 age 45 age 30 age 25

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82nd floor 75th floor 68th floor 61st floor 41st floor

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Teac he r

The story

o c . che e r o t r s super

28 km 24 km 20 km 16 km 8 km

28 km 24 km 20 km 16 km 8 km

28 km 24 km 20 km 16 km 8 km

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28 km 24 km 20 km 16 km 8 km

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45

Bakery goods The clues

Betty, Ben, Beau, Bonnie and Boris operated the five bakeries in the town of Brookview. One recent day they baked 60, 50, 40, 20 and 10 cakes. They baked 60, 50, 40, 20 and 10 pies. They baked 60, 50, 40, 20 and 10 muffins. However, no baker baked the same number of items more than once, and no baker baked the same number of any type of item as another baker. Based on the clues, match the bakers with the number of cakes, pies and muffins they baked that day.

1. No baker baked the same number of items more than once, and no baker baked the same number of any type of item as another baker.

2. Beau and Bonnie were the only two bakers who did not bake exactly 10 fewer cakes than another baker.

3. Bonnie baked fewer cakes than Betty, but Betty baked fewer cakes than Ben. 4. Betty baked exactly 10 fewer pies than Ben, and Boris baked exactly 10 fewer pies than Beau.

5. Betty baked exactly 10 fewer muffins than another baker.

6. Beau did not bake the fewest muffins, but he did bake exactly 10 fewer muffins than another baker.

r o e t s Bo r e p ok u S

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Teac he r

The story

Betty

Ben

Beau

Bonnie

Boris

60 cakes 50 cakes 40 cakes 20 cakes 10 cakes

60 cakes 50 cakes 40 cakes 20 cakes 10 cakes

60 cakes 50 cakes 40 cakes 20 cakes 10 cakes

60 cakes 50 cakes 40 cakes 20 cakes 10 cakes

60 cakes 50 cakes 40 cakes 20 cakes 10 cakes

60 pies 50 pies 40 pies 20 pies 10 pies

60 pies 50 pies 40 pies 20 pies 10 pies

60 pies 50 pies 40 pies 20 pies 10 pies

60 pies 50 pies 40 pies 20 pies 10 pies

60 pies 50 pies 40 pies 20 pies 10 pies

60 muffins 50 muffins 40 muffins 20 muffins 10 muffins

60 muffins 50 muffins 40 muffins 20 muffins 10 muffins

60 muffins 50 muffins 40 muffins 20 muffins 10 muffins

60 muffins 50 muffins 40 muffins 20 muffins 10 muffins

w ww 60 muffins 50 muffins 40 muffins 20 muffins 10 muffins

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m . u

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Maths perplexors

| 45

46

Flying frogs?

The clues

Larry, Laura, Luke, Lorrie and Livia were five frogs living together in Swanson Swamp. They enjoyed their lives in the swamp but grew bored in the absence of organised frog activities and decided to hold some contests with each other. Their first contest was to see who could eat the most flies in an hour. They ate an eye-popping 375, 350, 300, 275 and 260 flies in an hour. Their second contest was to see who could hop the most times in a minute. They hopped an astonishing 170, 160, 140, 130 and 120 times in a minute. Their final contest was to see who could croak the most times in a minute.

They croaked an ear-splitting 515, 500, 485, 450 and 400 times in a minute. Based on the clues, match the frogs with their number of flies, hops and croaks.

1.

2.

3.

4.

Larry ate exactly 25 fewer flies than Luke.

Lorrie ate exactly 25 more flies than Livia.

Of course, Larry did not eat 350 flies.

Lorrie and Livia’s combined hopping total was 80 less than Larry and Laura’s combined hopping total.

5. Larry croaked exactly 15 more times than Laura, and Luke croaked exactly 15 fewer times than Laura.

6. The best croaker was not the best at hopping.

7. Lorrie was not the worst at either croaking or hopping because another frog was the worst at both.

r o e t s Bo r e p ok u S

Larry

Laura

Luke

Lorrie

375 flies 350 flies 300 flies 275 flies 260 flies

375 flies 350 flies 300 flies 275 flies 260 flies

375 flies 350 flies 300 flies 275 flies 260 flies

375 flies 350 flies 300 flies 275 flies 260 flies

170 hops 160 hops 140 hops 130 hops 120 hops

170 hops 160 hops 140 hops 130 hops 120 hops

170 hops 160 hops 140 hops 130 hops 120 hops

515 croaks 500 croaks 485 croaks 450 croaks 400 croaks

515 croaks 500 croaks 485 croaks 450 croaks 400 croaks

ew i ev Pr

Teac he r

The story

Livia

375 flies 350 flies 300 flies 275 flies 260 flies

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

515 croaks 500 croaks 485 croaks 450 croaks 400 croaks

46 | Maths perplexors

. te

515 croaks 500 croaks 485 croaks 450 croaks 400 croaks

170 hops 160 hops 140 hops 130 hops 120 hops

m . u

w ww

170 hops 160 hops 140 hops 130 hops 120 hops

o c . che e r o t r s super

R.I.C. Publications®

515 croaks 500 croaks 485 croaks 450 croaks 400 croaks

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47

Lumberjacks are OK! The clues

Mike, Mary, Molly, Mona and Max were five lumberjacks working in the vast Worthington Forest.

During the annual Paul Bunyan festival, they competed against each other in two traditional lumberjack contests. The first contest was to see who could eat the most pancakes, and they ate 88, 80, 72, 62 and 54 pancakes at one sitting. The second contest was to see who could chop down the most trees in an hour, and they chopped down 97, 90, 83, 70 and 60 trees.

All of the lumberjacks loved wildflowers and they spent much of their leisure time collecting them. They had 150, 145, 140, 130 and 115 wildflowers in their collections. Based on the clues, match the lumberjacks with the number of pancakes they consumed, the number of trees they chopped down and the number of wildflowers in their collections.

1. Mary ate exactly 8 fewer pancakes than Mike, Mona ate exactly 8 fewer pancakes than Molly, and Max ate exactly 8 fewer pancakes than Mona.

2. Mona and Max chopped down a combined total of 153 trees.

3. Mary cut down exactly 20 more trees than Mona but not as many as Mike.

4. Mona collected exactly 15 more flowers than Mary, and Molly collected exactly 10 more flowers than Mary.

5. Max’s wildflower collection was larger than Mike’s wildflower collection.

r o e t s Bo r e p ok u S

Mike

Mary

Molly

Mona

ew i ev Pr

Teac he r

The story

Max

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y• 88 pancakes 80 pancakes 72 pancakes 62 pancakes 54 pancakes

88 pancakes 80 pancakes 72 pancakes 62 pancakes 54 pancakes

88 pancakes 80 pancakes 72 pancakes 62 pancakes 54 pancakes

97 trees 90 trees 83 trees 70 trees 60 trees

97 trees 90 trees 83 trees 70 trees 60 trees

97 trees 90 trees 83 trees 70 trees 60 trees

97 trees 90 trees 83 trees 70 trees 60 trees

97 trees 90 trees 83 trees 70 trees 60 trees

150 flowers 145 flowers 140 flowers 130 flowers 115 flowers

. te

www.ricpublications.com.au

m . u

88 pancakes 80 pancakes 72 pancakes 62 pancakes 54 pancakes

w ww

88 pancakes 80 pancakes 72 pancakes 62 pancakes 54 pancakes

o c . che e r o t r s super

150 flowers 145 flowers 140 flowers 130 flowers 115 flowers

R.I.C. Publications®

150 flowers 145 flowers 140 flowers 130 flowers 115 flowers

150 flowers 145 flowers 140 flowers 130 flowers 115 flowers

150 flowers 145 flowers 140 flowers 130 flowers 115 flowers

Maths perplexors

| 47

48

Smore the merrier

The story

The clues

Oscar, Olive, Owen, Ophelia and Opal went on a school camping trip. They kept a careful record of their camping activities and compared notes when they returned home. The discovered they had received 145, 130, 125, 115 and 99 insect bites. They had eaten 77, 72, 70, 63 and 56 smores. They had also eaten 99, 90, 80, 71 and 60 hot dogs on their three-day camping trip.

Based on the clues, match the campers with their insect bites, and their smore and hot dog consumption.

1. Add the number of smores Owen ate to the number of hot dogs Ophelia ate to determine the number of Olive’s insect bites.

2. Ophelia received exactly 15 fewer bites than another camper, and Owen received exactly 15 more bites than another camper.

3. Oscar ate exactly 10 more hot dogs than the camper who received the fewest insect bites.

4. Owen did not eat the most hot dogs.

5. Ophelia and Opal’s combined smore-eating total was 30 smores larger than the combined smoreeating total of the two campers who ate the fewest smores.

6. The camper who ate the most hot dogs ate the fewest smores and, of course, Opal ate fewer smores than Ophelia.

Teac he r

Note: A ‘smore’ or ’s’more’ is a campfire treat made with a toasted marshmallow and chocolate between two sweet biscuits.

Oscar

Owen

Ophelia

Opal

© R. I .

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w ww

77 smores 72 smores 70 smores 63 smores 56 smores

99 hot dogs 90 hot dogs 80 hot dogs 71 hot dogs 60 hot dogs

48 | Maths perplexors

145 bites 130 bites 125 bites 115 bites 99 bites

145 bites 130 bites 125 bites 115 bites 99 bites

145 bites 130 bites 125 bites 115 bites 99 bites

77 smores 72 smores 70 smores 63 smores 56 smores

77 smores 72 smores 70 smores 63 smores 56 smores

77 smores 72 smores 70 smores 63 smores 56 smores

. te

145 bites 130 bites 125 bites 115 bites 99 bites

77 smores 72 smores 70 smores 63 smores 56 smores

m . u

145 bites 130 bites 125 bites 115 bites 99 bites

Olive

ew i ev Pr

r o e t s Bo r e p ok u S

o c . che e r o t r s super

99 hot dogs 90 hot dogs 80 hot dogs 71 hot dogs 60 hot dogs

99 hot dogs 90 hot dogs 80 hot dogs 71 hot dogs 60 hot dogs

99 hot dogs 90 hot dogs 80 hot dogs 71 hot dogs 60 hot dogs

R.I.C. Publications®

99 hot dogs 90 hot dogs 80 hot dogs 71 hot dogs 60 hot dogs

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49

Racing woes The clues

Dirk, Dana, Diane, Daisy and David were five race car drivers. In a recent race, their cars all broke down after completing a different number of laps. Before dropping out of the race, they had completed 185, 170, 160, 145 and 120 laps. None of the drivers was the same age; they were 43, 40, 37, 30 and 25 years old. Before breaking down, they all reached different high speeds with their cars; they went 212, 200, 190, 188 and 187 kilometres per hour. Based on the clues, match the drivers with the number of laps they completed, their ages and their highest speeds.

1. If you multiplied Dirk’s age by 4, the answer would be the number of laps Dana completed, and if you multiplied Daisy’s age by 4, the answer would be the number of laps Daisy completed.

2. The car that reached the fastest speed completed the fewest laps.

3. Daisy completed fewer laps than Diane but more than David.

4. If you multiplied Dana’s age by 8, the answer would be Dirk’s highest speed.

5. Diane was not the oldest driver and she, of course, did not complete the most laps.

6. Daisy’s highest speed was faster than Diane’s highest speed but not as fast as David’s highest speed.

r o e t s Bo r e p ok u S

ew i ev Pr

Teac he r

The story

Dirk

Dana

Diane

Daisy

185 laps 170 laps 160 laps 145 laps 120 laps

185 laps 170 laps 160 laps 145 laps 120 laps

185 laps 170 laps 160 laps 145 laps 120 laps

185 laps 170 laps 160 laps 145 laps 120 laps

185 laps 170 laps 160 laps 145 laps 120 laps

43 years old 40 years old 37 years old 30 years old 25 years old

43 years old 40 years old 37 years old 30 years old 25 years old

43 years old 40 years old 37 years old 30 years old 25 years old

43 years old 40 years old 37 years old 30 years old 25 years old

43 years old 40 years old 37 years old 30 years old 25 years old

212 kph 200 kph 190 kph 188 kph 187 kph

212 kph 200 kph 190 kph 188 kph 187 kph

212 kph 200 kph 190 kph 188 kph 187 kph

212 kph 200 kph 190 kph 188 kph 187 kph

212 kph 200 kph 190 kph 188 kph 187 kph

w ww

. te

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David

Maths perplexors

| 49

50

Fruit tree bounty The clues

Ray, Rita, Rosie, Rex and Robert each owned three fruit trees. They each owned one apple tree, one peach tree, and one pear tree. One year, they decided to keep track of how much fruit each of their trees produced and compare the results. Their apple trees produced 950, 925, 900, 890 and 880 apples. Strangely, their peach trees produced 950, 925, 900, 890 and 880 peaches.

Stranger still, their pear trees also produced 950, 925, 900, 890 and 880 pears. Nobody had a fruit tree that produced the same number of fruit as another tree in their group of three fruit trees. If someone had an apple tree that produced 950 apples then none of his or her other two trees produced 950 peaches or pears. Based on the clues, match the names with the number of apples, peaches and pears their trees produced.

1. If someone had a fruit tree that produced 950 pieces of fruit, then none of his/her remaining two trees produced that same number of 950 pieces of fruit, and so on.

2. Ray and Rita’s apple trees produced a combined total of 1770 apples.

3. Robert’s apple tree produced 10 more apples than Rita’s apple tree and, of course, Rex’s apple tree did not produce the most apples.

4. The person whose peach tree produced the most peaches owned a pear tree that produced the fewest pears.

5. Robert’s pear tree produced exactly 10 more pears than Rex’s pear tree.

6. Rita’s peach tree produced exactly 25 more peaches than another person’s peach tree, and Ray’s peach tree produced more peaches than Rosie’s peach tree.

7. Ray’s pear tree did not produce the most pears.

950 apples 925 apples 900 apples 890 apples 880 apples

© I .

C.P bl i cat i ons Robert Rita R. Rosieu Rex •f orr evi ew pur posesonl y•

w ww

950 peaches 925 peaches 900 peaches 890 peaches 880 peaches 950 pears 925 pears 900 pears 890 pears 880 pears

50 | Maths perplexors

950 apples 925 apples 900 apples 890 apples 880 apples

950 apples 925 apples 900 apples 890 apples 880 apples

950 apples 925 apples 900 apples 890 apples 880 apples

950 peaches 925 peaches 900 peaches 890 peaches 880 peaches

950 peaches 925 peaches 900 peaches 890 peaches 880 peaches

950 peaches 925 peaches 900 peaches 890 peaches 880 peaches

950 pears 925 pears 900 pears 890 pears 880 pears

950 pears 925 pears 900 pears 890 pears 880 pears

950 pears 925 pears 900 pears 890 pears 880 pears

. te

950 apples 925 apples 900 apples 890 apples 880 apples

m . u

Ray

r o e t s Bo r e p ok u S

ew i ev Pr

Teac he r

The story

o c . che e r o t r s super

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950 peaches 925 peaches 900 peaches 890 peaches 880 peaches 950 pears 925 pears 900 pears 890 pears 880 pears

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Answers 1. Cheeky chipmunks

10. Flower power

Binky

Alvin

Patrick

Helga

Harry

Henry

Hilda

50 m 90 seeds 180 owls

60 m 100 seeds 125 owls

35 m 120 seeds 150 owls

12 m roses 9 m violets 3 m daisies 6 m petunias

9 m roses 12 m violets 6 m daisies 3 m petunias

6 m roses 3 m violets 9 m daisies 12 m petunias

3 m roses 6 m violets 12 m daisies 9 m petunias

Tom

Teresa

Terry

6 legs 5 coleslaw 61 chips

3 legs 6 coleslaw 70 chips

5 legs 3 coleslaw 79 chips

Nancy

Naomi

Nellie

11 years 4 sons 3 daughters

13 years 2 sons 4 daughters

15 years 3 sons 2 daughters

Rosie

Ruth

Rita

30 m 10 eggs 21 worms

35 m 7 eggs 33 worms

40 m 13 eggs 27 worms

2. Chicken pieces

r o e t s Bo r e p 12. Race memories o u k S

4. Tress a crowd

5. Farmer’s market Victor

600 apples 400 tomatoes 200 beetroot 800 potatoes

6. Nuts to you

Peter

Paula

Penny

Scout

Peggy

Rex

Belle

350 races 150 wins 60 jockeys

200 races 125 wins 70 jockeys

380 races 100 wins 75 jockeys

390 races 90 wins 45 jockeys

400 races 80 wins 40 jockeys

13. Beans to you Kirk

Kendra

900 red 850 red 1200 green 1250 green 855 yellow 865 yellow

Kathy

Kenny

Kevin

800 red 1100 green 875 yellow

795 red 1000 green 840 yellow

745 red 900 green 820 yellow

14. Let’s all do the monkey hop

Vinnie

Vera

Vivian

400 apples 600 tomatoes 800 beetroot 200 potatoes

800 apples 200 tomatoes 600 beetroot 400 potatoes

200 apples 800 tomatoes 400 beetroot 600 potatoes

Bonzo

Binko

Gummo

Harpo

Marlo

1000 bounces

750 bounces

1300 bounces

1250 bounces

1100 bounces

925 jumps

950 jumps

915 jumps

920 jumps

900 jumps

700 hops

680 hops

650 hops

720 hops

730 hops

Shane

Sophie

950 lemons 793 oranges 665 apples

975 lemons 800 oranges 630 apples

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y• 15. Garden bounty Seth

Sheena

Stella

Sylvia

700 acorns 355 pecans 899 walnuts 700 almonds

600 acorns 375 pecans 900 walnuts 900 almonds

500 acorns 335 pecans 888 walnuts 200 almonds

1125 lemons 683 oranges 735 apples

1000 lemons 1150 lemons 807 oranges 790 oranges 600 apples 700 apples

George

Greg

Gail

3rd in line 16 potatoes 40 bananas 15 apples

1st in line 18 potatoes 44 bananas 13 apples

4th in line 22 potatoes 24 bananas 11 apples

7. Grocery pokers

. te

8. Don’t dry this at home

Tom

Toula

Terry

Tina

Tex

Brown 384 eggs 640 g 80 kg

Jones 420 eggs 608 g 90 kg

Smith 312 eggs 704 g 85 kg

Black 468 eggs 768 g 110 kg

Noble 444 eggs 800 g 100 kg

Gino

Reggie

Ruth

Gail

Greg

Stall C

Stall D

Stall B

Stall A

Stall E

o c .

17. Stand by me che e r o t r s super

Alvin

Alice

Albert

Ava

14 socks 22 shirts 15 pants 11 scarves

16 socks 24 shirts 17 pants 9 scarves

18 socks 31 shirts 13 pants 8 scarves

22 socks 29 shirts 14 pants 7 scarves

3300 hot dogs 3800 hot dogs 4300 hot dogs

5000 hot dogs 4800 hot dogs

4700 burgers

4300 burgers

3300 burgers

3700 burgers

4600 burgers

6200 drinks

6500 drinks

8000 drinks

7600 drinks

6600 drinks

18. School picnics

9. Money in the bank Carl

Connie

Cliff

Coral

225 quarters 1200 dimes 1750 nickels 8700 pennies

250 quarters 1100 dimes 1800 nickels 8300 pennies

200 quarters 1000 dimes 2000 nickels 8000 pennies

190 quarters 900 dimes 1600 nickels 9000 pennies

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16. Farmer’s markup

Simon

m . u

w ww

Sam

650 acorns 350 pecans 911 walnuts 350 almonds

2nd in line 12 potatoes 32 bananas 17 apples

Patty

Champ

Sara

Greta

Porky

375 cupcakes 350 cupcakes 450 cupcakes 400 cupcakes 425 cupcakes 70 slices 75 slices 65 slices 50 slices 60 slices 800 scoops 850 scoops 900 scoops 750 scoops 700 scoops

ew i ev Pr

Teac he r

3. Marriage counts

11. Pig eaters

R.I.C. Publications®

Taft

Knox

Twain

Wilson

Adams

1250 students

825 students

1650 students

1450 students

650 students

1300 hot dogs 2000 hot dogs

2300 hot dogs 2500 hot dogs 2900 hot dogs

4000 chips

2400 chips

2600 chips

2300 chips

4600 chips

Maths perplexors

| 51

Answers 19. Baker’s dozen

28. Family bike trip

Betty

Benny

Bonnie

Barry

Beth

Linda

372 pies

312 pies

384 pies

420 pies

408 pies

8 years old 14 years old 1st in line 3rd in line 5 scoops 4 scoops

600 doughnuts 672 doughnuts 720 doughnuts 528 doughnuts 696 doughnuts 960 cookies

852 cookies

948 cookies

900 cookies

20. That’s just ducky Duke

Daisy

21. Gone fishing

Daphne

Joie

17 perch 17 bass 10 catfish

20 perch 28 bass 12 catfish

Teac he r

Devon 83 favourite 930 m 240 seconds

Taft

Knox

5 Pilgrims 10 Pilgrims 10 Americans 15 Americans 20 turkeys 5 turkeys

Twain

Wlson

Adams

15 Pilgrims 20 Pilgrims 25 Pilgrims 5 Americans 25 Americans 20 Americans 25 turkeys 15 turkeys 10 turkeys

Jim

Joy

Muffy

Fluffy

Hinky

Dinky

Moe

25 perch 25 bass 8 catfish

24 perch 26 bass 13 catfish

150 cats 250 owls 20 wives

125 cats 300 owls 9 wives

100 cats 100 owls 10 wives

50 cats 200 owls 5 wives

75 cats 150 owls 15 wives

22. Running backs

31. Nuts to count

Diane

Daryl

Dana

Donny

Binky

45 uniform 860 yds 74 passes

48 uniform 900 yds 70 passes

35 uniform 930 yds 63 passes

37 uniform 960 yds 60 passes

250 walnuts 200 walnuts 150 walnuts 100 walnuts 50 walnuts 200 pecans 250 pecans 50 pecans 150 pecans 100 pecans 100 almonds 150 almonds 250 almonds 50 almonds 200 almonds

Sara

Sally

Walt

Wilma

Willy

215 pencils 40 pens 350 crayons

220 pencils 30 pens 325 crayons

12 cm 300 bugs 2nd place

14 cm 275 bugs 1st place

18 cm 175 bugs 3rd place

Anna

23. Are you a loser?

Sandy

Rover

Nutly

32. The hole thing

Sammy

Squints

Winnie

Warren

9 cm 225 bugs 4th place

6 cm 250 bugs 5th place

© R. I .

C.Publ i cat i ons Shape up kids •f orr evi ew p33.u r p osesonl y•

200 pencils 195 pencils 175 pencils 20 pens 25 pens 45 pens 430 crayons 440 crayons 400 crayons

24. Pig town pride

Fido

ew i ev Pr

Jill

6 perch 19 bass 9 catfish

Sharon

Lucy 19 years old 5th in line 1 scoop

r o e t s B r 30. That’s mice to know o e p ok u S

Jack

40 uniform 850 yds 77 passes

Louis 17 years old 4th in line 2 scoops

29. Thanksgiving plays

Donnie

60 favourite 40 favourite 48 favourite 72 favourite 600 m 690 m 780 m 900 m 420 seconds 600 seconds 540 seconds 300 seconds

Dean

Lulu 16 years old 2nd in line 3 scoops

Alpha

Beta

1010 kg 425 oinks 18 L

1000 kg 450 oinks 20 L

Crown

Dofuss

Enid

Alex

1020 kg 415 oinks 21 L

900 kg 500 oinks 15 L

850 kg 420 oinks 22 L

40 triangles 70 triangles 60 triangles 50 triangles 30 triangles 70 squares 40 squares 50 squares 30 square 60 squares 70 pentagons 60 pentagons 50 pentagons 40 pentagons 30 pentagons

w ww

25. When pigs fly

Alice

34. Winter holiday fun

Andy

Arlene

m . u

912 cookies

Larry

Alpha

Beta

Crown

Dofuss

Enid

Alpha

Beta

Crown

Dofuss

Enid

Snorts 2610 m 345 minutes 494 taps

Porkly 2400 m 330 minutes 470 taps

Spamy 2520 m 315 minutes 500 taps

Grunto 2700 m 285 minutes 467 taps

Trotter 3000 m 300 minutes 497 taps

1300 Santas

1000 Santas

900 Santas

1400 Santas

1500 Santas

725 Frostys

700 Frostys

750 Frostys

650 Frostys

450 Frostys

26. It’s a hit

. te

o c . che e r o t r s super 36. Bug zappers

Biff

Betty

Byron

Bev

Baxter

70 singles 50 doubles 15 triples

90 singles 35 doubles 25 triples

87 singles 45 doubles 20 triples

93 singles 40 doubles 27 triples

85 singles 58 doubles 18 triples

27. How low can you get?

Tommy

Connie

Bert

Paula

Tina

bass 112 worms 224 leeches 900 m

catfish 110 worms 200 leeches 925 m

trout 100 worms 168 leeches 950 m

tuna 56 worms 165 leech 995 cm

perch 55 worms 100 leeches 1000 m

52 | Maths perplexors

2600 Rudolphs 2200 Rudolphs 2000 Rudolphs 3000 Rudolphs 2800 Rudolphs

35. Camelot?

Gigi

Winnie

Stan

Burt

Ginger

3 humps 17 days 50 yodels

2 humps 14 days 45 yodels

5 humps 13 days 60 yodels

1 hump 7 days 75 yodels

4 humps 10 days 85 yodels

Carl

Claude

Cass

Cher

Cora

200 flies 400 gnats 800 wasps

90 flies 180 gnats 1080 wasps

50 flies 500 gnats 1000 wasps

250 flies 300 gnats 600 wasps

270 flies 540 gnats 700 wasps

R.I.C. Publications®

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Answers 37. Cactuses factuses?

Drake

46. Flying frogs?

Dean

Dina

Debby

Dian

Larry

Laura

Luke

Lorrie

Livia

75 years old 70 years old 50 years old 95 years old 85 years old 950 blossom 475 blossoms 850 blossoms 750 blossoms 500 blossoms 15 cm 30 cm 20 cm 28 cm 14 cm

275 flies 160 hops 515 croaks

260 flies 170 hops 500 croaks

300 flies 140 hops 485 croaks

375 flies 130 hops 450 croaks

350 flies 120 hops 400 croaks

38. All abeard!

47. Lumberjacks are OK!

Alpha

Beta

Crown

Dofuss

Enid

Mike

Trevor 15 years old 10 cm long 10 cm wide

Tom 45 years old 15 cm long 9 cm wide

Tim 50 years old 20 cm long 8 cm wide

Tony 40 years old 18 cm long 7 cm wide

Troy 30 years old 17 cm long 5 cm wide

62 pancakes 54 pancakes 88 pancakes 80 pancakes 97 trees 90 trees 60 trees 70 trees 115 flowers 130 flowers 140 flowers 145 flowers

Molly

r o e t s Bo r e 48. Smore the merrier o p u k S

39. An eggsact count

Oscar

Jonas

Josie

John

300 red 210 yellow 170 purple

250 red 220 yellow 160 purple

200 red 160 yellow 150 purple

160 red 200 yellow 100 purple

Jill

180 red 180 yellow 120 purple

40. Tripping out

49. Racing woes Dirk

Jones

Smith

Brown

Black

Barnes

1200 km 600 stops 18 000 yet?

1400 km 700 stops 21 000 yet?

1750 km 750 stops 22 000 yet?

3000 km 800 stops 17 000 yet?

1900 km 850 stops 15 000 yet?

Olive

125 bites 130 bites 63 smores 56 smores 90 hot dogs 99 hot dogs

Dana

Mona

Owen

Ophelia

Opal

145 bites 70 smores 71 hot dogs

115 bites 77 smores 60 hot dogs

99 bites 72 smores 80 hot dogs

Diane

185 laps 120 laps 170 laps 30 years old 25 years old 37 years old 200 kph 212 kph 187 kph

50. Fruit tree bounty

Daisy

David

160 laps 40 years old 188 kph

145 laps 43 years old 190 kph

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

41. Climb every mountain

Ray

Chad

Chet

Carol

Connie

Carl

62 mts 1300 km 50 stitches

70 mts 600 km 40 stitches

44 mts 1500 km 10 stitches

88 mts 700 km 60 stitches

31 mts 1100 km 70 stitches

Rita

880 apples 890 apples 900 peaches 925 peaches 925 pears 950 pears

Max 72 pancakes 83 trees 150 flowers

ew i ev Pr

Jenny

Teac he r

Mary

Rosie

Rex

Robert

950 apples 925 apples 900 apples 890 peaches 950 peaches 880 peaches 900 pears 880 pears 890 pears

Tina

Tara

Timmy

Taylor

3 shirts 5 singlets 1 pants

5 shirts 4 singlets 2 pants

1 shirt 2 singlets 3 pants

2 shirts 1 singlet 4 pants

4 shirts 3 singlets 5 pants

w ww

Tom

43. Pirate figures Jack

10 ships 3400 coins 80 m

Jessie

. te

Jenny

Jerome

Jodi

o c . che e r o t r s super

14 ships 3700 coins 60 m

27 ships 3100 coins 20 m

23 ships 2000 coins 90 m

Ken

Kyle

Karen

Kathy

Kirk

61st floor age 45 28 km

68th floor age 30 20 km

75th floor age 50 24 km

82nd floor age 25 8 km

41st floor age 55 16 km

44. High life

m . u

42. Great Caesar’s goats

19 ships 2600 coins 100 m

45. Bakery goods Betty

Ben

Beau

Bonnie

Boris

40 cakes 10 pies 50 muffins

50 cakes 20 pies 60 muffins

60 cakes 50 pies 40 muffins

20 cakes 60 pies 10 muffins

10 cakes 40 pies 20 muffins

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R.I.C. Publications®

Maths perplexors

| 53