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RIC-6067 2.85/1161


Maths perplexors (Ages 9–10) 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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ISBN 978-1-74126-807-2 RIC–6067

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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.

Nutty squirrels ................................. 1 Who gives a hoot? ........................... 2 Cow contest .................................... 3 Oinkers aweigh ............................... 4 Chicken fun ..................................... 5 Basketball numbers ......................... 6 Three dog fight ................................ 7 Cats up ............................................ 8 The spitting image ........................... 9 The cookie munchers .................... 10 Flight plans .................................... 11 Down towns .................................. 12 Tripping out ................................... 13 Teething ring .................................. 14 Go fish .......................................... 15 Swats up? ...................................... 16 Worm up time ............................... 17 Australian idle ............................... 18 Watching the birdies ...................... 19 And the runner is ........................... 20 Hey, hey, we’re the monkeys ......... 21 Town pride .................................... 22 Speed limits ................................... 23 Ski for your life .............................. 24 Spending dogs ............................... 25 Hockey hits ................................... 26 Halloween fun ............................... 27 To bee or not to bee ....................... 28 Classy teachers .............................. 29 Rooster tales .................................. 30 Farmer plots ................................... 31 A cold season ................................ 32 Gorilla my dreams ......................... 33 Bear facts ....................................... 34 Selling ladybug scouts ................... 35 Hardworking chickens ................... 36 Goose down .................................. 37 A round of golf .............................. 38 It’s a hit! ........................................ 39 Counting scouts ............................. 40 It’s raining cats ............................... 41 Pig numbers .................................. 42 Batty towns .................................... 43 For the birds .................................. 44 Farm alphabet ................................ 45 Hockey hits ................................... 46 Food fight ...................................... 47 You’re elected ................................ 48 Writer’s cramp ............................... 49 Town pride .................................... 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.

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1

Nutty squirrels The clues

Three squirrels named Sam, Sally and Sarah were different ages. They were 2, 3 and 5 years old. They all collected nuts and had 23, 27 and 50 nuts in their collections. Recently, they held a race to see who could climb a tree the fastest and, naturally, they finished in 1st, 2nd and 3rd place. Based on the clues, match the squirrels with the number of nuts in their collection and their order of finish in the climbing contest.

1. Sally was not the fastest climber, did not have the fewest nuts, and her age would be the result of subtracting Sarah’s age from the oldest squirrel’s age. 2. The oldest squirrel was not the fastest climber, and the youngest squirrel was the slowest climber. 3. Sarah did not have the fewest nuts, and if you added the number of nuts in her collection to another squirrel’s nuts, the answer would equal the total of nuts in another squirrel’s collection.

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Sam

Sally

2 years old 3 years old 5 years old

2 years old 3 years old 5 years old

23 nuts 27 nuts 50 nuts

23 nuts 27 nuts 50 nuts

1st place 2nd place 3rd place

1st place 2nd place 3rd place

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The story

Sarah

2 years old 3 years old 5 years old 23 nuts 27 nuts 50 nuts

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2

Who gives a hoot? The clues

Oscar, Ollie and Olivia were three owls who enjoyed competing with each other in various contests. One day, they competed to see who could make the most hoots in a minute. They hooted 80, 46 and 34 hoots in a minute. After regaining their breath, they decided to see how many mice each could catch in an hour. They caught 61, 34 and 27 mice in an hour. During these contests, the owls wore different coloured hats. Their hats were red, green and blue. Based on the clues, match the owls with their hoots, their mice victims and their hat colours.

1. The owl in the red hat caught fewer mice than the owl in the green hat but more than the owl in the blue hat. 2. Oscar made fewer hoots than the owl in the green hat but more than Olivia, who never wore green. 3. The owl in the red hat, who was not Oscar, did not hoot the most.

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Oscar

Ollie

80 hoots 46 hoots 34 hoots

80 hoots 46 hoots 34 hoots

61 mice 34 mice 27 mice

61 mice 34 mice 27 mice

80 hoots 46 hoots 34 hoots 61 mice 34 mice 27 mice

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Olivia

red hat green hat blue hat

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3

Cow contest The clues

Three cows named Carol, Clara and Carmen decided to have a contest to see which one of them could produce the most litres of milk in a week. By the end of the week, they had squeezed out 191, 196 and 391 litres of milk. The cows were owned by farmers named Brown, Jones and Smith. The farms were different sizes; they were 250, 750 and 1500 hectares. Based on the clues, match the cows with their weekly milk production, their farmers and their farm sizes.

1. Carmen produced 1 more litre of milk than the other two cows added together. 2. If you subtracted Farmer Brown’s hectares from Farmer Jones’s hectares, the answer would equal Farmer Brown’s hectares. 3. Clara did not produce the most litres of milk, but at least she produced 1 more litre than another cow. 4. Farmer Smith’s cow produced the most milk, and Clara did not belong to Farmer Jones.

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Carol

Clara

191 litres 196 litres 391 litres

191 litres 196 litres 391 litres

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Carmen

191 litres 196 litres 391 litres

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250 hectares 750 hectares 1500 hectares

250 hectares 750 hectares 1500 hectares

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Farmer Brown Farmer Jones Farmer Smith 250 hectares 750 hectares 1500 hectares

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4

Oinkers aweigh

The story

Paula

174 kg 177 kg 178 kg

174 kg 177 kg 178 kg

tango waltz foxtrot

tango waltz foxtrot

348 minutes 354 minutes 356 minutes

Penrod

174 kg 177 kg 178 kg

tango waltz foxtrot

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348 minutes 354 minutes 356 minutes

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1. If you doubled the number of the weight of the heaviest pig, the answer would be the number of minutes the lightest pig danced the tango. 2. Oddly, if you doubled the number of the weight of the lightest pig, the answer would be the number of minutes the heaviest pig danced the waltz. 3. Penrod weighed more than Paula but less than Peggy.

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Peggy

The clues

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Three pigs named Peggy, Paula and Penrod weighed 174, 177 and 178 kg. They all loved to dance, and their favourite dances were the tango, the waltz and the foxtrot. The pigs had a contest to see who could dance their favourite dance the longest without stopping to rest. They danced for 348 minutes, 354 minutes and 356 minutes. Based on the clues, match the pigs with their weights, their favourite dances and the minutes they danced without stopping.

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5

Chicken fun The clues

Three chickens named Berniece, Bella and Bonnie decided to bring more excitement into their lives by holding a series of contests. The first contest was to see which one of them could lay the most eggs in a day. They laid, 16, 9 and 7 eggs for that contest. Next, they held a clucking contest to see which one of them could make the most clucks in a minute. They clucked 78, 62 and 17 clucks for that contest. Finally, they held a grubeating contest, and ate 27, 26 and 25 grubs in a minute. Based on the clues, match the chickens with their egglaying totals, their clucks per minute and their grubeating totals.

1. Between the two of them, Berniece and Bella ate 51 grubs, but Berniece ate less than Bella. 2. The chicken that ate the fewest grubs was the best clucker. 3. Add Bella’s clucks to her egg production to get the number of the best clucker’s clucks. 4. Bonnie laid fewer eggs than Berniece.

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Berniece

Bella

16 eggs 9 eggs 7 eggs

16 eggs 9 eggs 7 eggs

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Bonnie

16 eggs 9 eggs 7 eggs

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27 grubs 26 grubs 25 grubs

27 grubs 26 grubs 25 grubs

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78 clucks 62 clucks 17 clucks 27 grubs 26 grubs 25 grubs

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6

Basketball numbers The clues

Charles, Cassie and Calvin were all players on the Pleasant Ridge basketball team. Their uniform numbers were 24, 18 and 12. At a recent game, they scored 22, 21 and 15 points. They all wore different coloured sweatbands; they were pink, purple and puce. Based on the clues, match the children with their uniform numbers, their points scored and the colour of their sweatbands.

1. Calvin did not wear the lowest uniform number, and if you added his point total to his uniform number, the answer would equal 33. 2. Charles’ point total added to his uniform number would also equal 33. 3. Charles did not like pink, and the player who scored the most points liked purple.

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Charles

Cassie

uniform 24 uniform 18 uniform 12

uniform 24 uniform 18 uniform 12

22 points 21 points 15 points

22 points 21 points 15 points

uniform 24 uniform 18 uniform 12 22 points 21 points 15 points

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Calvin

pink purple puce

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pink purple puce

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Three dog fight The clues

Rover, Fido and Pepper were a beagle, a poodle and a doberman who enjoyed competing with each other. First, they had a contest to see who could make the most barks in a minute. They barked 247, 198 and 137 barks. Next, they had an ear-scratching contest, and they scratched 123, 103 and 77 scratches in a minute. Finally, they took a census of their flea populations and discovered they had 110, 63 and 47 fleas. Based on the clues, match the dogs with their breeds, their number of barks, their number of scratches and their number of fleas.

1. Subtract Rover’s barking total from the beagle’s barking total to determine the flea population of the doberman. 2. Fido was not a poodle and did not bark the most. 3. The dog with the most fleas did not scratch the most, and Pepper had more fleas than Rover. 4. The beagle scratched the least.

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Rover

Fido

Pepper

beagle poodle doberman

beagle poodle doberman

247 barks 198 barks 137 barks

247 barks 198 barks 137 barks

123 scratches 103 scratches 77 scratches

123 scratches 103 scratches 77 scratches

123 scratches 103 scratches 77 scratches

110 fleas 63 fleas 47 fleas

110 fleas 63 fleas 47 fleas

110 fleas 63 fleas 47 fleas

beagle poodle doberman 247 barks 198 barks 137 barks

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8

Cats up The clues

Tabby, Crabby and Flabby were three cats of different colours. They were blue, yellow and white. One recent day, they coughed up 24, 15 and 12 hairballs. On another day, they held a contest to see who could scare the most songbirds. They scared 251, 200 and 190 songbirds. At one time, all the cats had fallen from high places without injury. They fell 121, 109 and 62 metres. Based on the clues, match the cats with their colours, their number of hairballs, the number of songbirds they scared and the distances they fell.

1. Tabby and Crabby coughed up a total of 27 hairballs, but Tabby coughed up more hairballs than Crabby. 2. Crabby and Flabby fell a total of 183 metres, but Flabby did not fall as far as Crabby. 3. The yellow and white cats scared a total of 390 songbirds but neither of them coughed up the most hairballs. 4. The cat that fell the farthest was not yellow, and Crabby scared fewer songbirds than Tabby.

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Tabby

Crabby

blue yellow white

blue yellow white

24 hairballs 15 hairballs 12 hairballs

24 hairballs 15 hairballs 12 hairballs

blue yellow white

24 hairballs 15 hairballs 12 hairballs

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121 metres 109 metres 62 metres

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Flabby

251 songbirds 200 songbirds 190 songbirds

251 songbirds 200 songbirds 190 songbirds

121 metres 109 metres 62 metres

121 metres 109 metres 62 metres

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251 songbirds 200 songbirds 190 songbirds

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The spitting image The clues

George, Gregory and Gail were three friends whose last names were Figgle, Boggler and Wiggy. They once held a watermelon seed-spitting contest and spat their seeds 10.5, 6 and 4 metres. The children enjoyed collecting bottle caps and had collected 500, 230 and 210 bottle caps. One day, they held a hopping contest to see who could hop the most times without stopping. They hopped 620, 510 and 310 times. Based on the clues, match the friends with their last names, their seedspitting distances, their number of bottle caps and their number of hops.

1. Boggler hopped twice as many times as Figgle. 2. Subtract the number of metres George spat a seed from the number of bottle caps he owned to find the number of bottle caps Gregory owned. 3. Boggler spat a seed the farthest, Figgle was the worst spitter, but Figgle owned the most bottle caps.

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George

Gregory

Gail

Figgle Boggler Wiggy

Figgle Boggler Wiggy

10.5 metres 6 metres 4 metres

10.5 metres 6 metres 4 metres

500 caps 230 caps 210 caps

500 caps 230 caps 210 caps

500 caps 230 caps 210 caps

620 hops 510 hops 310 hops

620 hops 510 hops 310 hops

620 hops 510 hops 310 hops

Figgle Boggler Wiggy

10.5 metres 6 metres 4 metres

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10

The cookie munchers The clues

Beth, Bill and Barb all had different favourite colours. Their favourite colours were red, yellow and blue. One day, they held a cookie-eating contest, and they managed to eat 113, 79 and 34 biscuits in an hour. Of course, all the biscuits were healthy, low-fat and sugarfree. On another day, they held a disk-throwing contest and threw their disks 232.5, 118 and 116 metres. Finally, they held a blueberry-picking contest and picked 998, 760 and 750 blueberries in an hour. Based on the clues, match the names with their favourite colours, the number of biscuits eaten, their diskthrowing distances and the number of blueberries they picked in an hour.

1. If you subtracted Beth’s cookie-eating total from another child’s cookie-eating total, the answer would be the lowest cookie-eating total. 2. Barb did not eat the most biscuits but she did have the highest number in one of the remaining two contests. 3. The child who ate the most biscuits did not like red or blue, and the child who ate the fewest biscuits did not like red. 4. If you doubled Beth’s disk-throwing total, the answer would be Barb’s disk-throwing total. 5. Bill was not the best blueberry picker, but then he was not the worst blueberry picker either.

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Beth

Bill

red yellow blue

red yellow blue

Barb

red yellow blue

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232.5 metres 118 metres 116 metres

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998 blueberries 760 blueberries 750 blueberries

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113 biscuits 79 biscuits 34 biscuits

113 biscuits 79 biscuits 34 biscuits

232.5 metres 118 metres 116 metres

232.5 metres 118 metres 116 metres

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113 biscuits 79 biscuits 34 biscuits

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998 blueberries 760 blueberries 750 blueberries

998 blueberries 760 blueberries 750 blueberries

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Flight plans The clues

John, Jethro, Joan and Jill were a cow, a pig, a horse and a goat who decided to have a flying contest. They all climbed to the top of a silo and leaped off while flapping whatever they could in an effort to fly. They flew 6, 4, 3 and 2 metres before making crash landings. They all required minor medical treatment after their flights, which cost $500, $400, $250 and $200. Based on the clues, match the names with their animals, the distances they flew and their medical costs.

1. John flew twice as far as Joan, and Jethro flew twice as far as Jill, but Joan was not the worst flyer. 2. The medical expenses for the cow and the pig totalled $900 and, of course, John and Jethro were not either of those two animals. 3. The worst flyer was not the cow, and the best flyer was not the horse. 4. Joan’s medical expense was not the highest but it was still twice as costly as John’s medical expense.

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John

Jethro

Joan

cow pig horse goat

cow pig horse goat

cow pig horse goat

6 metres 4 metres 3 metres 2 metres

6 metres 4 metres 3 metres 2 metres

6 metres 4 metres 3 metres 2 metres

$500 $400 $250 $200

$500 $400 $250 $200

$500 $400 $250 $200

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Jill

cow pig horse goat

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$500 $400 $250 $200

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6 metres 4 metres 3 metres 2 metres

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12

Down towns The clues

One day, for no apparent reason, the towns of Glenview, Northbrook, Northfield and Deerfield decided to have a hole-digging contest to see which town could dig the deepest hole in a day. The towns, appealing to the civic pride of their citizens, urged them to help digging their town hole. At the end of the day, they had dug holes 23, 15.5, 14.5 and 7 metres deep. Not satisfied with the results of that contest, the towns decided to match their biggest eaters in a muffineating contest. Their biggest eaters were Sam, Sara, Saul and Sally who ate 178, 157, 92 and 89 muffins. Based on the clues, match the towns with the depth of their holes, their biggest eaters and the number of muffins consumed.

1. Subtract Glenview’s hole depth from Deerfield’s hole depth to discover Northfield’s hole depth. 2. Neither Sara nor Saul came from towns that dug either the deepest or the shallowest holes. 3. Sara ate twice as many muffins as Sally, but Saul did eat more muffins than Sam. 4. Sally did not live in Northfield, and Saul did not live in Northbrook. 5. Glenview’s new town motto became, ‘At least we are not the worst at digging holes’.

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Glenview

Northbrook

Northfield

23 metres 15.5 metres 14.5 metres 7 metres

23 metres 15.5 metres 14.5 metres 7 metres

23 metres 15.5 metres 14.5 metres 7 metres

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Sam Sara Saul Sally

Sam Sara Saul Sally

Sam Sara Saul Sally

178 muffins 157 muffins 92 muffins 89 muffins

178 muffins 157 muffins 92 muffins 89 muffins

178 muffins 157 muffins 92 muffins 89 muffins

23 metres 15.5 metres 14.5 metres 7 metres

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178 muffins 157 muffins 92 muffins 89 muffins

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Sam Sara Saul Sally

Deerfield

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Tripping out The clues

Ned, Nancy, Norman and Nellie took trips to Finland, Norway, France and Italy. They visited these countries for 28, 24, 14 and 7 days. At the airport, they were delayed 31, 27, 23 and 4 hours. Based on the clues, match the names with the countries they visited, the length of their visits and the hours they were delayed.

1. Subtract the number of hours Nellie was delayed from the number of hours Ned was delayed to find the number of hours Norman was delayed. 2. Neither Ned nor Nelly were delayed the least. 3. Norman did not take the longest trip, but his trip was twice as long as Ned’s trip. 4. Nancy’s trip to Italy lasted twice as long as the trip to Finland. 5. The longest delay happened on the trip to Norway.

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Ned

Nancy

Norman

Finland Norway France Italy

Finland Norway France Italy

Finland Norway France Italy

28 days 24 days 14 days 7 days

28 days 24 days 14 days 7 days

28 days 24 days 14 days 7 day

31 hours 27 hours 23 hours 4 hours

31 hours 27 hours 23 hours 4 hours

31 hours 27 hours 23 hours 4 hours

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Nellie

Finland Norway France Italy

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31 hours 27 hours 23 hours 4 hours

m . u

w ww

. te

28 days 24 days 14 days 7 days

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Maths perplexors

| 13


14

Teething ring The clues

Pete, Penny, Patty and Paul were four friendly dentists. Their last names were Pullem, Yanker, Bridge and Crown. One day they had a contest to see who could pull the most teeth in a day. That day, they pulled 102, 94, 51 and 47 teeth. After work, the dentists all relaxed by working on their stamp collections. They had 188, 171, 141 and 140 stamps in their collections. Based on the clues, match the dentists with their last names, the number of teeth they pulled and the number of stamps in their stamp collections.

1.

2.

Paul, whose last name was not Bridge or Crown, pulled twice as many teeth as Penny but not as many as Pete. Oddly, if you added the number of teeth Paul pulled to the number of teeth Penny pulled, the answer would be the number of stamps in Patty’s stamp collection. Penny’s last name was not Bridge or Crown, and Patty’s last name was not Bridge. If you subtracted the number for Patty’s stamp collection from the number of stamps in Yanker’s collection, the answer would be the number of teeth pulled by Yanker. Pullem collected more stamps than Pete.

r o e t s Bo r e p ok u S 3. 4.

5.

Pete

Penny

Patty

Pullem Yanker Bridge Crown

Pullem Yanker Bridge Crown

Pullem Yanker Bridge Crown

102 teeth 94 teeth 51 teeth 47 teeth

102 teeth 94 teeth 51 teeth 47 teeth

188 stamps 171 stamps 141 stamps 140 stamps

188 stamps 171 stamps 141 stamps 140 stamps

Paul

Pullem Yanker Bridge Crown

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

w ww

188 stamps 171 stamps 141 stamps 140 stamps

14 | Maths perplexors

. te

102 teeth 94 teeth 51 teeth 47 teeth

m . u

102 teeth 94 teeth 51 teeth 47 teeth

ew i ev Pr

Teac he r

The story

188 stamps 171 stamps 141 stamps 140 stamps

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15

Go fish The clues

Fred, Frank, Farrah and Felicity, whose last names were Hooker, Caster, Fisher and Bass, went on a fishing trip. They decided to have two fishing contests. The first contest was to see who caught the most fish in a day. They caught 43, 34, 17 and 7 fish that day. The second contest was to see who caught the heaviest fish that day; their fish weighed 10, 7, 6.5 and 4 kg. Based on the clues, match the first names with their last names, the total number of fish they caught and their heaviest fish.

1. Fred and Frank were not named Hooker or Bass and they caught a total of 24 fish together. 2. Fisher’s biggest fish weighed twice as much as the biggest fish caught by Bass. 3. Frank caught 10 more fish than Caster. 4. Farrah caught fewer fish than Bass. 5. The person who caught the fewest fish made up for it by catching the heaviest fish.

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

Fred

Frank

Farrah

Hooker Caster Fisher Bass

Hooker Caster Fisher Bass

Hooker Caster Fisher Bass

ew i ev Pr

Teac he r

The story

Felicity

Hooker Caster Fisher Bass

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• 43 fish 34 fish 17 fish 7 fish

10 kg 7 kg 6.5 kg 4 kg

10 kg 7 kg 6.5 kg 4 kg

10 kg 7 kg 6.5 kg 4 kg

. te

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43 fish 34 fish 17 fish 7 fish 10 kg 7 kg 6.5 kg 4 kg

m . u

43 fish 34 fish 17 fish 7 fish

w ww

43 fish 34 fish 17 fish 7 fish

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Maths perplexors

| 15


16

Swats up? The clues

Four mosquitoes named Bert, Becky, Byron and Buzz each had favourite body parts to bite. They like to bite ankles, necks, ears and noses. At a summer camp, they managed to bite 72, 70, 53 and 36 campers. Sadly, all of the mosquitoes met their final swats, but before they did, they were swatted at without effect 820, 717, 697 and 410 times. Based on the clues, match the mosquitoes with their favourite body parts to bite, the number of campers bitten and the number of times they were swatted at without injury.

1. Becky and Byron did not like to bite ears or noses, Byron was swatted at 20 times less than Bert, and Buzz was swatted at half as many times as another mosquito. 2. The mosquito that was swatted at the most only bit half as many campers as the ankle-biting mosquito. 3. Bert was more successful than the nose-biting mosquito at biting campers.

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

Bert

Becky

Byron

ankles necks ears noses

ankles necks ears noses

ankles necks ears noses

72 campers 70 campers 53 campers 36 campers

72 campers 70 campers 53 campers 36 campers

820 swats 717 swats 697 swats 410 swats

820 swats 717 swats 697 swats 410 swats

Buzz

ankles necks ears noses

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

w ww

820 swats 717 swats 697 swats 410 swats

. te

16 | Maths perplexors

72 campers 70 campers 53 campers 36 campers 820 swats 717 swats 697 swats 410 swats

m . u

72 campers 70 campers 53 campers 36 campers

ew i ev Pr

Teac he r

The story

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17

Worm up time The clues

Willy, Wilma, Wendy and Walter were four worms living together in the Glenview Apple Orchard. They thought their lives were getting boring, so they decided to have a contest to see who could bore into the most apples in a day. They bored into 142, 140, 72 and 70 apples. Not satisfied with that contest, they decided to see who could hold their breath the longest; they lasted for 28, 20, 15 and 10 minutes. Finally, they decided to relax by going for a swim in nearby Glenview Lake where they unfortunately had their tails bitten off by a catfish, a bass, a perch and a shark. Based on the clues, match the worms with their apple-boring totals, the length of time they held their breath and the fish that bit off their tails.

1. The catfish bit the tail off the worm who held its breath twice as long as Willy held his breath. 2. Wilma and Walter were not bitten by a catfish or a bass and, of course, Wilma did not hold her breath the longest. 3. The bass bit the tail off the worm that bored into the most apples. 4. Walter was not attacked by a perch, and Walter only bored into half as many apples as Wilma.

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

ew i ev Pr

Teac he r

The story

Willy

Wilma

Wendy

Walter

142 apples 140 apples 72 apples 70 apples

142 apples 140 apples 72 apples 70 apples

142 apples 140 apples 72 apples 70 apples

28 minutes 20 minutes 15 minutes 10 minutes

28 minutes 20 minutes 15 minutes 10 minutes

28 minutes 20 minutes 15 minutes 10 minutes

28 minutes 20 minutes 15 minutes 10 minutes

catfish bass perch shark

catfish bass perch shark

catfish bass perch shark

catfish bass perch shark

142 apples 140 apples 72 apples 70 apples

w ww

. te

www.ricpublications.com.au

m . u

© 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

Australian idle The clues

Linda, Larry, Lenny and Lucy all auditioned to be a part of the popular television contest, ‘Australia You Can Sing!’ They all chose to sing, ‘Oops, I Did It Again’. Unfortunately, they all made some mistakes; they made 330, 318, 168 and 159 mistakes. Even though they made so many mistakes, the judges were surprisingly impressed with their efforts. The judges said their songs were ‘powerful’, ‘inspiring’, ‘soulful’ and ‘passionate’. After the audition, the contestants were so relieved it was over that they all cried for different amounts of time; they cried for 180, 160, 90 and 75 minutes. Based on the clues, match the names with the number of mistakes they made, the judges’ words for them and the minutes they spent crying.

1. The judges did not call Larry and Lenny ‘soulful’ or ‘passionate’, even though they made the fewest mistakes. 2. The ‘passionate’ singer cried 15 minutes longer than the ‘soulful’ singer. 3. Linda made more mistakes than Lucy. 4. Larry only made half as many mistakes as Lucy but cried twice as long as Lucy did. 5. The ‘powerful’ singer made more mistakes than the ‘inspiring’ singer.

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

ew i ev Pr

Teac he r

The story

Linda

Larry

Lenny

330 mistakes 318 mistakes 168 mistakes 159 mistakes

330 mistakes 318 mistakes 168 mistakes 159 mistakes

330 mistakes 318 mistakes 168 mistakes 159 mistakes

‘powerful’ ‘inspiring’ ‘soulful’ ‘passionate’

‘powerful’ ‘inspiring’ ‘soulful’ ‘passionate’

‘powerful’ ‘inspiring’ ‘soulful’ ‘passionate’

180 minutes 160 minutes 90 minutes 75 minutes

180 minutes 160 minutes 90 minutes 75 minutes

180 minutes 160 minutes 90 minutes 75 minutes

330 mistakes 318 mistakes 168 mistakes 159 mistakes

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

w ww

180 minutes 160 minutes 90 minutes 75 minutes

18 | Maths perplexors

. te

m . u

‘powerful’ ‘inspiring’ ‘soulful’ ‘passionate’

Lucy

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19

Watching the birdies The clues

Four birds named Carl, Calvin, Cassie and Candi were a crow, a canary, a robin and a dove. For no real reason, the four of them decided to compete against each other in two contests. They decided to wear vests with their favourite numbers on them during the contests. The favourite numbers on their vests were 37, 33, 30 and 27. Their first contest was to see who could stuff the most seeds into their beaks; they stuffed 89, 85, 72 and 63 seeds in their beaks. The second contest was to see who could hang upside-down on a tree branch for the longest time. They hung upside-down for 61, 59, 43 and 31 minutes. Based on the clues, match the birds with their types, their vest numbers, their seed totals and the amount of time they hung upside-down.

1. Subtract Carl’s vest number from Calvin’s seed total to discover the number of minutes Candi spent hanging upside-down. 2. The robin and the dove held a total of 135 seeds in their beaks, while Carl and Calvin held a total of 174 seeds in their beaks. 3. Calvin’s vest number was smaller than Carl’s vest number, Candi was not a robin, and the robin had the highest vest number. 4. The crow and the canary hung upside-down for a combined total of 74 minutes. 5. Calvin was not a canary and the canary did not hang upside-down for the shortest time. 6. The dove held the fewest seeds in its beak.

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

Carl

Calvin

Cassie

crow canary robin dove

crow canary robin dove

crow canary robin dove

vest 37 vest 33 vest 30 vest 27

vest 37 vest 33 vest 30 vest 27

vest 37 vest 33 vest 30 vest 27

89 seeds 85 seeds 72 seeds 63 seeds

89 seeds 85 seeds 72 seeds 63 seeds

61 minutes 59 minutes 43 minutes 31 minutes

61 minutes 59 minutes 43 minutes 31 minutes

ew i ev Pr

Teac he r

The story

Candi

crow canary robin dove

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

61 minutes 59 minutes 43 minutes 31 minutes

. te

www.ricpublications.com.au

m . u

w ww 89 seeds 85 seeds 72 seeds 63 seeds

o c . che e r o t r s super

R.I.C. Publications®

vest 37 vest 33 vest 30 vest 27

89 seeds 85 seeds 72 seeds 63 seeds

61 minutes 59 minutes 43 minutes 31 minutes

Maths perplexors

| 19


20

And the runner is The clues

David, Darla, Deidre and Dirk were marathon runners from France, Spain, Scotland and Sweden. At a recent race, they wore the numbers 1, 2, 3 and 4 on their shirts. Oddly, in that race they finished in 1st, 2nd, 3rd and 4th place, but none of the runners’ shirt numbers matched the number in their order of finish. During the race, they drank 25, 50, 60 and 75 cups of water. Based on the clues, match the runners with their countries, their shirt numbers, their order of finish and the cups of water they drank.

1. No shirt numbers matched the place numbers for any of the runners. 2. If you added the numbers on the shirts of the runners from Spain and Scotland, the answer would be 3, and if you added their place numbers, the answer would also be 3. 3. Deidre and Dirk were not from Spain or Scotland. 4. Darla was not from Scotland, and if you subtracted the number of cups of water she drank from the number of cups of water the runner from Sweden drank, the answer would be the number of cups of water the winner of the race drank. 5. The 1st place runner drank the fewest cups of water. 6. Deidre did not wear the shirt with number 3 on it, and she was not from Sweden. 7. Dirk drank more cups of water than Deidre.

Darla

Deidre

France Spain Scotland Sweden

France Spain Scotland Sweden

shirt 1 shirt 2 shirt 3 shirt 4

shirt 1 shirt 2 shirt 3 shirt 4

shirt 1 shirt 2 shirt 3 shirt 4

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

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

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

25 cups 50 cups 60 cups 75 cups

25 cups 50 cups 60 cups 75 cups

France Spain Scotland Sweden

Dirk

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

w ww

25 cups 50 cups 60 cups 75 cups

20 | Maths perplexors

. te

France Spain Scotland Sweden shirt 1 shirt 2 shirt 3 shirt 4

m . u

David

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

ew i ev Pr

Teac he r

The story

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

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25 cups 50 cups 60 cups 75 cups

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21

Hey, hey, we’re the monkeys The clues

Four monkeys named Eliot, Elsie, Edward and Elvira wore shirts that were red, green, blue and yellow. They also wore pants that were red, green, blue and yellow. However, none of the monkeys wore shirts and pants of the same colour. On a recent day, they counted the number of bananas they had consumed that day. They had eaten 93, 60, 57 and 33 bananas. After counting bananas they went bananas and began screeching. They screeched 126, 90, 66 and 24 times. Based on the clues, match the monkeys with their shirt colours, their pant colours, the number of bananas eaten and the number of times they screeched.

1. No monkey wore the same colour for both shirt and pants. 2. Subtract the number of bananas eaten by the monkey in the yellow shirt from the bananaeating number of the monkey in the green shirt to determine the banana-eating number of the monkey in the blue shirt. 3. Eliot and Elsie did not wear red or yellow shirts, and between the two of them they ate a total of 153 bananas. 4. Edward did not eat the fewest bananas, and Elsie did not eat the most bananas. 5. Eliot and Edward did not wear yellow pants, Elvira did not wear red pants and, of course, Edward did not wear blue pants. 6. The monkey in the yellow shirt screeched more than the monkey in the red shirt and between the two of them they screeched a total of 216 times. 7. The monkey in the yellow pants did not screech the fewest times.

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

ew i ev Pr

Teac he r

The story

© R. I . C.Publ i cat i ons Eliot Elsie Edward Elvira •f orr evi ew pur posesonl y•

w ww

red pants green pants blue pants yellow pants 93 bananas 60 bananas 57 bananas 33 bananas

. te

126 screeches 90 screeches 66 screeches 24 screeches

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red shirt green shirt blue shirt yellow shirt

red shirt green shirt blue shirt yellow shirt

red pants green pants blue pants yellow pants

red pants green pants blue pants yellow pants

93 bananas 60 bananas 57 bananas 33 bananas

93 bananas 60 bananas 57 bananas 33 bananas

93 bananas 60 bananas 57 bananas 33 bananas

126 screeches 90 screeches 66 screeches 24 screeches

126 screeches 90 screeches 66 screeches 24 screeches

126 screeches 90 screeches 66 screeches 24 screeches

o c . che e r o t r s super

R.I.C. Publications®

red shirt green shirt blue shirt yellow shirt

m . u

red shirt green shirt blue shirt yellow shirt

red pants green pants blue pants yellow pants

Maths perplexors

| 21


22

Town pride The clues

The towns of Glenview, Northbrook, Northfield and Deerfield were led by mayors whose first names were Kevin, Kathy, Ken and Kizzy. Their last names were Daley, Jones, Smith and Quimby. Every year the four towns watched their mayors engage in friendly competitions with each other. This year, the mayors engaged in a pie-eating contest and they ate 106, 53, 40 and 20 pies. Another contest was held to determine who could slide the farthest from a running start in mud. They slid 66, 33, 19 and 15.5 metres. Based on the clues, match the towns with the mayor’s first and last names, the number of pies they ate and the distances they slid in mud.

1. Quimby ate half as many pies as the mayor of Northbrook, and Daley ate half as many pies as the mayor of Northfield. 2. The mayor of Glenview ate more pies than the mayor of Deerfield, and the mayor of Northbrook ate more pies than the mayor of Northfield. 3. Kizzy ate the fewest pies, Kevin ate the most pies, and Quimby ate fewer pies than Jones but more than Smith and Daley. 4. Deerfield’s mayor was not Smith, and Ken was not the mayor of Northfield. 5. Kathy slid half as far as Kizzy, and Quimby slid fewer metres than Jones.

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

Gleview

Northbrook

Northfield

Kevin Kathy Ken Kizzy

Kevin Kathy Ken Kizzy

Kevin Kathy Ken Kizzy

ew i ev Pr

Teac he r

The story

Daley Jones Smith Quimby

Daley Jones Smith Quimby

Daley Jones Smith Quimby

106 pies 53 pies 40 pies 20 pies

106 pies 53 pies 40 pies 20 pies

106 pies 53 pies 40 pies 20 pies

Kevin Kathy Ken Kizzy

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

w ww

106 pies 53 pies 40 pies 20 pies

66 metres 33 metres 19 metres 15.5 metres

22 | Maths perplexors

. te

m . u

Daley Jones Smith Quimby

Deerfield

o c . che e r o t r s super 66 metres 33 metres 19 metres 15.5 metres

66 metres 33 metres 19 metres 15.5 metres

R.I.C. Publications®

66metres 33 metres 19 metres 15.5 metres

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23

Speed limits The clues

Four turtles named Toby, Tom, Terry and Tyrone decided to race around their pond. They timed themselves and discovered that they raced around the pond in 300, 250, 150 and 125 minutes. They all reached amazing top speeds of 19, 16, 13 and 11 kilometres per hour before falling off the pace. To identify themselves to the spectators as they went whizzing past the grandstand, they painted numbers on their shells in four different colours. The numbers they chose were 22, 20, 19 and 15. The colours they chose were red, purple, orange and green. Based on the clues, match the turtles with their racing times in minutes, their top speeds in kilometres per hour, their shell numbers and the colour of their numbers.

1. If you added together the top two km/h numbers, the answer would be the purple number of the turtle that spent the most minutes racing around the pond. 2. Toby and Tom did not have red or purple numbers on their shells. 3. Tyrone did not take the most time racing around the pond. 4. Tom’s shell number was higher than Toby’s shell number, but Toby’s shell number was higher than Tyrone’s shell number. 5. Toby and Tyrone’s km/h numbers added together would equal 22. 6. Tom’s number was not green, and Tom’s km/h number was not the lowest. 7. Toby and Tom each took less than 250 minutes to race around the pond, but Toby did race around the pond in half the time it took Tyrone to race around the pond. 8. Toby’s top speed in km/h was less than Tyrone’s top speed in km/h.

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

ew i ev Pr

Teac he r

The story

© R. I . C.Publ i cat i ons Toby Tom Terry •f orr evi e w pur pos esonl y•Tyrone

w ww 19 km/h 16 km/h 13 km/h 11 km/h shell 22 shell 20 shell 19 shell 15

. te

red purple orange green

www.ricpublications.com.au

300 minutes 250 minutes 150 minutes 125 minutes

300 minutes 250 minutes 150 minutes 125 minutes

19 km/h 16 km/h 13 km/h 11 km/h

19 km/h 16 km/h 13 km/h 11 km/h

shell 22 shell 20 shell 19 shell 15

shell 22 shell 20 shell 19 shell 15

shell 22 shell 20 shell 19 shell 15

red purple orange green

red purple orange green

red purple orange green

o c . che e r o t r s super

R.I.C. Publications®

300 minutes 250 minutes 150 minutes 125 minutes

m . u

300 minutes 250 minutes 150 minutes 125 minutes

19 km/h 16 km/h 13 km/h 11 km/h

Maths perplexors

| 23


24

Ski for your life The clues

Henny, Penny, Molly and Polly were four turkeys who went on a skiing trip together. They all tried to go down the most dangerous slope on the mountain called ‘Twister’. They reached top speeds of 161, 145, 80.5 and 72 kilometres per hour before crashing and breaking a bone. They broke a tailbone, a wing bone, a wishbone, and a drumstick. They all recovered from their injuries but in different lengths of time. They healed in 57, 33, 24 and 15 days. While recovering, they all decided on a new sport to try instead of skiing. The new sports were softball, sailing, football and tennis. Based on the clues, match the turkeys with their top speeds, their broken bones, their recovery times and their new sports.

1. Henny’s top speed was twice as fast as Polly’s top speed, and Molly’s top speed was twice as fast as Penny’s top speed. 2. Oddly, if you subtracted Polly’s days of recovery from Molly’s days of recovery, the answer would be 9, but if you subtracted Molly’s days of recovery from Penny’s days of recovery, you would get the same answer. 3. The turkeys that reached the two highest top speeds broke a tailbone and a drumstick and decided to take up softball and football. 4. The turkey with the slowest top speed recovered in the shortest time and did not like boats. 5. The turkey with the highest top speed did not try football and did not break a drumstick. 6. The turkey that broke a wing bone recovered exactly 9 days faster than the tailbone breaker.

161 km/h 145 km/h 80.5 km/h 72 km/h

Penny

Molly

161 km/h 145 km/h 80.5 km/h 72 km/h

161 km/h 145 km/h 80.5 km/h 72 km/h

tailbone wing bone wishbone drumstick

tailbone wing bone wishbone drumstick

57 days 33 days 24 days 15 days

57 days 33 days 24 days 15 days

softball sailing football tennis

softball sailing football tennis

Polly

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

w ww

tailbone wing bone wishbone drumstick 57 days 33 days 24 days 15 days

softball sailing football tennis

24 | Maths perplexors

. te

161 km/h 145 km/h 80.5 km/h 72 km/h

tailbone wing bone wishbone drumstick

m . u

Henny

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

ew i ev Pr

Teac he r

The story

57 days 33 days 24 days 15 days

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R.I.C. Publications®

softball sailing football tennis

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25

Spending dogs The clues

Rover, Queenie, Duke and Gizmo were four dogs who lived in Glenview, Northbrook, Northfield and Deerfield. One day, they decided to fly to Broome for a holiday. Despite travelling on the same aeroplane, they all paid different amounts for their tickets. They paid $600, $550, $300 and $275. Later, they agreed that the best thing about the trip was the food. They all managed to eat their favourite foods, which were lobster, chicken, fish and steak. Of course, they all spent money on the trip and were out $1100, $850, $575 and $300. Based on the clues, match the dogs with their hometowns, their airfare costs, their favourite foods and the amount of money they spent.

1. Duke’s airfare was half as much as Rover’s airfare, and Queenie’s airfare was twice as much as Gizmo’s airfare. 2. The dogs from Glenview and Northbrook paid the two lowest airfares. 3. Gizmo paid less for airfare than Duke. 4. Add the dog from Northfield’s airfare to the dog from Northbrook’s airfare to find the amount of money the dog from Northfield spent. 5. Add the airfare of the steak-loving dog from Northbrook to the airfare of the lobster-loving dog from Glenview to reveal the amount of money spent by the dog from Deerfield who disliked meatloaf. 6. Duke spent more than Gizmo.

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

Rover

Queenie

Duke

Glenview Northbrook Northfield Deerfield

Glenview Northbrook Northfield Deerfield

Glenview Northbrook Northfield Deerfield

$600 airfare $550 airfare $300 airfare $275 airfare

$600 airfare $550 airfare $300 airfare $275 airfare

$600 airfare $550 airfare $300 airfare $275 airfare

lobster chicken fish steak

lobster chicken fish steak

$1100 spent $850 spent $575 spent $300 spent

$1100 spent $850 spent $575 spent $300 spent

ew i ev Pr

Teac he r

The story

Gizmo

Glenview Northbrook Northfield Deerfield

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

$1100 spent $850 spent $575 spent $300 spent

. te

www.ricpublications.com.au

m . u

w ww lobster chicken fish steak

$600 airfare $550 airfare $300 airfare $275 airfare

o c . che e r o t r s super

R.I.C. Publications®

lobster chicken fish steak

$1100 spent $850 spent $575 spent $300 spent

Maths perplexors

| 25


26

Hockey hits The clues

Jake, Jenny, Jerri and Jason were hockey players who had been playing hockey for 12, 11, 7 and 6 years. They counted the number of times they had been hit in the face with a hockey ball. They had been hit, 1500, 1200, 750 and 500 times. They all were missing teeth because of these hits; they had lost 12, 11, 7 and 6 teeth. The players all had nicknames; they were nicknamed ‘Toothy’, ‘Whizzer’, ‘Blinky’ and ‘Speedy’. Based on the clues, match the hockey players with the number of years they played, their number of hits in the face, their number of missing teeth and their nicknames.

1. At no time does the number of years they had played hockey match the number of missing teeth for any of the players. 2. Jake played 5 fewer years than Jerri, Jenny played 4 fewer years than Jerri, but Jerri played fewer years than Jason. 3. ‘Toothy’ lost the fewest teeth, Jenny and Jerri were not nicknamed ‘Toothy’ but they did not lose the most teeth either. 4. ‘Speedy’ lost 1 more tooth than ‘Blinky’. 5. Between the two of them, ‘Speedy’ and ‘Whizzer’ took an astounding 2700 hits in the face with a hockey ball. 6. Jenny took half as many hits to the face as ‘Whizzer’.

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

Jake

Jenny

Jerri

12 years 11 years 7 years 6 years

12 years 11 years 7 years 6 years

12 years 11 years 7 years 6 years

1500 hits 1200 hits 750 hits 500 hits

1500 hits 1200 hits 750 hits 500 hits

1500 hits 1200 hits 750 hits 500 hits

12 teeth 11 teeth 7 teeth 6 teeth

12 teeth 11 teeth 7 teeth 6 teeth

‘Toothy’ ‘Whizzer’ ‘Blinky’ ‘Speedy’

‘Toothy’ ‘Whizzer’ ‘Blinky’ ‘Speedy’

m . u

ew i ev Pr

Teac he r

The story

1500 hits 1200 hits 750 hits 500 hits

Jason

12 years 11 years 7 years 6 years

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

w ww

12 teeth 11 teeth 7 teeth 6 teeth

‘Toothy’ ‘Whizzer’ ‘Blinky’ ‘Speedy’

26 | Maths perplexors

. te

12 teeth 11 teeth 7 teeth 6 teeth

o c . che e r o t r s super

R.I.C. Publications®

‘Toothy’ ‘Whizzer’ ‘Blinky’ ‘Speedy’

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27

Halloween fun The clues

Nancy, Nick, Nathan and Naomi went trick or treating one recent Halloween. They were dressed as a witch, a clown, a goblin and a pirate. They went to 200, 175, 147 and 110 houses in their quest for treats. They collected 6, 5, 3 and 2.5 kg of treats, and after eating them all in one night they were sick for 14, 12, 7 and 6 hours. Two of them had matching numbers for kilograms of loot and amounts of time they were sick. Based on the clues, match the names with their costumes, the number of houses they visited, the kilograms of loot they collected and the number of hours they were sick.

1. Oddly, the numbers for kilograms of sweets and the numbers for hours being sick exactly matched for two of the children. 2. Nancy and Nick did not dress as a witch or a clown and they visited 375 houses between the two of them. 3. Nathan ate half as much confectionery as Nick, and Naomi ate half as much confectionery as Nancy. 4. Nathan was sick half as long as Nancy, and Naomi was sick half as long as Nick. 5. Naomi ate less confectionery than Nathan but was sick longer than Nathan. 6. The clown ate more confectionery than the witch, but the witch visited more houses than the clown. 7. Nick was not a goblin because it was the goblin who visited the most houses.

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

Nancy

Nick

Nathan

witch clown goblin pirate

witch clown goblin pirate

witch clown goblin pirate

200 houses 175 houses 147 houses 110 houses

200 houses 175 houses 147 houses 110 houses

200 houses 175 houses 147 houses 110 houses

6 kg 5 kg 3 kg 2.5 kg

6 kg 5 kg 3 kg 2.5 kg

6 kg 5 kg 3 kg 2.5 kg

14 hours 12 hours 7 hours 6 hours

14 hours 12 hours 7 hours 6 hours

ew i ev Pr

Teac he r

The story

Naomi

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

14 hours 12 hours 7 hours 6 hours

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200 houses 175 houses 147 houses 110 houses

m . u

w ww

. te

witch clown goblin pirate

6 kg 5 kg 3 kg 2.5 kg

14 hours 12 hours 7 hours 6 hours

Maths perplexors

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28

To bee or not to bee The clues

Bella, Baxter, Betsy and Byron were bees from different hives. The hives belonged to farmers Brown, White, Green and Black. The hives produced 17, 15, 8.5 and 7.5 kg of honey last season. One day, the bees grew tired of flying low and decided to have a contest to see who could fly the highest. They flew up 248, 232.5, 217 and 116 metres. The bees all had favourite flowers they enjoyed pollinating the most and these were roses, daisies, tulips and peonies. Based on the clues, match the bees with their farmers, the kilograms of honey they produced, the highest distances they flew and their favourite flowers.

1. Bella and Baxter did not enjoy pollinating roses and daisies and their hives did not belong to Farmer Brown or Farmer White. 2. Betsy and Byron flew up a total of 449.5 metres. 3. Farmer Black’s hive produced only half as much honey as Farmer White’s hive. 4. Farmer Green’s hive produced twice as much honey as Farmer Brown’s hive. 5. Byron did not live in Farmer Brown’s hive. 6. Baxter’s hive did not produce the most honey but it did not produce the least honey either. 7. Bella did not belong to Farmer Black’s hive and she flew up 15.5 metres higher than Byron. 8. Baxter disliked peonies, and the rose-loving bee flew up higher than the daisy-loving bee.

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

Bella

Betsy

Byron

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• Farmer Brown Farmer White Farmer Green Farmer Black

17 kg 15 kg 8.5 kg 7.5 kg

17 kg 15 kg 8.5 kg 7.5 kg

17 kg 15 kg 8.5 kg 7.5 kg

248 metres 232.5 metres 217 metres 116 metres

248 metres 232.5 metres 217 metres 116 metres

248 metres 232.5 metres 217 metres 116 metres

roses daisies tulips peonies

roses daisies tulips peonies

w ww

Farmer Brown Farmer White Farmer Green Farmer Black

roses daisies tulips peonies

28 | Maths perplexors

. te

Farmer Brown Farmer White Farmer Green Farmer Black 17 kg 15 kg 8.5 kg 7.5 kg

m . u

Farmer Brown Farmer White Farmer Green Farmer Black

Baxter

ew i ev Pr

Teac he r

The story

248 metres 232.5 metres 217 metres 116 metres

o c . che e r o t r s super

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roses daisies tulips peonies

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29

Classy teachers The clues

Ruth, Reggie, Roger and Retta taught 1st, 2nd, 3rd and 4th grades at the Pleasant Hill School. They had 12, 13, 14 and 15 girls in their classrooms and 12, 13, 14 and 15 boys in their classrooms. Coincidentally, they lived 19, 21, 22.5 and 24 kilometres from school. Of course, no classrooms had the same number of girls and boys in any classroom and none of the numbers for the teachers’ distances from school matched the number of girls or boys in their classrooms. Based on the clues, match the teachers with the grades they taught, the number of girls in their classrooms, the number of boys in their classrooms and the distances each teacher travelled to get to school.

1. None of the numbers for girls, boys and kilometres match for any of the teachers. 2. Retta taught one grade higher than Roger, Roger taught one grade higher than Reggie, and Ruth did not teach 4th grade. 3. Ruth and Reggie had a total of 29 girls and 29 boys in their classrooms. 4. Retta travelled farther than Roger, and Ruth did not travel as far as Reggie. 5. Retta had more boys than girls in her classroom, and Reggie did not have 14 boys in his classroom.

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

ew i ev Pr

Teac he r

The story

Ruth

Reggie

Roger

Retta

1st grade 2nd grade 3rd grade 4th grade

1st grade 2nd grade 3rd grade 4th grade

1st grade 2nd grade 3rd grade 4th grade

12 girls 13 girls 14 girls 15 girls

12 girls 13 girls 14 girls 15 girls

12 girls 13 girls 14 girls 15 girls

12 girls 13 girls 14 girls 15 girls

12 boys 13 boys 14 boys 15 boys

12 boys 13 boys 14 boys 15 boys

12 boys 13 boys 14 boys 15 boys

12 boys 13 boys 14 boys 15 boys

1st grade 2nd grade 3rd grade 4th grade

w ww 19 km 21 km 22.5 km 24 km

. te

www.ricpublications.com.au

m . u

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

o c . che e r o t r s super 19 km 21 km 22.5 km 24 km

R.I.C. Publications®

19 km 21 km 22.5 km 24 km

19 km 21 km 22.5 km 24 km

Maths perplexors

| 29


30

Rooster tales The clues

Rex, Ron, Ray and Rupert were four roosters who noticed they were getting to that age when you start to lose your feathers. They were 10, 9, 7 and 5 years old. They decided to count the number of feathers they lost in a day and discovered they lost 100, 70, 60 and 50 feathers. To take their minds off going bald, they decided to hold two contests. The first contest was to see who could cock-a-doodle-doo the longest without taking a breath. They cock-a-doodled for 55, 40, 30 and 15 seconds. The second contest was to see who could spit a corn kernel the farthest. Their corn-kernel spitting distances were 7, 6, 5 and 4 metres. Based on the clues, match the roosters with their ages, the number of feathers they lost, their cock-a-doodling times and their corn-spitting distances.

1. Ron was not the youngest rooster but he was 2 years younger than Ray, but then Rupert was also younger than Ray. 2. The youngest rooster lost twice as many feathers as the worst corn-kernel spitter. 3. Rex lost more feathers than Ron, but then again, Ron did not lose the fewest feathers. 4. Subtract Ray’s cock-a-doodling time from Rupert’s cock-a-doodling time to determine Rupert’s cornkernel spitting distance. 5. The rooster that lost the fewest feathers cock-adoodled longer than Ron. 6. The oldest rooster cock-a-doodled for the shortest time. 7. Rex spit a corn kernel farther than Ron, but Ron was not the worst corn-kernel spitter.

10 years old 9 years old 7 years old 5 years old

Ron

Ray

Rupert

10 years old 9 years old 7 years old 5 years old

10 years old 9 years old 7 years old 5 years old

10 years old 9 years old 7 years old 5 years old

100 feathers 70 feathers 60 feathers 50 feathers

100 feathers 70 feathers 60 feathers 50 feathers

100 feathers 70 feathers 60 feathers 50 feathers

55 seconds 40 seconds 30 seconds 15 seconds

55 seconds 40 seconds 30 seconds 15 seconds

7m 6m 5m 4m

7m 6m 5m 4m

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

w ww

100 feathers 70 feathers 60 feathers 50 feathers 55 seconds 40 seconds 30 seconds 15 seconds 7m 6m 5m 4m

30 | Maths perplexors

. te

m . u

Rex

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

ew i ev Pr

Teac he r

The story

55 seconds 40 seconds 30 seconds 15 seconds

o c . che e r o t r s super

R.I.C. Publications®

7m 6m 5m 4m

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31

Farmer plots The clues

John, Jolene, Joann and Jeff were four farmers who all owned farms of exactly 10 hectares. The farms were all divided in exactly the same way. Each farm consisted of one 1-hectare plot, one 2-hectare plot, one 3-hectare plot and one 4-hectare plot. One year, the farmers all planted exactly the same crops of corn, peas, beans and tomatoes. However, no farmer planted the same crop on the same sized hectare plot as any other farmer. Based on the clues, match the farmers with the size of the plots they devoted to each crop.

1. No farmer planted the same crop on the same sized plot as any other farmer. 2. John and Jolene planted a combined total of 7 hectares of corn and 7 hectares of peas. 3. Jeff planted more corn and beans than Joann, and John planted more corn and tomatoes than Jolene.

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

ew i ev Pr

Teac he r

The story

John

Jolene

Joann

Jeff

1 hectare corn 2 hectares corn 3 hectares corn 4 hectares corn

1 hectare corn 2 hectares corn 3 hectares corn 4 hectares corn

1 hectare corn 2 hectares corn 3 hectares corn 4 hectares corn

1 hectare peas 2 hectares peas 3 hectares peas 4 hectares peas

1 hectare peas 2 hectares peas 3 hectares peas 4 hectares peas

1 hectare peas 2 hectares peas 3 hectares peas 4 hectares peas

1 hectare beans 2 hectares beans 3 hectares beans 4 hectares beans

1 hectare beans 2 hectares beans 3 hectares beans 4 hectares beans

1 hectare beans 2 hectares beans 3 hectares beans 4 hectares beans

1 hectare tomatoes 2 hectares tomatoes 3 hectares tomatoes 4 hectares tomatoes

1 hectare tomatoes 2 hectares tomatoes 3 hectares tomatoes 4 hectares tomatoes

1 hectare tomatoes 2 hectares tomatoes 3 hectares tomatoes 4 hectares tomatoes

1 hectare corn 2 hectares corn 3 hectares corn 4 hectares corn

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

www.ricpublications.com.au

1 hectare beans 2 hectare beans 3 hectares beans 4 hectares beans

m . u

w ww

. te

1 hectare peas 2 hectares peas 3 hectares peas 4 hectares peas

1 hectare tomatoes 2 hectares tomatoes 3 hectares tomatoes 4 hectares tomatoes

o c . che e r o t r s super

R.I.C. Publications®

Maths perplexors

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32

A cold season The clues

Mark, Mary, Millie and Mac were four teachers at the Pleasant Valley School, and they taught 2nd, 3rd, 4th and 5th grades. It seemed as if everyone was catching a cold, and one day there were 14, 12, 11 and 7 students absent from class. The remaining students were busy coughing and sneezing on each other. The teachers decided to count the number of coughs and sneezes their classes made in an hour. Their classes coughed 210, 170, 105 and 65 times and sneezed 210, 170, 105 and 65 times, but no class coughed and sneezed the same number of times. Based on the clues, match the teachers with their grades, the number of absent students, the number of coughs and the number of sneezes.

1. No teacher recorded the same number of coughs as sneezes for any of their classrooms. 2. Mark and Mary did not teach at either the highest or lowest grade levels and they had a combined total of 26 students absent. 3. If you subtracted the number of coughs Millie recorded from the number of coughs Mary recorded, the answer would be the number of coughs Mac recorded. 4. Mac did not teach the highest grade, the 2nd grade had the fewest students absent, Mary taught a lower grade than Mark, and Mark did not have the most students absent. 5. Neither the 2nd grade nor the 5th grade made the most sneezes. 6. The 4th graders sneezed 40 fewer times than the 3rd graders. 7. The 5th graders coughed more than the 2nd graders.

2nd grade 3rd grade 4th grade 5th grade

Mary Millie ©R . I . C.Publ i c at i ons Mac •f orr evi ew pur posesonl y•

w ww

14 absent 12 absent 11 absent 7 absent

210 coughs 170 coughs 105 coughs 65 coughs

210 sneezes 170 sneezes 105 sneezes 65 sneezes

32 | Maths perplexors

. te

2nd grade 3rd grade 4th grade 5th grade

2nd grade 3rd grade 4th grade 5th grade

2nd grade 3rd grade 4th grade 5th grade

14 absent 12 absent 11 absent 7 absent

14 absent 12 absent 11 absent 7 absent

14 absent 12 absent 11 absent 7 absent

m . u

Mark

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 210 coughs 170 coughs 105 coughs 65 coughs

210 cough 170 coughs 105 coughs 65 coughs

210 sneezes 170 sneezes 105 sneezes 65 sneezes

210 sneezes 170 sneezes 105 sneezes 65 sneezes

R.I.C. Publications®

210 coughs 170 coughs 105 coughs 65 coughs

210 sneezes 170 sneezes 105 sneezes 65 sneezes

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33

Gorilla my dreams The clues

Brent, Betty, Bonita and Bert were four gorillas living together in the jungle. Things were getting boring in the rainforest, so they decided to hold a series of contests. The first was a coconut-eating contest; they ate 27, 20, 18 and 9 coconuts. The second was to see who could peel the most bananas in an hour; they peeled 350, 330, 300 and 277 bananas. The third contest was to see who could swing on a vine the farthest; they swung 211, 186, 185.5 and 67 metres. Their final contest was to see who had the most nits; they discovered 830, 700, 600 and 463 nits living in their hair. Based on the clues, match the gorillas with the number of coconuts eaten, the number of bananas they peeled, the metres they flew on a vine and the number of nits in their hair.

1. Each of the gorillas won one of the four contests. 2. Bonita and Bert ate a total of 47 coconuts and peeled a total of 680 bananas. 3. Brent had more nits than Betty, but Betty ate more coconuts than Brent and she swung farther on a vine than Brent did too. 4. Bonita managed to peel 50 more bananas than Betty, and Bert, who claimed he used a faulty vine, swung 143.5 metres less than the best vine swinger. 5. The worst vine swinger had the fewest nits, and Bonita had fewer nits than Betty. 6. Bonita swung fewer metres than Brent.

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

Brent

Betty

Bonita

27 coconuts 20 coconuts 18 coconuts 9 coconuts

27 coconuts 20 coconuts 18 coconuts 9 coconuts

27 coconuts 20 coconuts 18 coconuts 9 coconuts

350 bananas 330 bananas 300 bananas 277 bananas

350 bananas 330 bananas 300 bananas 277 bananas

350 bananas 330 bananas 300 bananas 277 bananas

211 metres 186 metres 185.5 metres 67 metres

211 metres 186 metres 185.5 metres 67 metres

211 metres 186 metres 185.5 metres 67 metres

830 nits 700 nits 600 nits 463 nits

830 nits 700 nits 600 nits 463 nits

ew i ev Pr

Teac he r

The story

Bert

27 coconuts 20 coconuts 18 coconuts 9 coconuts

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

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m . u

w ww 830 nits 700 nits 600 nits 463 nits

350 bananas 330 bananas 300 bananas 277 bananas

o c . che e r o t r s super

R.I.C. PublicationsÂŽ

211 metres 186 metres 185.5 metres 67 metres 830 nits 700 nits 600 nits 463 nits

Maths perplexors

| 33


34

Bear facts The clues

Four bears named Paul, Pamela, Peter and Peggy were living together in the Glenview National Forest in Alaska. As bears sometimes do, they began bragging about their deeds. When it came to eating picnic baskets, they had eaten 94, 87, 80 and 73 picnic baskets in their careers. They bragged about catching and eating salmon; they had eaten 47, 40, 39 and 37 salmon in their careers. They also bragged about finding wild bee’s honey and had eaten 15, 12, 9 and 8 kilograms of honey in their careers. All the numbers were verified by careful records kept by forest rangers at the park. Since they all had such illustrious careers, the bears decided to form a food-foraging team. They each wanted to name the team something different. They liked the names ‘Teddies’, ‘Raiders’, ‘Salmonettes’ and ‘Honeybears’. Based on the clues, match the bears with the number of picnic baskets eaten, the number of salmon caught and eaten, the kilograms of honey eaten and the name they wanted to call their team.

1. Peter was the only bear who was not the best at anything, and he did not want to call the team ‘Teddies’ or ‘Raiders’. 2. Paul and Pamela ate a total of 181 picnic baskets, but Pamela’s salmon-eating total was exactly half of Paul’s picnic basket total. 3. Peggy ate 7 fewer picnic baskets than Pamela, and Peter ate more salmon than Peggy but less than Paul. 4. Pamela ate more kilograms of honey than Peter, but Pamela ate less honey than Paul. 5. The bear that ate the most honey wanted to call the team ‘Salmonettes’, and the bear that ate the most salmon wanted to call the team ‘Raiders’.

94 baskets 87 baskets 80 baskets 73 baskets

Pamela Peter ©R . I . C.Publ i c at i ons Peggy •f orr evi ew pur posesonl y•

w ww

47 salmon 40 salmon 39 salmon 37 salmon

15 kg honey 12 kg honey 9 kg honey 8 kg honey

‘Teddies’ ‘Raiders’ ‘Salmonettes’ ‘Honeybears’

34 | Maths perplexors

. te

94 baskets 87 baskets 80 baskets 73 baskets

94 baskets 87 baskets 80 baskets 73 baskets

94 baskets 87 baskets 80 baskets 73 baskets

47 salmon 40 salmon 39 salmon 37 salmon

47 salmon 40 salmon 39 salmon 37 salmon

47 salmon 40 salmon 39 salmon 37 salmon

15 kg honey 12 kg honey 9 kg honey 8 kg honey

15 kg honey 12 kg honey 9 kg honey 8 kg honey

‘Teddies’ ‘Raiders’ ‘Salmonettes’ ‘Honeybears’

‘Teddies’ ‘Raiders’ ‘Salmonettes’ ‘Honeybears’

m . u

Paul

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

ew i ev Pr

Teac he r

The story

15 kg honey 12 kg honey 9 kg honey 8 kg honey

o c . che e r o t r s super

R.I.C. Publications®

‘Teddies’ ‘Raiders’ ‘Salmonettes’ ‘Honeybears’

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35

Selling ladybug scouts The clues

Four Ladybug Scouts named June, Joan, Jean and Josie, whose last names were Smith, Jones, Carter and Bolton, went out one day to sell biscuits. They sold 193, 180, 175 and 160 boxes of biscuits. To sell this many boxes, the Ladybug Scouts went to many houses and rang many doorbells. They rang 99, 94, 90 and 80 doorbells. At the same time they were selling biscuits, the Ladybug Scouts were also selling raffle tickets for charity. They sold 100, 90, 87 and 80 raffle tickets. Based on the clues, match the first names with the last names, the boxes of biscuits sold, the doorbells rung and the raffle tickets sold.

1. June sold more boxes of biscuits than Smith and Bolton, but fewer than Jones. 2. Joan was not Smith or Bolton, and Josie sold fewer boxes of biscuits than Bolton. 3. The number of doorbells Joan rang was half of June’s biscuit box number. 4. Josie did not ring the most doorbells, but she rang more doorbells than June. 5. June sold 10 fewer raffle tickets than Josie, but Joan sold 10 fewer raffle tickets than June.

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

June

Joan

Jean

Smith Jones Carter Bolton

Smith Jones Carter Bolton

Smith Jones Carter Bolton

193 boxes 180 boxes 175 boxes 160 boxes

193 boxes 180 boxes 175 boxes 160 boxes

193 boxes 180 boxes 175 boxes 160 boxes

99 doorbells 94 doorbells 90 doorbells 80 doorbells

99 doorbells 94 doorbells 90 doorbells 80 doorbells

99 doorbells 94 doorbells 90 doorbells 80 doorbells

100 tickets 90 tickets 87 tickets 80 tickets

100 tickets 90 tickets 87 tickets 80 tickets

ew i ev Pr

Teac he r

The story

Josie

Smith Jones Carter Bolton

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

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www.ricpublications.com.au

o c . che e r o t r s super

R.I.C. Publications®

99 doorbells 94 doorbells 90 doorbells 80 doorbells

m . u

w ww

100 tickets 90 tickets 87 tickets 80 tickets

193 boxes 180 boxes 175 boxes 160 boxes

100 tickets 90 tickets 87 tickets 80 tickets

Maths perplexors

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36

Hardworking chickens The clues

Four chickens named Sally, Sarah, Shari and Sheila all worked for Farmer Brown. Farmer Brown’s chickens all worked 20 hours a day. Farmer Brown created a work schedule for his chickens that detailed exactly what tasks the chickens would be doing for every hour of their work day, and for exactly how long they would be working at each task they were assigned. Farmer Brown had two strict rules. The first rule was that the chickens would be working in 2, 4, 6 or 8 hour shifts at each task. The second rule was that no chicken would work the same number of hours at any task that any other chicken was working at. The tasks were pecking, flapping, clucking and egg-laying. Based on the clues, try and figure out Farmer Brown’s work schedule for each chicken.

1. Be sure you understand, if one chicken worked a 2-hour shift at a job, no other chicken would work a 2-hour shift at that same job, and that chicken that worked a 2-hour shift would not work another 2-hour shift that same day. This rule is true for all the shifts and all the tasks. 2. Sally and Sarah spent a combined total of 6 hours pecking and a combined total of 6 hours flapping. 3. Sheila worked a longer egg-laying shift than Shari, and she also worked a longer flapping shift than Shari as well. 4. Sally worked a longer egg-laying shift than Sarah, and she also flapped longer than Sarah.

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

Sally

Sarah

Shari

2 hours pecking 4 hours pecking 6 hours pecking 8 hours pecking

2 hours pecking 4 hours pecking 6 hours pecking 8 hours pecking

2 hours pecking 4 hours pecking 6 hours pecking 8 hours pecking

2 hours flapping 4 hours flapping 6 hours flapping 8 hours flapping

2 hours flapping 4 hours flapping 6 hours flapping 8 hours flapping

2 hours flapping 4 hours flapping 6 hours flapping 8 hours flapping

2 hours clucking 4 hours clucking 6 hours clucking 8 hours clucking

2 hours clucking 4 hours clucking 6 hours clucking 8 hours clucking

2 hours egg-laying 4 hours egg-laying 6 hours egg-laying 8 hours egg-laying

2 hours egg-laying 4 hours egg-laying 6 hours egg-laying 8 hours egg-laying

ew i ev Pr

Teac he r

The story

Sheila

2 hours pecking 4 hours pecking 6 hours pecking 8 hours pecking

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

2 hours egg-laying 4 hours egg-laying 6 hours egg-laying 8 hours egg-laying

36 | Maths perplexors

. te

m . u

w ww

2 hours clucking 4 hours clucking 6 hours clucking 8 hours clucking

2 hours flapping 4 hours flapping 6 hours flapping 8 hours flapping

2 hours clucking 4 hours clucking 6 hours clucking 8 hours clucking

o c . che e r o t r s super

R.I.C. Publications®

2 hours egg-laying 4 hours egg-laying 6 hours egg-laying 8 hours egg-laying

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37

Goose down The clues

Four geese named Greta, Gail, Gertie and Greg belonged to four different flocks. They were the North, South, East and West flocks. The flocks were of four different sizes and had 790, 625, 500 and 290 members. The four geese were chosen to represent their flocks in the annual goose-honking contest to see which goose could honk the most honks in a minute. They honked 99, 74, 60 and 57 times in a minute. All of the geese strained their honkers and had to take pills to help heal their honker strains. They took 24, 18, 16 and 10 pills. Based on the clues, match the geese with their flocks, the populations of their flocks, their number of honks in a minute and their pill consumption.

1. Greg belonged to a flock that had 290 fewer members than Gail’s flock, and Gertie’s flock had more members than the West flock had. 2. Greg and Gertie were not members of the South flock, and the East flock had the most members. 3. Greg took 8 fewer pills than Greta, and Gail took 8 fewer pills than Gertie. 4. The goose from the East flock did not take the fewest pills. 5. Greta honked more than Gail, but Gail honked more than both Gertie and Greg. 6. The slowest honker took the fewest pills.

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

ew i ev Pr

Teac he r

The story

Greta

Gail

Gertie

Greg

North flock South flock East flock West flock

North flock South flock East flock West flock

North flock South flock East flock West flock

790 members 625 members 500 members 290 members

790 members 625 members 500 members 290 members

790 members 625 members 500 members 290 members

790 members 625 members 500 members 290 members

99 honks 74 honks 60 honks 57 honks

99 honks 74 honks 60 honks 57 honks

99 honks 74 honks 60 honks 57 honks

99 honks 74 honks 60 honks 57 honks

North flock South flock East flock West flock

w ww 24 pills 18 pills 16 pills 10 pills

. te

www.ricpublications.com.au

m . u

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

o c . che e r o t r s super 24 pills 18 pills 16 pills 10 pills

R.I.C. Publications®

24 pills 18 pills 16 pills 10 pills

24 pills 18 pills 16 pills 10 pills

Maths perplexors

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38

A round of golf The clues

Albert, Alice, Andy and Anna went out together and played a round of golf. They were not very good at the game. They played nine holes and took 286, 225, 170 and 160 strokes to finish the game. Many of their shots went so wild that they lost golf balls. They lost 73, 60, 50 and 23 golf balls during the game. The foursome was pretty hard on their golf clubs as well, and during this game they broke 10, 8, 7 and 5 golf clubs. The lone bright spot during the day was the fact that they all hit one fairly long drive. These drives were 93, 84, 74 and 62 metres. Based on the clues, match the golfers with their strokes, their lost golf balls, their number of broken clubs and their longest drives.

1. Andy hit the ball 9.3 metres less than Alice, and Alice hit the ball 31 metres farther than Albert. 2. If you multiplied the number of golf clubs Anna broke by the number of golf clubs Andy broke, the answer would be the number of golf balls Alice lost. 3. Anna lost more golf balls than Andy, but Andy did not lose the fewest golf balls. 4. If you subtracted the number of strokes Anna took from the number of strokes Andy took, the answer would be the number of clubs Anna broke. 5. The golfer who took the most strokes did not lose the fewest golf balls. 6. Albert broke fewer golf clubs than Alice.

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

Albert

Alice

Andy

286 strokes 225 strokes 170 strokes 160 strokes

286 strokes 225 strokes 170 strokes 160 strokes

286 strokes 225 strokes 170 strokes 160 strokes

73 golf balls 60 golf balls 50 golf balls 23 golf balls

73 golf balls 60 golf balls 50 golf balls 23 golf balls

10 clubs 8 clubs 7 clubs 5 clubs

10 clubs 8 clubs 7 clubs 5 clubs

93 metres 84 metres 74 metres 62 metres

93 metres 84 metres 74 metres 62 metres

Anna

286 strokes 225 strokes 170 strokes 160 strokes

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

w ww

10 clubs 8 clubs 7 clubs 5 clubs

93 metres 84 metres 74 metres 62 metres

38 | Maths perplexors

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73 golf balls 60 golf balls 50 golf balls 23 golf balls

m . u

73 golf balls 60 golf balls 50 golf balls 23 golf balls

ew i ev Pr

Teac he r

The story

10 clubs 8 clubs 7 clubs 5 clubs

o c . che e r o t r s super

R.I.C. Publications®

93 metres 84 metres 74 metres 62 metres

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39

It’s a hit! The clues

Hal, Harriet, Homer and Hilda were the four best players on the Pleasant Ridge baseball team. At the end of the season it was discovered that each one of them had made exactly 126 hits. They hit 47, 31, 25 and 23 singles. They hit 47, 31, 25 and 23 doubles. They hit 47, 31, 25 and 23 triples. They hit 47, 31, 25 and 23 home runs. However, no player hit the same number of singles, doubles, triples and home runs as any other player, and no player made the same number of hits for more than one category. In other words, if a player hit 47 singles that player did not hit 47 doubles, triples or home runs. Based on the clues, match the players with the number of hits they made in each of the four categories.

1. Harriet and Homer hit a combined total of 48 singles and 78 home runs. 2. Hal and Hilda hit a combined total of 48 triples. 3. Hal hit more singles than Hilda, and Homer hit more doubles than Harriet. 4. Homer hit more home runs than triples, and Hal hit more home runs than Hilda.

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

ew i ev Pr

Teac he r

The story

Hal

Harriet

Homer

Hilda

47 singles 31 singles 25 singles 23 singles

47 single 31 singles 25 singles 23 singles

47 singles 31 singles 25 singles 23 singles

47 doubles 31 doubles 25 doubles 23 doubles

47 doubles 31 doubles 25 doubles 23 doubles

47 doubles 31 doubles 25 doubles 23 doubles

47 doubles 31 doubles 25 doubles 23 doubles

47 triples 31 triples 25 triples 23 triples

47 triples 31 triples 25 triples 23 triples

47 triples 31 triples 25 triples 23 triples

47 triples 31 triples 25 triples 23 triples

47 singles 31 singles 25 singles 23 singles

w ww

. te

47 home runs 31 home runs 25 home runs 23 home runs

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m . u

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

o c . che e r o t r s super 47 home runs 31 home runs 25 home runs 23 home runs

R.I.C. Publications®

47 home runs 31 home runs 25 home runs 23 home runs

47 home runs 31 home runs 25 home runs 23 home runs

Maths perplexors

| 39


40

Counting scouts The clues

Bob, Bill, Baxter and Bart were four excellent Junior Scouts. They had earned 65, 50, 45 and 25 merit badges. They had helped 175, 160, 120 and 80 old ladies cross streets. They had gone on 350, 320, 240 and 80 nature hikes. On these nature hikes they saw and identified 175, 160, 80 and 40 different species of birds. Based on the clues, match the Junior Scouts with their merit badges, the number of old ladies they helped, the number of nature hikes taken and the number of birds identified.

1. Baxter earned half as many merit badges as Bob despite helping twice as many old ladies cross streets as Bob did. 2. Multiply the number of birds Bob identified by 3 to determine the number of old ladies Bill helped cross streets. 3. Bill earned 20 more merit badges than Baxter earned. 4. Bob went on 3 times as many nature hikes as Bill, and Baxter’s hiking number was double his bird identification number. 5. Neither Baxter not Bart identified the most birds.

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

Bob

Bill

Baxter

65 badges 50 badges 45 badges 25 badges

65 badges 50 badges 45 badges 25 badges

65 badges 50 badges 45 badges 25 badges

ew i ev Pr

Teac he r

The story

175 old ladies 160 old ladies 120 old ladies 80 old ladies

175 old ladies 160 old ladies 120 old ladies 80 old ladies

175 old ladies 160 old ladies 120 old ladies 80 old ladies

350 hikes 320 hikes 240 hikes 80 hikes

350 hikes 320 hikes 240 hikes 80 hikes

350 hikes 320 hikes 240 hikes 80 hikes

65 badges 50 badges 45 badges 25 badges

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

w ww

350 hikes 320 hikes 240 hikes 80 hikes 175 birds 160 birds 80 birds 40 birds

40 | Maths perplexors

. te

m . u

175 old ladies 160 old ladies 120 old ladies 80 old ladies

Bart

o c . che e r o t r s super 175 birds 160 birds 80 birds 40 birds

175 birds 160 birds 80 birds 40 birds

R.I.C. Publications®

175 birds 160 birds 80 birds 40 birds

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41

It’s Raining Cats The clues

Tabby, Fluffy, Gizmo and Grace were four female cats who had produced 23, 20, 15 and 12 kittens in their lifetimes. At one time or another all four cats had fallen from high places without injury. Their highest falling distances were 32, 31, 29 and 27 metres. Each of them had used up a different number of their nine lives and had used 7, 5, 4 and 3 lives. The four cats all shared a passion for catching mice and had caught 700, 500, 480 and 400 mice in their lifetimes. Based on the clues, match the cats with their kitten totals, the distances they fell, the number of lives they used up and the number of mice they caught.

1. Fluffy had 3 more kittens than Tabby, and Gizmo had 3 fewer kittens than Grace. 2. Fluffy fell exactly 1.86 metres farther than Gizmo, but Tabby fell exactly 1.86 metres farther than Fluffy. 3. Gizmo did not have the fewest kittens, and Fluffy did not have the most kittens. 4. Subtract the number of lives Fluffy used up from the number of lives Gizmo used up to find the number of lives Tabby used up. 5. Multiply the number of lives Fluffy used up by the number of metres Tabby fell to determine the number of mice Grace caught. 6. Fluffy caught more mice than Tabby but not as many as Gizmo. 7. The cat that caught the most mice did not produce the fewest kittens.

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

Tabby

Fluffy

Gizmo

23 kittens 20 kittens 15 kittens 12 kittens

23 kittens 20 kittens 15 kittens 12 kittens

23 kittens 20 kittens 15 kittens 12 kittens

32 metres 31 metres 29 metres 27 metres

32 metres 31 metres 29 metres 27 metres

32 metres 31 metres 29 metres 27 metres

7 lives 5 lives 4 lives 3 lives

7 lives 5 lives 4 lives 3 lives

700 mice 500 mice 480 mice 400 mice

700 mice 500 mice 480 mice 400 mice

ew i ev Pr

Teac he r

The story

Grace

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

. te

700 mice 500 mice 480 mice 400 mice

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o c . che e r o t r s super

R.I.C. Publications®

32 metres 31 metres 29 metres 27 metres

m . u

w ww 7 lives 5 lives 4 lives 3 lives

23 kittens 20 kittens 15 kittens 12 kittens

7 lives 5 lives 4 lives 3 lives

700 mice 500 mice 480 mice 400 mice

Maths perplexors

| 41


42

Pig numbers The clues

Porky, Puggly, Muggly and Buggly were four pigs who loved the numbers 11, 12, 13 and 14 so much that they each put one of those four numbers on the four clothing items they wore each day. They always wore a hat, a scarf, a shirt and a pair of pants each day with one of their favourite numbers on each item of clothing. However, the pigs insisted that no other pig could wear the same number on any item of clothing as another pig on that day. So, if a pig wore number 11 on his hat that pig would not wear number 11 on any other item of clothing he wore that day, and no other pig would wear number 11 on his hat that day either. Based on the clues, match the pigs with the numbers they wore on each item of clothing that day.

1. Remember, the pigs all wore all four numbers each day, but no two pigs wore the same number for the same item of clothing that day. 2. If you added the number on Porky’s hat to the number on Puggly’s hat, the answer would be 23. 3. If you added Muggly’s hat number to Puggly’s hat number, the answer would be 26. 4. If you added Muggly’s scarf number to Buggly’s scarf number, the answer would be 27. 5. Porky’s shirt number was smaller than Puggly’s shirt number and, of course, Muggly did not wear number 11 on his pants that day.

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

Porky

Puggly

Muggly

11 hat 12 hat 13 hat 14 hat

11 hat 12 hat 13 hat 14 hat

11 hat 12 hat 13 hat 14 hat

ew i ev Pr

Teac he r

The story

11 scarf 12 scarf 13 scarf 14 scarf

11 scarf 12 scarf 13 scarf 14 scarf

11 scarf 12 scarf 13 scarf 14 scarf

11 shirt 12 shirt 13 shirt 14 shirt

11 shirt 12 shirt 13 shirt 14 shirt

11 shirt 12 shirt 13 shirt 14 shirt

11 hat 12 hat 13 hat 14 hat

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

w ww

11 shirt 12 shirt 13 shirt 14 shirt

11 pants 12 pants 13 pants 14 pants

42 | Maths perplexors

. te

m . u

11 scarf 12 scarf 13 scarf 14 scarf

Buggly

o c . che e r o t r s super 11 pants 12 pants 13 pants 14 pants

11 pants 12 pants 13 pants 14 pants

R.I.C. Publications®

11 pants 12 pants 13 pants 14 pants

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43

Batty towns The clues

The towns of Glenview, Northbrook, Northfield and Deerfield were always trying to outdo each other. One year, they decided to see who could grow the heaviest pumpkin. They grew pumpkins that weighed 427.5, 405, 360 and 337.5 kilograms. All the towns had belfries, of which they were very proud, and they decided to see which town had the most bats in their belfries. They counted their bats and discovered they had 1500, 1300, 1250 and 1000 bats in their belfries. The towns then took a census of their cat and dog populations and found they had 8700, 8500, 7500 and 7300 cats, and they had 9300, 9100, 8700 and 8400 dogs. At the end of the day, all the towns were happy because each one of them led the list in one of the four categories. Based on the clues, match the towns with their heaviest pumpkin, the number of bats in their belfries, their cat populations and their dog populations.

1. Each town was at the top of the list in exactly one of the four categories. 2. Northfield’s pumpkin was 22.5 kilograms heavier than Deerfield’s pumpkin, and Northbrook’s pumpkin was 22.5 kilograms heavier than Glenview’s pumpkin. 3. Glenview’s new town motto was, ‘At least we did not grow the smallest pumpkin’. 4. Northbrook had 200 more cats than Glenview, and Deerfield had 200 more cats than Northfield, but Northfield did not have the fewest cats. 5. Northfield did not have the most dogs. 6. Glenview had fewer bats in its belfry than Northbrook but not the fewest. 7. The town with the fewest dogs had the most cats and, of course, Northbrook had more dogs than Northfield.

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

Glenview

Northbrook

Northfield

427.5 kg 405 kg 360 kg 337.5 kg

427.5 kg 405 kg 360 kg 337.5 kg

427.5 kg 405 kg 360 kg 337.5 kg

1500 bats 1300 bats 1250 bats 1000 bats

1500 bats 1300 bats 1250 bats 1000 bats

1500 bats 1300 bats 1250 bats 1000 bats

8700 cats 8500 cats 7500 cats 7300 cats

8700 cats 8500 cats 7500 cats 7300 cats

9300 dogs 9100 dogs 8700 dogs 8400 dogs

9300 dogs 9100 dogs 8700 dogs 8400 dogs

ew i ev Pr

Teac he r

The story

Deerfield

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

. te

9300 dogs 9100 dogs 8700 dogs 8400 dogs

www.ricpublications.com.au

o c . che e r o t r s super

R.I.C. Publications®

1500 bats 1300 bats 1250 bats 1000 bats

m . u

w ww 8700 cats 8500 cats 7500 cats 7300 cats

427.5 kg 405 kg 360 kg 337.5 kg

8700 cats 8500 cats 7500 cats 7300 cats

9300 dogs 9100 dogs 8700 dogs 8400 dogs

Maths perplexors

| 43


44

For the birds The clues

Hank, Hilda, Horace and Hester were four dedicated birdwatchers. One recent day they went to four different areas of the Taylor National Forest to take a census of the types and numbers of birds in their area. They saw and counted 622, 601, 579 and 557 crows. They saw and counted 751, 711, 700 and 660 geese. They saw and counted 530, 525, 475 and 450 ducks. They saw and counted 233, 200, 167 and 134 robins. Based on the clues, match the birdwatchers with the crows, geese, ducks and robins they saw and counted in their areas of the forest.

1. Hilda saw exactly 22 more crows than Hank, and Horace saw exactly 22 fewer crows than Hank. 2. Hank saw exactly 40 more geese than Hilda, and Horace saw exactly 40 more geese than Hester. 3. Hilda did not see the fewest geese or robins in her area, and she saw exactly 50 fewer ducks than Horace. 4. Hank did not see the most ducks, and he saw exactly 33 fewer robins than Hester. 5. Neither Hilda nor Horace saw the most robins.

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

Hank

Hilda

Horace

622 crows 601 crows 579 crows 557 crows

622 crows 601 crows 579 crows 557 crows

622 crows 601 crows 579 crows 557 crows

751 geese 711 geese 700 geese 660 geese

751 geese 711 geese 700 geese 660 geese

530 ducks 525 ducks 475 ducks 450 ducks

530 ducks 525 ducks 475 ducks 450 ducks

530 ducks 525 ducks 475 ducks 450 ducks

233 robins 200 robins 167 robins 134 robins

233 robins 200 robins 167 robins 134 robins

233 robins 200 robins 167 robins 134 robins

Hester

622 crows 601 crows 579 crows 557 crows

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

w ww

44 | Maths perplexors

. te

751 geese 711 geese 700 geese 660 geese

530 ducks 525 ducks 475 ducks 450 ducks

m . u

751 geese 711 geese 700 geese 660 geese

ew i ev Pr

Teac he r

The story

233 robins 200 robins 167 robins 134 robins

o c . che e r o t r s super

R.I.C. Publications®

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45

Farm alphabet The clues

Farms A, B, C and D were four farms of exactly 20 hectares each. These 20-hectare farms were divided into identical plots of 2, 4, 6 and 8 hectares. The farms all grew exactly the same crops of corn, beans, squash and spinach. However, no farm devoted the same sized plot to the same crops. If one farm grew 2 hectares of corn, then no other farm grew 2 hectares of corn and, of course, that farm could not grow 2 hectares of another crop as it had already used its 2-hectare plot growing corn. Based on the clues, match the farms with the correct number of hectares devoted to each crop.

1. No farm devoted the same sized plot to growing the same crop. 2. Farms A and B planted a combined total of 14 hectares of corn and 14 hectares of squash. 3. Farms B and C planted a combined total of 8 hectares of spinach. 4. Farms A and C planted a combined total of 8 hectares of squash.

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

Farm A

Farm B

Farm C

2 corn 4 corn 6 corn 8 corn

2 corn 4 corn 6 corn 8 corn

2 corn 4 corn 6 corn 8 corn

2 beans 4 beans 6 beans 8 beans

2 beans 4 beans 6 beans 8 beans

2 beans 4 beans 6 beans 8 beans

2 squash 4 squash 6 squash 8 squash

2 squash 4 squash 6 squash 8 squash

2 squash 4 squash 6 squash 8 squash

2 spinach 4 spinach 6 spinach 8 spinach

2 spinach 4 spinach 6 spinach 8 spinach

2 spinach 4 spinach 6 spinach 8 spinach

ew i ev Pr

Teac he r

The story

Farm D

2 corn 4 corn 6 corn 8 corn

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

www.ricpublications.com.au

o c . che e r o t r s super

R.I.C. Publications®

2 squash 4 squash 6 squash 8 squash

m . u

w ww

. te

2 beans 4 beans 6 beans 8 beans

2 spinach 4 spinach 6 spinach 8 spinach

Maths perplexors

| 45


46

Hockey hits The clues

June, Jack, Joan and John played hockey for Jacksonville Hockey Club. They wore numbers 23, 19, 17 and 15 on their uniforms. By the end of the season they had scored 37, 33, 32 and 29 goals. They had been conked on the head with a hockey ball 58, 50, 41 and 31 times. They had been made to serve 120, 100, 80 and 60 minutes in the penalty box. Based on the clues, match the hockey players with their uniform numbers, their goals, their conks on the head and their penalty times.

1. June and John’s uniform numbers add up to 32. 2. The player who scored the fewest goals was conked on the head the most times. 3. Jack did not have the highest uniform number, and John did not have the lowest uniform number. 4. June scored exactly 4 more goals than John, and Jack scored exactly 4 more goals than June. 5. The highest scorer was conked on the head the least, and Joan was indeed conked in the head more than June. 6. Joan’s penalty time was an hour less than June’s penalty time and, of course, John’s penalty time was less than Jack’s penalty time.

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

June

Jack

Joan

uniform 23 uniform 19 uniform 17 uniform 15

uniform 23 uniform 19 uniform 17 uniform 15

uniform 23 uniform 19 uniform 17 uniform 15

ew i ev Pr

Teac he r

The story

37 goals 33 goals 32 goals 29 goals

37 goals 33 goals 32 goals 29 goals

37 goals 33 goals 32 goals 29 goals

58 conks 50 conks 41 conks 31 conks

58 conks 50 conks 41 conks 31 conks

58 conks 50 conks 41 conks 31 conks

uniform 23 uniform 19 uniform 17 uniform 15

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

w ww

58 conks 50 conks 41 conks 31 conks

120 minutes 100 minutes 80 minutes 60 minutes

46 | Maths perplexors

. te

m . u

37 goals 33 goals 32 goals 29 goals

John

o c . che e r o t r s super 120 minutes 100 minutes 80 minutes 60 minutes

120 minutes 100 minutes 80 minutes 60 minutes

R.I.C. Publications®

120 minutes 100 minutes 80 minutes 60 minutes

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47

Food fight The clues

Bruno, Betsy, Byron and Bertha all owned sandwich shops. One recent evening after they had closed for the day, they got together and compared food sales for the day. They had sold 175, 150, 137 and 130 hot dogs. Oddly, they discovered they had sold 175, 150, 137 and 130 burgers. Odder still, they had sold 175, 150, 137 and 130 pies. Astonishingly, they had sold 175, 150, 137 and 130 sandwiches. Each shop had the honour of leading the sales of one of the four food items and, of course, no sandwich shop sold the same number of any food item as another shop sold that day. Based on the clues, match the sandwich shop owners with the number of hot dogs, burgers, pies and sandwiches they sold that day.

1. Each shop owner sold the most of one of the four food items, and no shop owner sold the same number for more than one food item. 2. Byron and Bertha sold 267 hot dogs and the same number of burgers. 3. Betsy and Bertha sold 280 hot dogs, and Betsy and Byron sold 280 sandwiches.

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

ew i ev Pr

Teac he r

The story

Bruno

Betsy

Byron

Bertha

175 hot dogs 150 hot dogs 137 hot dogs 130 hot dogs

175 hot dogs 150 hot dogs 137 hot dogs 130 hot dogs

175 hot dogs 150 hot dogs 137 hot dogs 130 hot dogs

175 burgers 150 burgers 137 burgers 130 burgers

175 burgers 150 burgers 137 burgers 130 burgers

175 burgers 150 burgers 137 burgers 130 burgers

175 burgers 150 burgers 137 burgers 130 burgers

175 pies 150 pies 137 pies 130 pies

175 pies 150 pies 137 pies 130 pies

175 pies 150 pies 137 pies 130 pies

175 pies 150 pies 137 pies 130 pies

175 hot dogs 150 hot dogs 137 hot dogs 130 hot dogs

w ww

. te

175 sandwiches 150 sandwiches 137 sandwiches 130 sandwiches

www.ricpublications.com.au

m . u

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

o c . che e r o t r s super 175 sandwiches 150 sandwiches 137 sandwiches 130 sandwiches

R.I.C. Publications®

175 sandwiches 150 sandwiches 137 sandwiches 130 sandwiches

175 sandwiches 150 sandwiches 137 sandwiches 130 sandwiches

Maths perplexors

| 47


48

You’re elected The clues

Ester, Eliot, Eve and Eddie all campaigned for the position of mayor of Murphyville. They spent $9300, $9000, $8900 and $8700 on their campaigns. During the campaign they kissed 375, 370, 340 and 310 babies. They also shook 1500, 1400, 1300 and 1100 hands. On Election Day, they received 11000, 9000, 7000 and 3000 votes. Based on the clues, match the campaigners with the money they spent on their campaigns, the babies kissed, the hands shaken and the votes received.

1. One candidate’s handshaking total multiplied by 10 equaled the vote total of that candidate. 2. Another candidate spent exactly one dollar for each vote received. 3. Ester and Eliot kissed a total of 650 babies, and Ester and Eddie shook a total of 2900 hands. 4. Eve shook exactly 100 fewer hands than Ester. 5. Eve and Eddie spent the least on their campaigns. 6. The candidate with the most votes kissed the fewest babies, while the candidate who kissed the most babies also shook the most hands. 7. Eve spent more than Eddie and received exactly 2000 fewer votes than another candidate.

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

Ester

Eliot

Eve

$9300 $9000 $8900 $8700

$9300 $9000 $8900 $8700

$9300 $9000 $8900 $8700

375 kisses 370 kisses 340 kisses 310 kisses

375 kisses 370 kisses 340 kisses 310 kisses

375 kisses 370 kisses 340 kisses 310 kisses

1500 hands 1400 hands 1300 hands 1100 hands

1500 hands 1400 hands 1300 hands 1100 hands

11 000 votes 9000 votes 7000 votes 3000 votes

11 000 votes 9000 votes 7000 votes 3000 votes

m . u

ew i ev Pr

Teac he r

The story

375 kisses 370 kisses 340 kisses 310 kisses

Eddie

$9300 $9000 $8900 $8700

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

w ww

1500 hands 1400 hands 1300 hands 1100 hands

11 000 votes 9000 votes 7000 votes 3000 votes

48 | Maths perplexors

. te

1500 hands 1400 hands 1300 hands 1100 hands

o c . che e r o t r s super

R.I.C. Publications®

11 000 votes 9000 votes 7000 votes 3000 votes

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49

Writer’s cramp The clues

Danny, Darla, Denise and David were four hardworking authors. Their ages were 55, 47, 39 and 30 years old. Their writing output was quite remarkable; they had published 77, 68, 59 and 51 short stories in their careers. They had also published 42, 34, 30 and 27 fullsized books in their careers. On a recent trip to promote their latest books, the authors had travelled 15 617, 12 880, 12 075 and 11 270 kilometres. Based on the clues, match the authors with their ages, their number of short stories, their number of books and their number of kilometres travelled.

1. Danny was exactly 8 years older than Darla, and Denise was older than David but she was not the oldest author. 2. One author’s age and number of books published match exactly. 3. The oldest author wrote the fewest books. 4. Darla wrote more books than Denise. 5. Denise travelled exactly 805 km less than Danny, but David travelled exactly 805 km less than Denise. 6. The author who wrote the fewest short stories travelled the least, and the author who travelled the longest distance wrote the most short stories. 7. Danny wrote exactly 9 more short stories than another author wrote.

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

Danny

Darla

Denise

ew i ev Pr

Teac he r

The story

David

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• 55 years old 47 years old 39 years old 30 years old

77 stories 68 stories 59 stories 51 stories

77 stories 68 stories 59 stories 51 stories

77 stories 68 stories 59 stories 51 stories

42 books 34 books 30 books 27 books

42 books 34 books 30 books 27 books

42 books 34 books 30 books 27 books

15 617 km 12 880 km 12 075 km 11 270 km

15 617 km 12 880 km 12 075 km 11 270 km

15 617 km 12 880 km 12 075 km 11 270 km

. te

www.ricpublications.com.au

55 years old 47 years old 39 years old 30 years old

o c . che e r o t r s super

R.I.C. Publications®

77 stories 68 stories 59 stories 51 stories

m . u

55 years old 47 years old 39 years old 30 years old

w ww

55 years old 47 years old 39 years old 30 years old

42 books 34 books 30 books 27 books

15 617 km 12 880 km 12 075 km 11 270 km

Maths perplexors

| 49


50

Town pride The clues

Ever competitive, the towns of Glenview, Northbrook, Northfield and Deerfield decided on a series of contests to settle, once and for all, the question of which town was the best. The first contest pitted each town’s town cow in a milk production contest. The cows produced, in a single day, 110, 91, 77 and 73 litres of milk. The second contest was to determine which town’s town pig weighed the most. The pigs weighed in at 358, 338, 317 and 314.5 kilograms. The third contest was to see which town’s town gorilla could stuff the most peanuts in its mouth. The gorillas stuffed 900, 888, 876 and 850 peanuts in their mouths. The fourth, and final, contest was to see which town’s town chicken was the fastest pecker. Their chickens pecked an amazing 275, 260, 250 and 235 pecks in a minute. Based on the clues, match the towns with their cow’s milk production, their pig’s weights, their gorilla’s peanut-stuffing totals and their chicken’s pecking performances.

1. Each town won exactly one contest, and each town did the worst in exactly one contest. 2. Glenview and Northbrook’s total milk production was exactly 125 litres of milk. 3. Northbrook and Northfield’s total milk production was exactly 140 litres of milk. 4. Glenview’s town pig was a mere 2.7 kg heavier than Northbrook’s town pig. 5. Northbrook’s town gorilla stuffed exactly one dozen fewer peanuts in his mouth than another town’s town gorilla. 6. Northfield’s town gorilla stuffed more than a dozen more peanuts in his mouth than the next worst peanut-stuffing total. 7. Glenview’s town chicken pecked faster than Deerfield’s town chicken.

100 litres 91 litres 77 litres 73 litres

Northfield ©Northbrook R. I . C.Publ i cat i ons Deerfield •f orr evi ew pur posesonl y•

w ww

358 kg 338 kg 317 kg 314.5 kg

900 peanuts 888 peanuts 876 peanuts 850 peanuts 275 pecks 260 pecks 250 pecks 235 pecks

50 | Maths perplexors

. te

100 litres 91 litres 77 litres 73 litres

100 litres 91 litres 77 litres 73 litres

100 litres 91 litres 77 litres 73 litres

358 kg 338 kg 317 kg 314.5 kg

358 kg 338 kg 317 kg 314.5 kg

358 kg 338 kg 317 kg 314.5 kg

m . u

Glenview

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 900 peanuts 888 peanuts 876 peanuts 850 peanuts

900 peanuts 888 peanuts 876 peanuts 850 peanuts

275 pecks 260 pecks 250 pecks 235 pecks

275 pecks 260 pecks 250 pecks 235 pecks

R.I.C. Publications®

900 peanuts 888 peanuts 876 peanuts 850 peanuts 275 pecks 260 pecks 250 pecks 235 pecks

www.ricpublications.com.au


Answers 1. Nutty squirrels

10. The cookie munchers

Sam

Sally

Sarah

Beth

Bill

Barb

5 years old 23 nuts 2nd place

2 years old 50 nuts 3rd place

3 years old 27 nuts 1st place

red 79 biscuits 116 metres 998 blueberries

yellow 113 biscuits 118 metres 760 blueberries

blue 34 biscuits 232.5 metres 750 blueberries

Oscar

Ollie

Olivia

11. Flight plans

46 hoots 27 mice blue hat

80 hoots 61 mice green hat

34 hoots 34 mice red hat

Carol

Clara

Carmen

191 litres Farmer Jones 1500 hectares

196 litres Farmer Brown 750 hectares

391 litres Farmer Smith 250 hectares

Glenview

Northbrook

Northfield

Deerfield

15.5 metres Saul 157 muffins

14.5 metres Sara 178 muffins

7 metres Sam 92 muffins

23 metres Sally 89 muffins

Peggy

Paula

Penrod

13. Tripping out

178 kg waltz 348 minutes

174 kg tango 356 minutes

177 kg foxtrot 354 minutes

Ned

Nancy

Norway 7 days 31 hours

Italy 28 days 23 hours

Berniece

Bella

Bonnie

14. Teething ring

9 eggs 78 clucks 25 grubs

16 eggs 62 clucks 26 grubs

7 eggs 17 clucks 27 grubs

Pete

Penny

Bridge 102 teeth 140 stamps

Charles

Cassie

Calvin

uniform 12 21 points puce

uniform 24 22 points purple

uniform 18 15 points pink

Fido

Pepper

16. Swats up?

doberman 198 barks 103 scratches 110 fleas

beagle 247 barks 77 scratches 63 fleas

Bert

Becky

ears 70 campers 717 swats

2. Who gives a hoot?

Jethro

Joan

Jill

goat 6.2 metres $200

horse 4.34 metres $250

cow 3.1 metres $400

pig 2.17 metres $500

r o e t s Bo r e p 12. Down towns o u k S

4. Oinkers aweigh

5. Chicken fun

ew i ev Pr

Teac he r

3. Cow contest

John

Norman

Nellie

Finland 14 days 4 hours

France 24 days 27 hours

© R. I . C.Publ i cat i ons 6. Basketball numbers •f orr evi ew pur p osesonl y• 15. Go fish

poodle 137 barks 123 scratches 47 fleas

8. Cats up

. te

Paul

Yanker 47 teeth 188 stamps

Crown 51 teeth 141 stamps

Pullem 94 teeth 171 stamps

Fred Frank

Farrah

Felicity

Caster 7 fish 10 kg

Fisher 17 fish 7 kg

Hooker 34 fish 6.5 kg

Bass 43 fish 4 kg

Byron

Buzz

necks 36 campers 820 swats

ankles 72 campers 697 swats

noses 53 campers 410 swats

m . u

Rover

w ww

7. Three dog fight

Patty

o c . che e r o t r s super 17. Worm up time

Tabby

Crabby

Flabby

Willy

Wilma

Wendy

Walter

yellow 15 hairballs 200 songbirds 109 metres

white 12 hairballs 190 songbirds 121 metres

blue 24 hairballs 251 songbirds 62 metres

142 apples 10 minutes bass perch

140 apples 15 minutes catfish

72 apples 20 minutes shark

70 apples 28 minutes

Linda

Larry

Lenny

Lucy

George

Gregory

Gail

Wiggy 6 metres 230 caps 510 hops

Boggler 10.5 metres 210 caps 620 hops

Figgle 4 metres 500 caps 310 hops

330 mistakes ‘soulful’ 75 minutes

159 mistakes ‘inspiring’ 180 minutes

168 mistakes ‘powerful’ 160 minutes

318 mistakes ‘passionate’ 90 minutes

9. The spitting image

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18. Australian idle

Maths perplexors

| 51


Answers 19. Watching the birdies

27. Halloween fun

Carl

Calvin

Cassie

Candi

Nancy

Nick

Nathan

Naomi

canary vest 30 85 seeds 43 minutes

crow vest 27 89 seeds 31 minutes

robin vest 37 72 seeds 61 minutes

dove vest 33 63 seeds 59 minutes

goblin 200 houses 5 kg 12 hours

pirate 175 houses 6 kg 14 hours

clown 110 houses 3. kg 6 hours

witch 147 houses 2.5 kg 7 hours

28. To bee or not to bee

20. And the runner is Darla

Deidre

Dirk

Scotland shirt 2 1st place 25 cups

Spain shirt 1 2nd place 50 cups

France shirt 4 3rd place 60 cups

Sweden shirt 3 4th place 75 cups

Elsie

Edward

Elvira

blue shirt yellow pants 60 bananas 66 screeches

red shirt green pants 57 bananas 90 screeches

yellow shirt blue pants 33 bananas 126 screeches

Glenview

Northbrook

Northfield

Deerfield

Ken Quimby 53 pies 15.5 metres

Kevin Jones 106 pies 19 metres

Kathy Smith 40 pies 33 metres

Kizzy Daley 20 pies 66 metres

Toby

Tom

Terry

Tyrone

125 minutes 16 km/h shell 19 green

150 minutes 13 km/h shell 20 orange

300 minutes 12 km/h shell 22 purple

250 minutes 19 km/h shell 15 red

Ruth

Reggie

Roger

Retta

1st grade 15 girls 14 boys 12 kilometres

2nd grade 14 girls 15 boys 13 kilometres

3rd grade 13 girls 12 boys 14 kilometres

4th grade 12 girls 13 boys 15 kilometres

Rex

Ron

Ray

Rupert

10 years old 70 feathers 15 seconds 7 metres

7 years old 60 feathers 30 seconds 6 metres

9 years old 50 feathers 40 seconds 4 metres

5 years old 100 feathers 55 seconds 5 metres

John

Jolene

Joann

Jeff

4 corn 3 peas 1 beans 2 tomatoes

3 corn 4 peas 2 beans 1 tomatoes

1 corn 2 peas 3 beans 4 tomatoes

2 corn 1 peas 4 beans 3 tomatoes

32. A cold season

Penny

Molly

Polly

80.5 km/h wishbone 33 days sailing

161 km/h tailbone 24 days softball

72 km/h wing bone 15 days tennis

w ww

145 km/h drumstick 57 days football

Farmer White 17.1 kg 232.5 metres roses

© R. I . C.Pu l i cat i ons 31.b Farmer plots •f orr evi ew pur posesonl y•

24. Ski for your life Henny

Byron

Farmer Brown 7.65 kg 217 metres daisies

30. Rooster tales

22. Town pride

23. Speed limits

Betsy

Farmer Black 8.55 kg 116 metres tulips

ew i ev Pr

green shirt red pants 93 bananas 24 screeches

Baxter

Farmer Green 15.3 kg 248 metres peonies

25. Spending dogs Rover

Queenie

Deerfield $600 airfare chicken $575 spent

Northfield $550 airfare fish $850 spent

. te Duke

Mark

Mary

4th grade 12 absent 210 coughs 170 sneezes

3rd grade 14 absent 170 coughs 210 sneezes

m . u

Eliot

Teac he r

21. Hey, hey, we’re the monkeys

Bella

r o e t s Bo r e p ok 29. Classy teachers u S

David

Millie

Mac

5th grade 11 absent 105 coughs 65 sneezes

2nd grade 7 absent 65 coughs 105 sneezes

o c . che e r o t r s super

Northbrook $300 airfare steak $1100 spent

33. Gorilla my dreams

Gizmo

Glenview $275 airfare lobster $300 spent

Brent

Betty

Bonita

Bert

9 coconuts 277 bananas 186 metres 830 nits

18 coconuts 300 bananas 211 metres 700 nits

20 coconuts 350 bananas 186 metres 600 nits

27 coconuts 330 bananas 67 metres 463 nits

Paul

Pamela

Peter

Peggy

94 baskets 40 salmon 12 L honey ‘Teddies’

87 baskets 47 salmon 9 L honey ‘Raiders’

73 baskets 39 salmon 8 L honey ‘Honeybears’

80 baskets 37 salmon 15 L honey ‘Salmonettes’

34. Bear facts

26. Hockey hits Jake

Jenny

Jerri

Jason

6 years 1200 hits 12 teeth ‘Speedy’

7 years 750 hits 11 teeth ‘Blinky’

11 years 1500 hits 7 teeth ‘Whizzer’

12 years 500 hits 6 teeth ‘Toothy’

52 | Maths perplexors

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Answers 35. Selling ladybug scouts

43. Batty towns

June

Joan

Jean

Josie

Glenview

Northbrook

Northfield

Deerfield

Carter 180 boxes 80 doorbells 90 tickets

Jones 193 boxes 90 doorbells 80 tickets

Bolton 175 boxes 99 doorbells 87 tickets

Smith 160 boxes 94 doorbells 100 tickets

405 kg 1250 bats 7300 cats 9300 dogs

427.5 kg 1300 bats 7500 cats 9100 dogs

360 kg 1500 bats 8500 cats 8700 dogs

337.5 kg 1000 bats 8700 cats 8400 dogs

36. Hardworking chickens Sally

Sarah

2 hrs pecking 4 hrs flapping 6 hrs clucking 8 hrs egg-laying

44. For the birds

r o e t s Bo r e p o u k 45. Farm alphabet S Sheila

Hank

Hilda

Horace

Hester

4 hrs pecking 2 hrs flapping 8 hrs clucking 6 hrs egg-laying

8 hrs pecking 6 hrs flapping 4 hrs clucking 2 hrs egg-laying

6 hrs pecking 8 hrs flapping 2 hrs clucking 4 hrs egg-laying

579 crows 751 geese 450 ducks 200 robins

601 crows 711 geese 475 ducks 167 robins

557 crows 700 geese 525 ducks 134 robins

622 crows 660 geese 530 ducks 233 robins

Greta

Gail

Gertie

Greg

Farm A

Farm B

Farm C

Farm D

South flock 290 members 99 honks 18 pills

East flock 790 members 74 honks 16 pills

North flock 625 members 60 honks 24 pills

West flock 500 members 57 honks 10 pills

8 corn 2 beans 6 squash 4 spinach

6 corn 4 beans 8 squash 2 spinach

4 corn 8 beans 2 squash 6 spinach

2 corn 6 beans 4 squash 8 spinach

Albert

Alice

Andy

Anna

June

Jack

Joan

John

225 strokes 23 golf balls 7 clubs 62 m

286 strokes 50 golf balls 8 clubs 93 m

170 strokes 60 golf balls 5 clubs 84 m

160 strokes 73 golf balls 10 clubs 74 m

uniform 15 33 goals 41 conks 120 minutes

uniform 19 37 goals 31 conks 100 minutes

uniform 23 32 goals 50 conks 60 minutes

uniform 17 29 goals 58 conks 80 minutes

Harriet

Homer

Hilda

Bruno

Betsy

Byron

Bertha

25 singles 23 doubles 47 triples 31 home runs

23 singles 25 doubles 31 triples 47 home runs

31 singles 47 doubles 25 triples 23 home runs

175 hot dogs 150 burgers 130 pies 137 sandwiches

150 hot dogs 175 burgers 137 pies 130 sandwiches

137 hot dogs 130 burgers 175 pies 150 sandwiches

130 hot dogs 137 burgers 150 pies 175 sandwiches

Teac he r

37. Goose down

38. A round of golf

Hal 47 singles 31 doubles 23 triples 25 home runs

© R. I . C.Publ i cat i ons 47. Food fight •f orr evi ew pur posesonl y•

40. Counting scouts

48. You’re elected

Bill

Baxter

Bart

Ester

Eliot

45 badges 120 old ladies 80 hikes 175 birds

25 badges 160 old ladies 320 hikes 160 birds

65 badges 175 old ladies 350 hikes 80 birds

$9000 340 kisses 1400 hands 9000 votes

w ww

Bob

50 badges 80 old ladies 240 hikes 40 birds

41. It’s raining cats

. te

m . u

39. It’s a hit

46. Hockey hits

ew i ev Pr

Shari

Eve

Eddie

$9300 310 kisses 1100 hands 11 000 votes

$8900 370 kisses 1300 hands 7000 votes

$8700 375 kisses 1500 hands 3000 votes

o c . che e r o t r s super 49. Writer’s cramp

Tabby

Fluffy

Gizmo

Grace

Danny

Darla

Denise

David

12 kittens 100 metres 3 lives 480 mice

15 kittens 94 metres 4 lives 500 mice

20 kittens 88 metres 7 lives 700 mice

23 kittens 102 metres 5 lives 400 mice

55 yrs old 68 stories 27 books 12 880 km

47 yrs old 77 stories 42 books 15 617 km

39 yrs old 59 stories 34 books 12 075 km

30 yrs old 51 stories 30 books 11 270 km

Porky

Puggly

Muggly

Buggly

Glenview

Northbrook

Northfield

Deerfield

11 hat 12 scarf 13 shirt 14 pants

12 hat 11 scarf 14 shirt 13 pants

14 hat 13 scarf 11 shirt 12 pants

13 hat 14 scarf 12 shirt 11 pants

73 L 317 kg 900 peanuts 260 pecks

77 L 314.5 kg 888 peanuts 275 pecks

91 L 358 kg 876 peanuts 235 pecks

100 L 337.5 kg 850 peanuts 250 pecks

42. Pig numbers

50. Town pride

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Maths Perplexors: Ages 9-10  

This series of blackline master mathematics logic puzzles requires enquiring minds to use the process of elimination to find answers. Buy n...