Issuu on Google+

Vi ew in

g

sa

m pl

e

6066 - - - MATHS PERPLEXORS

6066


Maths perplexors (Ages 8–9)

This master may only be reproduced by the original purchaser for use with their class(es). The publisher prohibits the loaning or onselling of this master for the purposes of reproduction.

Published by Prim-Ed Publishing 2013 under licence to MindWare Holdings Inc. Copyright © 2007 MindWare Holdings Inc. This version copyright © Prim-Ed Publishing 2013

Copyright Notice Blackline masters or copy masters are published and sold with a limited copyright. This copyright allows publishers to provide teachers and schools with a wide range of learning activities without copyright being breached. This limited copyright allows the purchaser to make sufficient copies for use within their own education institution. The copyright is not transferable, nor can it be onsold. Following these instructions is not essential but will ensure that you, as the purchaser, have evidence of legal ownership to the copyright if inspection occurs.

ISBN 978-1-84654-675-4 PR–6066

Titles available in this series: Maths perplexors (Ages 8–9) Maths perplexors (Ages 9–10) Maths perplexors (Ages 10–11) Maths perplexors (Ages 11–12) Maths perplexors (Ages 12–13)

m pl

e

For your added protection in the case of copyright inspection, please complete the form below. Retain this form, the complete original document and the invoice or receipt as proof of purchase. Name of Purchaser:

Vi ew in

g

sa

Date of Purchase:

Supplier:

School Order# (if applicable):

Signature of Purchaser:

Internet websites

In some cases, websites or specific URLs may be recommended. While these are checked and rechecked at the time of publication, the publisher has no control over any subsequent changes which may be made to webpages. It is strongly recommended that the class teacher checks all URLs before allowing pupils to access them.

View all pages online

Website: www.prim-ed.com


Introduction

Contents

Maths perplexors are deductive logic puzzles. They are specifically designed to challenge and extend mainstream or more able maths pupils. It is strongly recommended that the teacher models the process of deductive reasoning once or twice with the pupils, 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.

Bakers get the blues ......................... 1 A croc pot? ...................................... 2 Beehive yourself! ............................. 3 A fair worming! ............................... 4 Snap out of it! .................................. 5 And the whinny is … ....................... 6 Parrot party ...................................... 7 Happy webbing day ........................ 8 A carrot caper .................................. 9 Barking lots ................................... 10 Coffee lorries ................................. 11 Just dropping by ............................ 12 You auto know .............................. 13 Sneeze the day! ............................. 14 Coconuts downriver ...................... 15 Cat in a hat .................................... 16 Giraffe losers? ................................ 17 A fair time ..................................... 18 Camping delights ........................... 19 A raft of thrills ................................ 20 Artful lodgers ................................. 21 The defence rests ........................... 22 I suspect fowl play ......................... 23 Climb every mountain ................... 24 The old fishing hole ....................... 25 One 24-hour sty ............................ 26 Nuts we lost .................................. 27 In this corner ................................. 28 You’re fired up! .............................. 29 And the dinner is ........................... 30 Eating elephants ............................ 31 Garden of eatin’ ............................ 32 Did you trip? ................................. 33 Town talent .................................... 34 Lost without you ............................ 35 Anyone want a buggy ride? ............ 36 A tough race .................................. 37 You ain’t lion ................................. 38 Tree fruitful .................................... 39 Charity drop .................................. 40 The farmers are plotting ................. 41 A win-win-win situation ................ 42 Go buy the book ........................... 43 It’s a dog’s life ................................ 44 Camel crossing .............................. 45 Pet shop sales ................................ 46 It’s in the cards .............................. 47 Check your toytals ......................... 48 Classy flower power ...................... 49 Who is the dealer? ......................... 50 Answers ................................... 51–53

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.

sa

m pl

e

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.

Puzzles

Where to use Maths perplexors

Vi ew in

g

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 pupils. 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 pupils to consolidate and expand on what they have learnt in the classroom. 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, pupils can share and strengthen these skills. Whole-class challenges Teacher assistance may be required with some pupils; modelling is an effective strategy. ‘Extras’ This is mainly a fun activity/challenge for the more mathematically able or advanced pupils.

www.prim-ed.com

Prim-Ed Publishing

Maths perplexors

| iii


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 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 Gail 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

40 flies 20 flies 10 flies

e

8 years old 4 years old 2 years old

40 flies 20 flies 10 flies

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

Vi ew in

8 years old 4 years old 2 years old

sa

Greg Gail Gordon

g

m pl

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.

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.

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

Now that we know Gordon is the oldest gecko and he ate 10 flies, and we know that Gail ate 20 flies because she ate twice as many flies as Gordon, circle 20 flies under Gail and complete the crossing out; we know that Greg ate 40 flies. Clue 1 says multiplying Greg’s age by 10 reveals the number of flies he ate. Since we now know he ate 40 flies, we must conclude he is 4 years old because 4 x 10 = 40.

iv | Maths perplexors

Prim-Ed Publishing

www.prim-ed.com


1

Bakers get the blues

Three bakers named Nate, Nellie and Nick all received a large shipment of fresh blueberries. All three bakers decided to make both blueberry pies and muffins with their shipments. They made 15, 10 and 5 blueberry pies, and they made 15, 10 and 5 blueberry muffins. Based on the clues, match the bakers with the number of pies and muffins they baked.

15 pies 10 pies 5 pies

15 muffins 10 muffins 5 muffins

15 muffins 10 muffins 5 muffins

Nick 15 pies 10 pies 5 pies 15 muffins 10 muffins 5 muffins

Vi ew in

15 pies 10 pies 5 pies

sa

Nellie

g

1. No baker baked the same number of pies as he or she baked muffins. 2. Together, Nate and Nellie baked a total of 25 pies. 3. Both Nate and Nellie baked more pies than muffins. 4. Together, Nellie and Nick baked a total of 25 muffins.

m pl

Nate

The clues

e

The story

www.prim-ed.com

Prim-Ed Publishing

Maths perplexors

|1


2

A croc pot?

Sherman, Alice and Bert were three friendly elephants who agreed to carry three groups of baboons across a crocodile-infested river at no charge. The baboons were in groups of 20, 16 and 12. Due to a lack of seatbelts, a different number of baboons fell off each elephant and were chased by the grateful crocodiles. Each elephant lost either 8, 6 or 4 baboons during the tragic river crossing. Of course, from the point of view of the crocodiles, the river crossing was a snapping good time! Based on the clues, match the elephants with the size of the baboon group they started out with and the number of baboons they lost in the river.

1. Sherman carried 16 baboons safely across the river. 2. Alice carried 8 baboons safely across the river.

Alice

20 baboons 16 baboons 12 baboons

20 baboons 16 baboons 12 baboons

8 lost 6 lost 4 lost

8 lost 6 lost 4 lost

Bert 20 baboons 16 baboons 12 baboons 8 lost 6 lost 4 lost

Vi ew in

g

sa

m pl

Sherman

The clues

e

The story

2 | Maths perplexors

Prim-Ed Publishing

www.prim-ed.com


3

Beehive yourself!

Three bees named Buzz, Bill and Bob sat around the hive one evening discussing the events of the day. Each had kept count of the number of flowers visited that day and discovered they had visited 200, 150 and 100 flowers. These bees all thought it was their job to sting as many people as possible. That day, they had stung 25, 20 and 10 people. Based on the clues, match the bees with the number of flowers they visited and the number of people they stung.

Buzz 200 flowers 150 flowers 100 flowers

200 flowers 150 flowers 100 flowers

25 stings 20 stings 10 stings

25 stings 20 stings 10 stings

Bob 200 flowers 150 flowers 100 flowers 25 stings 20 stings 10 stings

Vi ew in

g

Bill

m pl

1. Buzz visited more flowers than Bob. 2. Bill stung more people than Bob. 3. Bill visited more flowers than Buzz. 4. Buzz stung more people than Bill.

sa

The clues

e

The story

www.prim-ed.com

Prim-Ed Publishing

Maths perplexors

|3


4

A fair worming!

The story

Ruth, Rita and Rolanda were three robins who lived in the same neighbourhood in River Forest. One day, they ate 11, 9 and 7 juicy worms and, oddly enough, they laid 11, 9 and 7 beautiful blue eggs. Based on the clues, match the robins with the number of worms they ate and the number of eggs they laid that day.

1. Between them, Ruth and Rolanda ate a total of 18 worms and laid a total of 18 eggs. 2. Rita ate two more worms than Ruth and laid two more eggs than Rolanda.

11 worms 9 worms 7 worms

11 worms 9 worms 7 worms

11 eggs 9 eggs 7 eggs

11 eggs 9 eggs 7 eggs

11 worms 9 worms 7 worms 11 eggs 9 eggs 7 eggs

Vi ew in

g

sa

Rolanda

e

Rita

m pl

Ruth

The clues

4 | Maths perplexors

Prim-Ed Publishing

www.prim-ed.com


5

Snap out of it!

The story

Three snapping turtles named Sarah, Shane and Sidney were very proud of their snappy snapping. They held a contest to see who could snap the most times in a minute. During the contest, they snapped 300, 275 and 250 times in a minute. The turtles were different ages; they were 16, 14 and 12 years old. Based on the clues, match the turtles with their snapping numbers and their ages.

300 snaps 275 snaps 250 snaps

16 years old 14 years old 12 years old

16 years old 14 years old 12 years old

300 snaps 275 snaps 250 snaps 16 years old 14 years old 12 years old

Vi ew in

g

300 snaps 275 snaps 250 snaps

Sidney

m pl

Shane

sa

1. The fastest snapper was the youngest turtle, and the oldest turtle was the slowest snapper. 2. Sarah was 4 years older than Shane.

e

Sarah

The clues

www.prim-ed.com

Prim-Ed Publishing

Maths perplexors

|5


6

And the whinny is…

The story

Hiram, Hank and Hannah were three horses who climbed the fence to get into Farmer Brown’s apple orchard to eat as many apples as they could before he could stop them. They ate 75, 70 and 65 apples. Later, in the stable, they decided to hold a contest to see who could swat the most flies with one tail swish. Oddly enough, they swatted 75, 70 and 65 flies with one tail swish. Based on the clues, match the horses with the number of apples they ate and the number of flies they swatted.

1. Only one horse had the same number for both apples eaten and flies swatted. 2. Hiram’s number of apples was higher than his number of flies. 3. Hannah’s number of flies was higher than her number of apples. 4. Hank did not eat the most apples, but he ate more apples than Hannah.

75 apples 70 apples 65 apples

75 apples 70 apples 65 apples

75 flies 70 flies 65 flies

75 flies 70 flies 65 flies

75 apples 70 apples 65 apples 75 flies 70 flies 65 flies

Vi ew in

g

sa

Hannah

e

Hank

m pl

Hiram

The clues

6 | Maths perplexors

Prim-Ed Publishing

www.prim-ed.com


7

Parrot party

The story

Polly, Peter and Paul were three parrots who loved to go to parties and eat and drink until their stomachs ached. At one party, they drank 16, 13 and 11 cups of punch, and they ate 25, 23 and 22 cupcakes. Based on the clues, match the parrots with the number of cups of punch they drank and the number of cupcakes they ate.

Peter

16 cups 13 cups 11 cups

16 cups 13 cups 11 cups

Paul

m pl

1. Together, Peter and Paul drank a total of 29 cups of punch. 2. Together, Polly and Peter ate 48 cupcakes and they drank half that many cups of punch. 3. Polly was on a diet and did not eat the most cupcakes.

e

Polly

The clues

16 cups 13 cups 11 cups

Vi ew in

g

sa

25 cupcakes 25 cupcakes 25 cupcakes 23 cupcakes 23 cupcakes 23 cupcakes 22 cupcakes 22 cupcakes 22 cupcakes

www.prim-ed.com

Prim-Ed Publishing

Maths perplexors

|7


8

Happy webbing day

The story

Sylvia, Sharon and Shana were three spiders who all made their living by catching and eating flies they caught in their webs. One day, they spun webs that were 12, 10 and 9 cm across. Oddly enough, that day they caught 12, 10 and 9 flies. Based on the clues, match the spiders with the sizes of their webs and the number of flies they caught.

Sylvia

The clues 1. No spiders matched the number of the width of their webs, in cm, with the number of flies they caught. 2. The spider with the smallest web caught the most flies. 3. Together, Sylvia and Sharon caught fewer than 20 flies. 4. Sharon did not have the largest web.

Sharon

Shana

12 flies 10 flies 9 flies

sa

12 flies 10 flies 9 flies

12 flies 10 flies 9 flies

Vi ew in

g

m pl

e

12 cm 12 cm 12 cm 10 cm 10 cm 10 cm 9 cm 9 cm 9 cm

8 | Maths perplexors

Prim-Ed Publishing

www.prim-ed.com


9

A carrot caper

Spike, Mike and Rex were three rascally rabbits who decided to raid Farmer Brown’s heavily guarded carrot patch. One night, they sneaked into the carrot patch and picked and stuffed their pockets with 35, 30 and 25 juicy carrots. However, one of the rabbits tripped the alarm and lights started flashing and sirens started wailing and the rabbits were forced to run for their lives. As they ran, they began to drop carrots; they dropped 15, 10 and 5 carrots. Based on the clues, match the rabbits with the number of carrots they picked and the number of carrots they dropped.

35 picked 30 picked 25 picked

35 picked 30 picked 25 picked

15 dropped 10 dropped 5 dropped

15 dropped 10 dropped 5 dropped

Rex 35 picked 30 picked 25 picked 15 dropped 10 dropped 5 dropped

Vi ew in

g

Mike

sa

1. Mike escaped with only 10 carrots remaining in his pockets. 2. Spike escaped with exactly twice as many carrots in his pockets as Mike.

m pl

Spike

The clues

e

The story

www.prim-ed.com

Prim-Ed Publishing

Maths perplexors

|9


10

Barking lots

Biff, Byron and Belle were three dogs who enjoyed doing two things. They enjoyed chasing postal workers and barking. They kept a record of their chasing careers; they had chased 13, 9 and 5 postal workers. They held a contest to see who could bark the most times in 20 seconds without drawing a breath; they barked 55, 49 and 43 times. Based on the clues, match the dogs with the number of postal workers they chased and the number of times they barked in 20 seconds.

55 barks 49 barks 43 barks

13 postal workers 9 postal workers 5 postal workers 55 barks 49 barks 43 barks

Belle

13 postal workers 9 postal workers 5 postal workers 55 barks 49 barks 43 barks

Vi ew in

g

Byron

m pl

13 postal workers 9 postal workers 5 postal workers

1. Byron chased 4 more postal workers than Biff. 2. The dog that was the slowest barker chased the most postal workers. 3. Byron was a better barker than Biff.

sa

Biff

The clues

e

The story

10 | Maths perplexors

Prim-Ed Publishing

www.prim-ed.com


11

Coffee lorries

Peter, Pam and Penny were lorry drivers. They drove lorries that had 18, 12 and 6 wheels. One day, they drove their lorries 320 kilometres, 240 kilometres and 180 kilometres, and they drank 20, 15 and 10 cups of coffee. Based on the clues, match the drivers with the number of wheels on their lorries, the kilometres they drove, and the number of cups of coffee they drank.

Peter

1. The driver with the fewest wheels did not drive the most kilometres or drink the most cups of coffee. 2. Pam drank more cups of coffee than Peter. 3. Penny’s lorry had more wheels than Pam’s lorry. 4. Peter drove exactly 80 more kilometres than Penny, and his lorry had more wheels than Penny’s lorry.

Pam

Penny

18 wheels 12 wheels 6 wheels

320 kilometres 240 kilometres 180 kilometres

320 kilometres 240 kilometres 180 kilometres

320 kilometres 240 kilometres 180 kilometres

20 cups 15 cups 10 cups

20 cups 15 cups 10 cups

20 cups 15 cups 10 cups

www.prim-ed.com

sa g

m pl

18 wheels 12 wheels 6 wheels

Vi ew in

The clues

e

The story

Prim-Ed Publishing

18 wheels 12 wheels 6 wheels

Maths perplexors

| 11


12

Just dropping by

Mary, Martha and Mabel were waitresses at a busy restaurant. One day, they discovered they had each carried 900 items. They each had carried 300 cups of coffee, 300 glasses of water, and 300 plates of toast. However, they all had a bad day and had dropped 30, 20 and 10 cups of coffee, 30, 20 and 10 glasses of water, and 30, 20 and 10 plates of toast. Based on the clues, match the waitresses with the number of cups, glasses and plates they dropped.

The clues 1. All the waitresses dropped some cups, glasses and plates, but it was discovered that each waitress had dropped exactly 60 items. 2. Martha dropped more cups and glasses than Mary. 3. Mabel dropped more glasses than Martha.

Martha

30 cups 20 cups 10 cups

30 cups 20 cups 10 cups

30 glasses 20 glasses 10 glasses

30 glasses 20 glasses 10 glasses

30 plates 20 plates 10 plates

30 plates 20 plates 10 plates

12 | Maths perplexors

Vi ew in

g

sa

m pl

Mary

e

The story

Prim-Ed Publishing

Mabel 30 cups 20 cups 10 cups 30 glasses 20 glasses 10 glasses 30 plates 20 plates 10 plates

www.prim-ed.com


13

You auto know

Alex, Alice and Anne met at a petrol station one day and began discussing their driving experiences. They had been driving 35, 30 and 25 years. Oddly enough, during their years of driving, they had 35, 30 and 25 flat tyres. Stranger still, they discovered that their cars gave them 35, 30 and 25 kilometres per litre. Based on the clues, match the drivers with their years of driving, their number of flat tyres, and their kilometres per litre.

Anne

35 years 30 years 25 years

35 years 30 years 25 years

35 years 30 years 25 years

35 flat tyres 30 flat tyres 25 flat tyres

35 flat tyres 30 flat tyres 25 flat tyres

35 flat tyres 30 flat tyres 25 flat tyres

35 kilometres per litre 30 kilometres per litre 25 kilometres per litre

Vi ew in

3 5 kilometres per litre 30 kilometres per litre 25 kilometres per litre

sa

Alice

g

1. No driver had the same number for more than one category. If a driver drove for 35 years then that same driver did not have 35 flats or 35 kilometres per litre, and so on. 2. Alice drove more years than Anne, and Alex had more flat tyres than Alice. 3. Alice’s car had higher kilometres per litre than Anne’s car. 4. The driver with the fewest flat tyres did not drive the car that got the highest kilometres per litre.

m pl

Alex

The clues

e

The story

www.prim-ed.com

Prim-Ed Publishing

35 kilometres per litre 30 kilometres per litre 25 kilometres per litre

Maths perplexors

| 13


Sneeze the day!

The story

Nancy, Nick and Nora all suffered from terrible head colds. For no good reason, they kept track of how many times they sneezed and coughed, and how many tissues they used in a day. They sneezed 100, 95 and 80 times. They coughed 96, 80 and 75 times. They each started with 500 tissues and used 180, 155 and 130 tissues. Based on the clues, match the names with the number of times they sneezed and coughed, and the number of tissues they used that day.

1. Nancy sneezed more than she coughed, used exactly one tissue for each sneeze and cough, and had exactly 320 tissues remaining out of the 500 she started with. 2. Nora also used exactly one tissue for each sneeze and cough she made that day.

Nick

100 sneezes 95 sneezes 80 sneezes

100 sneezes 95 sneezes 80 sneezes

96 coughs 80 coughs 75 coughs

96 coughs 80 coughs 75 coughs

180 tissues 155 tissues 130 tissues

14 | Maths perplexors

g

sa

e

Nancy

The clues

m pl

14

100 sneezes 95 sneezes 80 sneezes 96 coughs 80 coughs 75 coughs 180 tissues 155 tissues 130 tissues

Vi ew in

180 tissues 155 tissues 130 tissues

Nora

Prim-Ed Publishing

www.prim-ed.com


15

Coconuts downriver

The story

The clues 1. After crossing the river, both Booker and Boomer were left with only 14 coconuts each. 2. The monkey with the most coconuts left after crossing the river ate the most bananas. 3. Booker ate fewer bananas than Boomer. 4. The monkey who started with the most coconuts before crossing the river did not eat the fewest bananas.

m pl

e

Bonkly, Booker and Boomer were three monkeys who liked to collect coconuts and put them away for a rainy day. One day, they had collected 28, 26 and 25 coconuts. Unfortunately, as they were crossing the river on their way home, they dropped some of their coconuts in the river and they were carried downstream. They dropped 14, 12 and 8 coconuts that tragic day. To console themselves after they lost part of their coconut collections, they ate 50, 45 and 40 bananas at one sitting. Based on the clues, match the monkeys with their original coconut collection numbers, the number of coconuts they dropped, and the number of bananas they ate.

Bonkly

14 dropped 12 dropped 8 dropped

50 bananas 45 bananas 40 bananas

www.prim-ed.com

28 coconuts 26 coconuts 25 coconuts

14 dropped 12 dropped 8 dropped

14 dropped 12 dropped 8 dropped

50 bananas 45 bananas 40 bananas

50 bananas 45 bananas 40 bananas

Vi ew in

Prim-Ed Publishing

Boomer

28 coconuts 26 coconuts 25 coconuts

sa

28 coconuts 26 coconuts 25 coconuts

g

Booker

Maths perplexors

| 15


16

Cat in a hat

Bucky, Huckly and Mouser were three cats who owned rather large wardrobes. They owned 11, 9 and 7 hats. They also owned 9, 7 and 5 vests, and 7, 5 and 3 scarves. Based on the clues, match the cats with the number of hats, vests and scarves they owned.

The clues 1. Bucky owned exactly two more hats than Huckly, and Huckly owned exactly two more vests than Bucky. 2. Mouser owned exactly two more scarves than Huckly. 3. Huckly’s number of scarves was exactly two less than his number of hats. 4. Bucky’s number of hats was exactly two more than his number of vests.

Huckly

11 hats 9 hats 7 hats

11 hats 9 hats 7 hats

9 vests 7 vests 5 vests

9 vests 7 vests 5 vests

7 scarves 5 scarves 3 scarves

7 scarves 5 scarves 3 scarves

16 | Maths perplexors

sa

m pl

Bucky

e

The story

Mouser 11 hats 9 hats 7 hats 9 vests 7 vests 5 vests

Vi ew in

g

7 scarves 5 scarves 3 scarves

Prim-Ed Publishing

www.prim-ed.com


17

Giraffe losers? The clues

The story

Gail, Gordon and Gilda were three giraffes who became friends when they met each other at the local chiropractor. Their necks were 4, 3 and 2 metres long and needed almost constant treatment. They shared the same hobby of racing lions at every opportunity; they had raced 33, 30 and 27 lions. One day, they all realised they had lost their wallets while racing the lions. They lost 36, 32 and 25 gold coins when they lost their wallets. Based on the clues, match the giraffes with their neck lengths, the number of lions they raced, and the amount of money they lost with their wallets.

m pl

e

1. The giraffe with the longest neck did not lose the most coins or race the most lions. 2. The giraffe with the shortest neck did not lose the most coins but lost more coins than Gilda. 3. Gail’s neck was longer than Gordon’s neck. 4. Gilda raced more lions than Gail.

Gail

33 lions 30 lions 27 lions

4 metres 3 metres 2 metres

33 lions 30 lions 27 lions

33 lions 30 lions 27 lions

Vi ew in

Gilda

4 metres 3 metres 2 metres

sa

4 metres 3 metres 2 metres

g

Gordon

36 coins 36 coins 36 coins 32 coins 32 coins 32 coins 25 coins 25 coins 25 coins

www.prim-ed.com

Prim-Ed Publishing

Maths perplexors

| 17


A fair time

The story

Three roosters named Roger, Roland and Ryan took a trip to the local community fair. At the fair, they ate 18, 16 and 14 bags of peanuts. They ate 18, 16 and 14 sandwiches, and they drank 11, 10 and 9 cups of soft drink. Based on the clues, match the roosters with the number of bags of peanuts they ate, the number of sandwiches they ate, and the number of cups of soft drink they drank.

18 sandwiches 16 sandwiches 14 sandwiches

18 bags peanuts 16 bags peanuts 14 bags peanuts

18 bags peanuts 16 bags peanuts 14 bags peanuts

18 sandwiches 16 sandwiches 14 sandwiches

18 sandwiches 16 sandwiches 14 sandwiches

11 cups soft drink 10 cups soft drink 9 cups soft drink

11 cups soft drink 10 cups soft drink 9 cups soft drink

Vi ew in

11 cups soft drink 10 cups soft drink 9 cups soft drink

Ryan

m pl

Roland

sa

18 bags peanuts 16 bags peanuts 14 bags peanuts

1. Roland consumed a total of 45 food and drink items. 2. Roger consumed a total of 37 food items. 3. Ryan ate more bags of peanuts than Roland.

g

Roger

The clues

e

18

18 | Maths perplexors

Prim-Ed Publishing

www.prim-ed.com


19

Camping delights

Jake, Jane and Jill went on a week-long camping trip to the River Forest mountains in the USA. They each interacted with wild creatures a different number of times. They were chased by bears 20, 15 and 10 times. They were scared by coyotes 30, 25 and 20 times. They were bitten by snakes 8, 6 and 4 times. Based on the clues, match the names with the number of bears that chased them, the number of coyotes that scared them, and the number of snakes that bit them.

30 coyotes 25 coyotes 20 coyotes

8 snakes 6 snakes 4 snakes

www.prim-ed.com

20 bears 15 bears 10 bears

30 coyotes 25 coyotes 20 coyotes

30 coyotes 25 coyotes 20 coyotes

8 snakes 6 snakes 4 snakes

8 snakes 6 snakes 4 snakes

sa

Prim-Ed Publishing

Jill

20 bears 15 bears 10 bears

g

20 bears 15 bears 10 bears

Jane

Vi ew in

1. Jane was scared by more coyotes than Jake, but Jake was chased by fewer bears than Jane. 2. Jill interacted with a total of 38 bears, coyotes and snakes. 3. Jane was not bitten by as many snakes as Jake.

m pl

Jake

The clues

e

The story

Maths perplexors

| 19


20

A raft of thrills

Henry, Hilda and Harriet were three experienced rafting guides who conducted raft tours of the River Forest rapids. They had been guides for 14, 10 and 8 years. One day, they started out with 20, 17 and 12 passengers in their rafts. Unfortunately, some of the passengers in each raft did not hold on tightly enough and were tossed out of the rafts and had to float down the rapids on their own. The number of passengers who were tossed out of each raft was 7, 5 and 3 very wet passengers. Based on the clues, match the guides with their years of experience, the number of passengers they started with, and the number of passengers who went overboard.

Hilda

Harriet

14 years 10 years 8 years

20 passengers 17 passengers 12 passengers

20 passengers 17 passengers 12 passengers

20 passengers 17 passengers 12 passengers

7 overboard 5 overboard 3 overboard

7 overboard 5 overboard 3 overboard

7 overboard 5 overboard 3 overboard

20 | Maths perplexors

g

sa

14 years 10 years 8 years

Vi ew in

1. The least experienced guide ended the run down the rapids with 17 passengers still in the raft. 2. The most experienced guide ended the run down the rapids with only 5 very frightened passengers still in the raft. 3. Henry had been a guide exactly 2 years longer than Hilda.

m pl

Henry

The clues

e

The story

Prim-Ed Publishing

14 years 10 years 8 years

www.prim-ed.com


21

Artful lodgers

Cathy, Carol and Chuck were three professional artists who lived in the same boarding house. At the end of the year, they compared their painting sales. They sold 25, 23 and 21 landscapes. They sold 30, 25 and 20 portraits. They sold 25, 15 and 10 waterscapes, and 18, 16 and 14 paintings of dogs with big eyes. Based on the clues, match the artists with the number of landscapes, portraits, waterscapes and dog paintings they sold that year.

1. If you added the sales of Carol’s and Chuck’s dog paintings, the answer would be the number of Cathy’s portrait sales. 2. Chuck specialised in waterscapes and sold as many of them as Cathy and Carol put together. 3. Cathy sold a total of 33 landscapes and waterscapes. 4. Carol sold more dog paintings than waterscapes. 5. Chuck sold a grand total of 89 paintings for the year.

Carol

m pl

Cathy

The clues

e

The story

Chuck

25 landscapes 23 landscapes 21 landscapes

25 landscapes 23 landscapes 21 landscapes

25 landscapes 23 landscapes 21 landscapes

30 portraits 25 portraits 20 portraits

30 portraits 25 portraits 20 portraits

30 portraits 25 portraits 20 portraits

25 waterscapes 15 waterscapes 10 waterscapes

18 dogs 16 dogs 14 dogs

www.prim-ed.com

g

sa

25 waterscapes 15 waterscapes 10 waterscapes

18 dogs 16 dogs 14 dogs

18 dogs 16 dogs 14 dogs

Vi ew in

25 waterscapes 15 waterscapes 10 waterscapes

Prim-Ed Publishing

Maths perplexors

| 21


The defence rests

The story

Maxine, Melvin and Maggie were three criminal defence lawyers who happened to meet while they were on holiday in the Bahamas. They had been practising law for 15, 10 and 5 years. During the past year they had tried a total of 100, 95 and 90 cases. Out of those cases tried they had lost only 20, 15 and 10 cases. Oddly enough, they were on holiday for 20, 15 and 10 days. Based on the clues, match the lawyers with their years of experience, the number of cases they tried, the number of cases they lost, and the number of days they were on holiday.

Melvin 15 years 10 years 5 years

100 cases 95 cases 90 cases

100 cases 95 cases 90 cases

20 cases lost 15 cases lost 10 cases lost

20 days 15 days 10 days

22 | Maths perplexors

g

sa

15 years 10 years 5 years

Maggie 15 years 10 years 5 years 100 cases 95 cases 90 cases

20 cases lost 15 cases lost 10 cases lost

20 cases lost 15 cases lost 10 cases lost

20 days 15 days 10 days

20 days 15 days 10 days

Vi ew in

1. Maxine and Melvin both won exactly 85 cases. 2. No lawyers matched their number of cases lost with their number of holiday days. 3. The lawyer with the least experience took the longest holiday and lost the fewest cases. 4. Melvin was more experienced than Maxine. 5. The most experienced lawyer won a total of 70 cases.

e

Maxine

The clues

m pl

22

Prim-Ed Publishing

www.prim-ed.com


I suspect fowl play

The story

Gertie, Grace and Greta were a chicken, a duck and a turkey who all played baseball for Farmer Brown’s baseball team. They were the three best hitters on the team. Last season, they hit 100, 75 and 50 singles. They hit 90, 80 and 70 doubles. They hit 75, 60 and 55 triples, and they hit 56, 54 and 48 home runs. Based on the clues, match the baseball players with the number of singles, doubles, triples and home runs they hit during the season.

Grace

Greta

100 singles 75 singles 50 singles

100 singles 75 singles 50 singles

90 doubles 80 doubles 70 doubles

90 doubles 80 doubles 70 doubles

90 doubles 80 doubles 70 doubles

75 triples 60 triples 55 triples

56 home runs 54 home runs 48 home runs

www.prim-ed.com

g

sa

100 singles 75 singles 50 singles

75 triples 60 triples 55 triples

75 triples 60 triples 55 triples

56 home runs 54 home runs 48 home runs

56 home runs 54 home runs 48 home runs

Vi ew in

1. Both Grace and Greta hit more singles than doubles. 2. Grace hit more triples than doubles. 3. Gertie hit more singles than home runs. 4. Grace hit the same number of singles and triples. 5. Greta hit more home runs than triples, and Gertie hit more doubles than Greta.

m pl

Gertie

The clues

e

23

Prim-Ed Publishing

Maths perplexors

| 23


24

Climb every mountain

The story

The clues 1. Oddly enough, no climber had matching numbers for years of experience, mountains climbed and countries visited. 2. Darlene climbed more mountains than Diane. 3. David was more experienced than Darlene. 4. Diane visited more countries than David. 5. David climbed more mountains than Darlene. 6. The least experienced climber fell the farthest, and Diane did not fall as far as David.

Diane

m pl

e

Diane, David and Darlene were three experienced mountain climbers. They had been climbing for 14, 13 and 11 years. Oddly enough, in that time, they climbed 14, 13 and 11 mountains. Although they did not all climb a mountain in every country they visited, they all travelled to 14, 13 and 11 countries to look at mountains. None of them had ever been seriously injured, but they all had fallen while climbing; they fell 15 metres, 14 metres and 12 metres. Based on the clues, match the climbers with their years of experience, the number of mountains they climbed, the number of countries they visited, and the distances they fell.

David

14 years 13 years 11 years

14 years 13 years 11 years

14 mountains 13 mountains 11 mountains

14 mountains 13 mountains 11 mountains

14 countries 13 countries 11 countries

15 metres 14 metres 12 metres

24 | Maths perplexors

14 years 13 years 11 years 14 mountains 13 mountains 11 mountains

14 countries 13 countries 11 countries

14 countries 13 countries 11 countries

15 metres 14 metres 12 metres

15 metres 14 metres 12 metres

Vi ew in

g

sa

Darlene

Prim-Ed Publishing

www.prim-ed.com


25

The old fishing hole

Inez, Ivan and Irene had fabulous luck fishing at their favourite River Forest fishing hole. They were fishing for fun so they released every fish they caught. We can guess that the fish did not have as much fun as Inez, Ivan and Irene, though. They caught 25, 23 and 21 trout. They caught 22, 20 and 19 bass. They caught 21, 20 and 18 salmon, and 19, 18 and 17 tuna. Based on the clues, match the names with the number of trout, bass, salmon and tuna they caught that day.

Inez

1. Inez caught more bass than trout, and she also caught more salmon than tuna. 2. Both Ivan and Irene caught more salmon than bass. 3. Ivan caught a combined total of 45 trout and bass and, of course, Ivan caught more salmon than bass. 4. Irene caught a combined total of 39 salmon and tuna.

Ivan

Irene

25 trout 23 trout 21 trout

22 bass 20 bass 19 bass

22 bass 20 bass 19 bass

22 bass 20 bass 19 bass

21 salmon 20 salmon 18 salmon

21 salmon 20 salmon 18 salmon

21 salmon 20 salmon 18 salmon

19 tuna 18 tuna 17 tuna

19 tuna 18 tuna 17 tuna

19 tuna 18 tuna 17 tuna

www.prim-ed.com

sa g

m pl

25 trout 23 trout 21 trout

Vi ew in

The clues

e

The story

Prim-Ed Publishing

25 trout 23 trout 21 trout

Maths perplexors

| 25


One 24-hour sty

The story

Three pigs named Snorts, Pixie and Trotter spent the same amount of time doing the same things every 24-hour day. They ate, they slept and they oinked. They ate for 10, 8 and 6 hours every day. They slept for 10, 8 and 6 hours every day. They oinked for 10, 8 and 6 hours every day. When the day was over, they started the next day doing the same things for the same amount of time. Every day they ate 27, 23 and 19 kilograms of fresh swill during their different eating times. Based on the clues, match the pigs with their eating, sleeping and oinking times, and with the kilograms of swill they consumed.

Snorts

The clues 1. Snorts and Pixie spent a combined total of 14 hours eating. 2. Snorts and Trotter spent a combined total of 14 hours sleeping. 3. The pig who spent the most hours eating ate the smallest amount of swill. 4. The pig who spent the least time oinking did not eat the largest amount of swill. 5. Snorts slept exactly 2 hours less than Pixie.

Pixie

e

26

Trotter

10 hrs eating 8 hrs eating 6 hrs eating

10 hrs eating 8 hrs eating 6 hrs eating

10 hrs sleeping 8 hrs sleeping 6 hrs sleeping

10 hrs sleeping 8 hrs sleeping 6 hrs sleeping

10 hrs sleeping 8 hrs sleeping 6 hrs sleeping

10 hrs oinking 8 hrs oinking 6 hrs oinking

10 hrs oinking 8 hrs oinking 6 hrs oinking

10 hrs oinking 8 hrs oinking 6 hrs oinking

27 kg swill 23 kg swill 19 kg swill

27 kg swill 23 kg swill 19 kg swill

27 kg swill 23 kg swill 19 kg swill

26 | Maths perplexors

Vi ew in

g

sa

m pl

Prim-Ed Publishing

10 hrs eating 8 hrs eating 6 hrs eating

www.prim-ed.com


27

Nuts we lost

The story

The clues 1. Steve still knew the locations of 60 walnuts, and Shirley still knew the locations of 60 walnuts. 2. Shirley still knew the locations of 60 almonds. 3. Sheldon hid 6 fewer almonds than walnuts. 4. Shirley hid more walnuts than Steve, and Sheldon lost more almonds than Steve.

m pl

e

Steve, Sheldon and Shirley were three squirrels living in the same neighbourhood in the lovely village of River Forest. All summer long they gathered walnuts and almonds and hid them so they could use them later when the nuts were not so plentiful. They hid 75, 70 and 65 walnuts. They hid 72, 69 and 60 almonds. Unfortunately, all three squirrels were somewhat absent-minded and forgot where they hid some of their nuts and lost them. They lost 10, 7 and 5 walnuts, and they lost 12, 10 and 6 almonds. Based on the clues, match the squirrels with the number of walnuts and almonds they hid, and the number of walnuts and almonds they lost.

Steve

Sheldon

Shirley

75 walnuts hidden 70 walnuts hidden 65 walnuts hidden

75 walnuts hidden 70 walnuts hidden 65 walnuts hidden

72 almonds hidden 69 almonds hidden 60 almonds hidden

72 almonds hidden 69 almonds hidden 60 almonds hidden

72 almonds hidden 69 almonds hidden 60 almonds hidden

10 walnuts lost 7 walnuts lost 5 walnuts lost

10 walnuts lost 7 walnuts lost 5 walnuts lost

10 walnuts lost 7 walnuts lost 5 walnuts lost

12 almonds lost 10 almonds lost 6 almonds lost

12 almonds lost 10 almonds lost 6 almonds lost

12 almonds lost 10 almonds lost 6 almonds lost

www.prim-ed.com

g

Vi ew in

sa

75 walnuts hidden 70 walnuts hidden 65 walnuts hidden

Prim-Ed Publishing

Maths perplexors

| 27


28

In this corner

The story

Biff, Benny and Boris were professional boxers. They had been boxing for 12, 10 and 8 years. They had won 20, 18 and 15 fights. They had lost 6, 5 and 3 fights. During their careers, they had their noses painfully broken 16, 14 and 10 times. Based on the clues, match the boxers with their years of experience, the number of fights they won, the number of fights they lost, and the number of broken noses they had suffered.

1. Benny boxed two years longer than Biff, and Boris boxed two years more than Benny. 2. Benny did not win as many fights as Biff, but Benny lost fewer fights than Biff. 3. Benny fought a total of 20 fights in his career. 4. Biff won more fights than Boris. 5. The boxer who won the most fights broke his nose the fewest times, and the boxer who won the fewest fights broke his nose the most times.

12 years 10 years 8 years

12 years 10 years 8 years

20 won 18 won 15 won

20 won 18 won 15 won

6 lost 5 lost 3 lost

16 noses 14 noses 10 noses

28 | Maths perplexors

g

sa

e

Benny

m pl

Biff

The clues

Boris 12 years 10 years 8 years 20 won 18 won 15 won 6 lost 5 lost 3 lost

16 noses 14 noses 10 noses

16 noses 14 noses 10 noses

Vi ew in

6 lost 5 lost 3 lost

Prim-Ed Publishing

www.prim-ed.com


29

You‘re fired up!

Frank, Farrah, and Felicity were three experienced firefighters. They had been going to fires for 25, 23 and 20 years. During their careers, they had saved the lives of 100, 95 and 90 adult women. They had saved the lives of 96, 91 and 89 adult men. They had saved the lives of 93, 90 and 88 babies. Based on the clues, match the firefighters with their years of experience and the number of women, men and babies they saved.

25 years 23 years 20 years 100 women 95 women 90 women

96 men 91 men 89 men

93 babies 90 babies 88 babies

www.prim-ed.com

25 years 23 years 20 years

100 women 95 women 90 women

100 women 95 women 90 women

Vi ew in

Prim-Ed Publishing

Felicity

25 years 23 years 20 years

sa

Farrah

g

1. Felicity was more experienced than the firefighter who saved the fewest babies. 2. Frank was more experienced than the firefighter who saved the most babies. 3. Felicity saved more men than women. 4. Frank saved more babies than Farrah. 5. Felicity saved more babies than men. 6. Frank saved more men than Farrah, and Frank saved more women than men.

m pl

Frank

The clues

e

The story

96 men 91 men 89 men

96 men 91 men 89 men

93 babies 90 babies 88 babies

93 babies 90 babies 88 babies

Maths perplexors

| 29


30

And the dinner is ‌

Hector, Harriet and Hester owned fast food shops and sold sandwiches, pies and sausage rolls. One day, they decided to hold a contest to see who could sell the most of these three food items. The contest ended in a threeway tie because they all sold exactly 600 food items. They sold 250, 200 and 150 sandwiches. They sold 250, 200 and 150 pies. They sold 250, 200 and 150 sausage rolls. Since they all ended up selling the same number of food items, they decided the winner of the contest would be based on the sale of the most soft drinks. Based on the clues, match the owners with the number of sandwiches, pies, sausage rolls and soft drinks they sold.

250 pies 200 pies 150 pies

250 sausage rolls 200 sausage rolls 150 sausage rolls

250 soft drinks 200 soft drinks 150 soft drinks

30 | Maths perplexors

m pl

Hester

250 sandwiches 200 sandwiches 150 sandwiches

250 sandwiches 200 sandwiches 150 sandwiches

250 pies 200 pies 150 pies

250 pies 200 pies 150 pies

sa

Harriet

g

250 sandwiches 200 sandwiches 150 sandwiches

1. Hector sold exactly 50 more sandwiches than Harriet. 2. Hester sold exactly 50 more pies than Hector, and Hester sold exactly 50 more sausage rolls than Hector as well. 3. Harriet sold exactly 50 more pies than Hester. 4. Based solely on soft drink sales, Harriet did not win the contest, but she did sell more soft drinks than Hector.

Vi ew in

Hector

The clues

e

The story

250 sausage rolls 200 sausage rolls 150 sausage rolls

250 sausage rolls 200 sausage rolls 150 sausage rolls

250 soft drinks 200 soft drinks 150 soft drinks

250 soft drinks 200 soft drinks 150 soft drinks

Prim-Ed Publishing

www.prim-ed.com


Eating elephants

The story

Dwayne, Darla and Daphne were three elephants who dined together at an all-you-can-eat pie buffet restaurant before the restaurant had to close because the elephants consumed too many pies. The elephants ate 500, 450 and 400 cherry pies. They ate 400, 350 and 300 apple pies. They ate 800, 700 and 600 peach pies. They ate 600, 500 and 400 pumpkin pies. They ate 450, 400 and 350 blueberry pies. Based on the clues, match the elephants with the number of cherry, apple, peach, pumpkin and blueberry pies they ate.

500 cherry 450 cherry 400 cherry

400 apple 350 apple 300 apple

800 peach 700 peach 600 peach

400 apple 350 apple 300 apple

Daphne 500 cherry 450 cherry 400 cherry 400 apple 350 apple 300 apple

800 peach 700 peach 600 peach

800 peach 700 peach 600 peach

600 pumpkin 500 pumpkin 400 pumpkin

600 pumpkin 500 pumpkin 400 pumpkin

600 pumpkin 500 pumpkin 400 pumpkin

450 blueberry 400 blueberry 350 blueberry

450 blueberry 400 blueberry 350 blueberry

450 blueberry 400 blueberry 350 blueberry

www.prim-ed.com

Vi ew in

500 cherry 450 cherry 400 cherry

sa

Darla

g

1. Dwayne ate more cherry pies than Darla, and Darla ate more apple pies than Daphne. 2. Daphne ate fewer peach pies than Darla, and Darla ate fewer blueberry pies than Daphne. 3. Darla ate more pumpkin pies than Dwayne, and Daphne ate more cherry pies than Dwayne. 4. Dwayne ate more apple pies than Darla, and Darla ate fewer peach pies than Dwayne. 5. Daphne ate more blueberry pies than pumpkin pies. 6. Darla ate more blueberry pies than apple pies.

m pl

Dwayne

The clues

e

31

Prim-Ed Publishing

Maths perplexors

| 31


Garden of eatin‘

The story

George, Gail and Gregory were three serious vegetable gardeners. They picked and ate every single vegetable they grew in their gardens. They grew, picked and ate 60, 55 and 50 tomatoes. They grew, picked and ate 59, 54 and 49 cucumbers. They grew, picked and ate 50, 49 and 48 potatoes. They grew, picked and ate 49, 45 and 40 radishes. They grew, picked and ate 42, 39 and 35 green peppers. Based on the clues, match the gardeners with the number of tomatoes, cucumbers, potatoes, radishes and peppers they grew, picked and ate.

1. George grew more cucumbers than tomatoes. 2. Gregory grew more potatoes than cucumbers. 3. George grew more tomatoes than Gregory. 4. Gail grew more potatoes than radishes. 5. Gregory grew more peppers than radishes. 6. The gardener who grew the most tomatoes did not grow the smallest number of any other vegetable.

Gail

m pl

George

The clues

60 tomatoes 55 tomatoes 50 tomatoes

60 tomatoes 55 tomatoes 50 tomatoes

59 cucumbers 54 cucumbers 49 cucumbers

59 cucumbers 54 cucumbers 49 cucumbers

50 potatoes 49 potatoes 48 potatoes

49 radishes 45 radishes 40 radishes

42 peppers 39 peppers 35 peppers

g

sa

32 | Maths perplexors

e

32

Gregory 60 tomatoes 55 tomatoes 50 tomatoes 59 cucumbers 54 cucumbers 49 cucumbers 50 potatoes 49 potatoes 48 potatoes

49 radishes 45 radishes 40 radishes

49 radishes 45 radishes 40 radishes

42 peppers 39 peppers 35 peppers

42 peppers 39 peppers 35 peppers

Vi ew in

50 potatoes 49 potatoes 48 potatoes

Prim-Ed Publishing

www.prim-ed.com


33

Did you trip?

The story

The clues 1. The traveller who visited the most countries was not sick the most days. 2. The traveller who spent the most days travelling was sick the fewest days. 3. Toula and Tammy visited a combined total of 29 museums and 29 parks. 4. Toula visited more countries than Tammy and was sick for exactly one more day than Tori. 5. Tammy went to more museums than parks. 6. The traveller who visited the fewest parks did not visit the fewest countries. 7. Toula travelled exactly two days less than Tori.

m pl

e

Toula, Tammy and Tori loved to travel to different countries during their summer holidays. One holiday season, they visited 32, 30 and 28 different countries in 32, 30 and 28 days of travel. During the course of their travels, they visited 16, 15 and 14 museums, and 16, 15 and 14 national parks. Unfortunately, they all suffered from cases of food poisoning and were sick for 6, 5 and 4 days. Based on the clues, match the travellers with the number of countries they visited, the number of days they travelled, the number of museums and parks they visited, and the number of days they were sick.

Toula

32 countries 30 countries 28 countries

32 days travel 30 days travel 28 days travel

32 days travel 30 days travel 28 days travel

32 days travel 30 days travel 28 days travel

16 museums 15 museums 14 museums

16 museums 15 museums 14 museums

16 museums 15 museums 14 museums

16 parks 15 parks 14 parks

16 parks 15 parks 14 parks

16 parks 15 parks 14 parks

6 days sick 5 days sick 4 days sick

6 days sick 5 days sick 4 days sick

6 days sick 5 days sick 4 days sick

www.prim-ed.com

sa

Tori

32 countries 30 countries 28 countries

g

32 countries 30 countries 28 countries

Vi ew in

Tammy

Prim-Ed Publishing

Maths perplexors

| 33


Town talent

The story

Mopeville

The clues 1. All the towns had the most in at least one category, but one town had the most yodellers and acrobats, and another town had the most jugglers and dancers. 2. Loopin had more yodellers than Kookston, but Kookston had more acrobats than Loopin. 3. Kookston had exactly 25 fewer jugglers than Loopin. 4. The town with the fewest dancers had the most magicians and, of course, Mopeville had more magicians than Loopin.

m pl

Mopeville, Kookston and Loopin were three competitive neighbouring towns. The town mayors were always talking about which town was the best. At a meeting, the mayors got into a discussion over which town had the most talented citizens in five very important categories. The towns had a census to count the number of citizens who possessed these talents. The census revealed they had 200, 190 and 180 citizens who could yodel. They had 500, 475 and 450 citizens who could juggle. They had 250, 245 and 240 citizens who were magicians. They had 315, 300 and 285 flamenco dancers. They had 290, 280 and 275 acrobats. Based on the clues, match the towns with the number of yodellers, jugglers, magicians, dancers and acrobats they had as citizens.

e

34

Kookston

Loopin

200 yodellers 190 yodellers 180 yodellers

200 yodellers 190 yodellers 180 yodellers

200 yodellers 190 yodellers 180 yodellers

500 jugglers 475 jugglers 450 jugglers

500 jugglers 475 jugglers 450 jugglers

500 jugglers 475 jugglers 450 jugglers

250 magicians 245 magicians 240 magicians

250 magicians 245 magicians 240 magicians

250 magicians 245 magicians 240 magicians

315 dancers 300 dancers 285 dancers

315 dancers 300 dancers 285 dancers

315 dancers 300 dancers 285 dancers

290 acrobats 280 acrobats 275 acrobats

290 acrobats 280 acrobats 275 acrobats

290 acrobats 280 acrobats 275 acrobats

34 | Maths perplexors

Vi ew in

g

sa

Prim-Ed Publishing

www.prim-ed.com


35

Lost without you

The story

The clues 1. Bjorn had the most of two of the five lost items, and Bixby had the most of two of the five lost items. 2. Bjorn had the fewest of two of the five lost items, and Bixby had the fewest of three of the five lost items. 3. Bunky had exactly 25 more shoes than Bixby, and Bixby had exactly 50 more gym shorts than Bunky. 4. Bjorn had fewer beanies than Bixby. 5. Bunky had more pens than Bjorn.

m pl

e

Bunky, Bjorn and Bixby were three secretaries for three different schools. Among their many duties, they were in charge of the lost property at their schools. At a meeting, they compared the five most commonly lost items at their schools. They had 500, 475 and 450 lost shoes. They had 700, 650 and 600 rather fragrant pairs of gym shorts. They had 200, 195 and 190 pairs of glasses. They had 196, 189 and 187 ballpoint pens. They had 660, 590 and 550 knitted beanies. Based on the clues, match the secretaries with the number of shoes, gym shorts, glasses, ballpoint pens and beanies they were holding in their lost property.

Bunky

500 shoes 475 shoes 450 shoes

700 gym shorts 650 gym shorts 600 gym shorts

700 gym shorts 650 gym shorts 600 gym shorts

700 gym shorts 650 gym shorts 600 gym shorts

200 glasses 195 glasses 190 glasses

200 glasses 195 glasses 190 glasses

200 glasses 195 glasses 190 glasses

196 pens 189 pens 187 pens

196 pens 189 pens 187 pens

196 pens 189 pens 187 pens

660 beanies 590 beanies 550 beanies

660 beanies 590 beanies 550 beanies

660 beanies 590 beanies 550 beanies

sa

Bixby

500 shoes 475 shoes 450 shoes

g

500 shoes 475 shoes 450 shoes

Vi ew in

Bjorn

www.prim-ed.com

Prim-Ed Publishing

Maths perplexors

| 35


Anyone want a buggy ride?

The story

Clem, Charly and Callie were three competitive pest exterminators. One day, they decided to hold a contest to see who could exterminate the most of five common household pests in an hour. The contest began and they zapped 1200, 1100 and 1000 cockroaches in an hour. They dispatched 1150, 1050 and 950 ants in an hour. They eliminated 800, 795 and 780 bedbugs in an hour. They clobbered 785, 750 and 735 fleas in an hour. They smashed 625, 620 and 615 ticks in an hour. Based on the clues, match the exterminators with the number of cockroaches, ants, bedbugs, fleas and ticks they did away with in an hour.

1150 ants 1050 ants 950 ants

800 bedbugs 795 bedbugs 780 bedbugs

785 fleas 750 fleas 735 fleas

625 ticks 620 ticks 615 ticks

36 | Maths perplexors

m pl

Callie

1200 cockroaches 1100 cockroaches 1000 cockroaches

1200 cockroaches 1100 cockroaches 1000 cockroaches

1150 ants 1050 ants 950 ants

1150 ants 1050 ants 950 ants

800 bedbugs 795 bedbugs 780 bedbugs

800 bedbugs 795 bedbugs 780 bedbugs

785 fleas 750 fleas 735 fleas

785 fleas 750 fleas 735 fleas

625 ticks 620 ticks 615 ticks

625 ticks 620 ticks 615 ticks

sa

Charly

g

1200 cockroaches 1100 cockroaches 1000 cockroaches

1. Clem exterminated the most of three of the five types of pests, and Charly eliminated the most of two of the five types of pests. 2. Clem exterminated the fewest of two of the five types of pests, and Charly eliminated the fewest of three of the five types of pests. 3. Callie exterminated more ants and ticks than Clem.

Vi ew in

Clem

The clues

e

36

Prim-Ed Publishing

www.prim-ed.com


A tough race

The story

Oscar, Olive and Oona were the only three candidates running for the office of mayor of the town of Mayville. It was a close race and all three candidates worked very hard during their campaigns. They gave 495, 490 and 480 speeches. They made 990, 980 and 950 solemn promises. They made 770, 760 and 750 sincere pledges. They made 500, 475 and 450 rock solid commitments. Election day finally arrived and they received 6500, 6450 and 6400 votes. Based on the clues, match the candidates with their number of speeches, promises, pledges, commitments and votes.

495 speeches 490 speeches 480 speeches 990 promises 980 promises 950 promises

770 pledges 760 pledges 750 pledges

500 commitments 475 commitments 450 commitments

495 speeches 490 speeches 480 speeches

990 promises 980 promises 950 promises

990 promises 980 promises 950 promises

Vi ew in

6500 votes 6450 votes 6400 votes

www.prim-ed.com

Prim-Ed Publishing

Oona

495 speeches 490 speeches 480 speeches

sa

Olive

g

1. The winner of the election made the most promises and pledges and the fewest speeches and commitments. 2. The candidate who finished in second place made the most speeches and commitments and the fewest promises and pledges. 3. Olive received exactly 50 more votes than Oscar. 4. Olive made more commitments than Oscar.

m pl

Oscar

The clues

e

37

770 pledges 760 pledges 750 pledges

770 pledges 760 pledges 750 pledges

500 commitments 475 commitments 450 commitments

500 commitments 475 commitments 450 commitments

6500 votes 6450 votes 6400 votes

6500 votes 6450 votes 6400 votes

Maths perplexors

| 37


38

You ain‘t lion

Three African lions named Mongo, Bongo and Tongo were badly in need of grooming advice and pest control. The big cats were infested with 600, 500 and 490 fleas. They were sorely bothered by 500, 490 and 480 nits. They suffered from 485, 480 and 475 ear mites. Because of all the scratching they did, they had 25, 23 and 21 bald spots in their fur. As if all this was not enough, the fierce felines hacked up 15, 14 and 13 hair balls every day. Based on the clues, match the lions with their number of fleas, nits, ear mites, bald spots and hair balls.

1. Mongo had exactly 10 more fleas than nits. 2. Tongo had exactly 10 more nits than Bongo. 3. Mongo had the highest number in two of the five categories, and Bongo had the highest number in two of the five categories. 4. Tongo had more ear mites than Mongo. 5. Tongo had a combined total of 36 bald spots and hair balls.

Bongo

600 fleas 500 fleas 490 fleas

600 fleas 500 fleas 490 fleas

500 nits 490 nits 480 nits

500 nits 490 nits 480 nits

485 ear mites 480 ear mites 475 ear mites

25 bald spots 23 bald spots 21 bald spots

15 hair balls 14 hair balls 13 hair balls

38 | Maths perplexors

Vi ew in

g

sa

m pl

Mongo

The clues

e

The story

Tongo 600 fleas 500 fleas 490 fleas 500 nits 490 nits 480 nits

485 ear mites 480 ear mites 475 ear mites

485 ear mites 480 ear mites 475 ear mites

25 bald spots 23 bald spots 21 bald spots

25 bald spots 23 bald spots 21 bald spots

15 hair balls 14 hair balls 13 hair balls

15 hair balls 14 hair balls 13 hair balls

Prim-Ed Publishing

www.prim-ed.com


39

Tree fruitful

The story

The clues 1. Edward had only two trees that gave him a combined total of 1000 pieces of fruit, and Elaine had only two trees that produced a combined total of 1000 pieces of fruit. 2. Elaine and Elsie’s trees produced a combined total of 700 peaches and 700 limes. 3. Of course, Elsie’s lemon tree produced more lemons than Elaine’s lemon tree. 4. Elaine had exactly one tree that produced exactly 300 pieces of fruit. 5. Edward’s lemon tree produced more lemons than Elaine’s lemon tree. 6. Elsie had exactly two trees that produced exactly 300 pieces of fruit each.

m pl

e

Edward, Elaine and Elsie all had the same five types of fruit trees growing in their gardens. They each had a peach, an apple, a lemon, a lime and a pear tree in their gardens. One year, they kept a careful record of the fruit production of each of their trees and compared the results. They grew 500, 400 and 300 peaches. They grew 500, 400 and 300 apples. They grew 500, 400 and 300 lemons. They grew 500, 400 and 300 limes. They grew 500, 400 and 300 pears. Based on the clues, match the gardeners with the number of peaches, apples, lemons, limes and pears they grew.

500 peaches 400 peaches 300 peaches 500 apples 400 apples 300 apples

Elsie 500 peaches 400 peaches 300 peaches

500 apples 400 apples 300 apples

500 apples 400 apples 300 apples

500 lemons 400 lemons 300 lemons

500 lemons 400 lemons 300 lemons

500 lemons 400 lemons 300 lemons

500 limes 400 limes 300 limes

500 limes 400 limes 300 limes

500 limes 400 limes 300 limes

500 pears 400 pears 300 pears

500 pears 400 pears 300 pears

500 pears 400 pears 300 pears

Vi ew in

500 peaches 400 peaches 300 peaches

g

Elaine

sa

Edward

www.prim-ed.com

Prim-Ed Publishing

Maths perplexors

| 39


40

Charity drop 1. Faye successfully carried and served exactly 20 more main dishes than Fran. 2. The volunteer who successfully carried the most main dishes dropped the fewest main dishes and the fewest drinks as well. 3. Fred successfully carried a combined total of exactly 860 main dishes and drinks. 4. Fran successfully carried more drinks than Faye, and Fran dropped exactly 5 more dishes than Faye. 5. Fred dropped exactly 5 more drinks than Fran. 6. The volunteer who dropped the most dishes earned the least tips and, of course, Faye earned more tips than Fran.

sa

Fran

Faye

400 dish success 380 dish success 360 dish success

400 dish success 380 dish success 360 dish success

525 drink success 500 drink success 475 drink success

525 drink success 500 drink success 475 drink success

525 drink success 500 drink success 475 drink success

15 dish drop 10 dish drop 5 dish drop

15 dish drop 10 dish drop 5 dish drop

25 drink drop 20 drink drop 15 drink drop

25 drink drop 20 drink drop 15 drink drop

675 tips 650 tips 625 tips

675 tips 650 tips 625 tips

15 dish drop 10 dish drop 5 dish drop

25 drink drop 20 drink drop 15 drink drop

675 tips 650 tips 625 tips

40 | Maths perplexors

Vi ew in

400 dish success 380 dish success 360 dish success

g

Fred

The clues

m pl

Fred, Fran and Faye volunteered to wait on tables at a fundraising dinner to help raise money they could donate to charity. As amateurs, they did pretty well, but they did drop some main dishes and some drinks that they carried. They successfully carried and served 400, 380 and 360 main dishes. They successfully carried and served 525, 500 and 475 drinks. However, they dropped 15, 10 and 5 main dishes. They also dropped 25, 20 and 15 drinks. Despite the mishaps, they earned 675 tips, 650 tips and 625 tips, which they donated to charity. Based on the clues, match the volunteers with the number of main dishes and drinks they successfully carried and served, the number of main dishes and drinks they dropped, and the amount of tips they earned.

e

The story

Prim-Ed Publishing

www.prim-ed.com


41

The farmers are plotting

The story

The clues 1. Farmers Smith and Jones planted 500 hectares of corn and 1100 hectares of peppers. 2. Farmers Brown and Smith planted 500 hectares of beetroot and 1100 hectares of pumpkins. 3. Farmer Jones planted less corn than Farmer Smith, and Farmer Smith planted more peppers than Farmer Jones.

m pl

e

Farmers Brown, Smith and Jones each owned farms of exactly 2700 hectares. Each farmer divided his land into identical 200-, 300-, 400-, 500-, 600- and 700-hectare plots of land. All the farmers planted the exact same crops of corn, beetroot, beans, peppers, onions and pumpkins on their different-sized plots of land. However, all three farmers had different ideas when it came to deciding which of the crops should be planted on each differentsized plot of land. No farmer planted the same sized plot with the same crop as another farmer did. Based on the clues, match the farmers with the crops they planted on each different-sized plot of land.

Brown

200 corn 300 corn 400 corn

Jones

200 corn 300 corn 400 corn

200 corn 300 corn 400 corn

200 beetroot 300 beetroot 400 beetroot

200 beetroot 300 beetroot 400 beetroot

sa

Smith

200 beetroot 300 beetroot 400 beetroot

200 beans 300 beans 400 beans

200 beans 300 beans 400 beans

200 beans 300 beans 400 beans

500 peppers 600 peppers 700 peppers

500 peppers 600 peppers 700 peppers

500 peppers 600 peppers 700 peppers

500 onions 600 onions 700 onions

500 onions 600 onions 700 onions

500 onions 600 onions 700 onions

500 pumpkins 600 pumpkins 700 pumpkins

500 pumpkins 600 pumpkins 700 pumpkins

500 pumpkins 600 pumpkins 700 pumpkins

Vi ew in

g

www.prim-ed.com

Prim-Ed Publishing

Maths perplexors

| 41


42

A win-win-win situation The clues 1. Teresa and Theda sold 35 big screen TVs and 65 digital cameras. 2. Thomas and Theda sold 55 digital cameras and 30 big screen TVs. 3. Theda sold more radios than computers, and Teresa sold more DVD players than mobile phones.

e

Thomas, Teresa and Theda worked as salespeople at a local electronics shop. The owner of the shop decided to hold a month-long sales contest to encourage his employees to sell as many products as possible. The winner would be awarded 100 shares of the corporation’s stock. At the end of the month, it was discovered that it was a three-way tie as each salesperson sold exactly 135 items. They sold 20, 15 and 10 big screen TVs. They sold 20, 15 and 10 radios. They sold 20, 15 and 10 laptop computers. They sold 35, 30 and 25 DVD players. They sold 35, 30 and 25 mobile phones. They sold 35, 30 and 25 digital cameras. Of course, no salesperson sold the same number of any item more than once. Based on the clues, match the salespeople with the number of TVs, radios, computers, DVD players, mobile phones and cameras they sold.

m pl

The story

Teresa

20 TVs 15 TVs 10 TVs

20 TVs 15 TVs 10 TVs

20 TVs 15 TVs 10 TVs

20 radios 15 radios 10 radios

20 radios 15 radios 10 radios

20 radios 15 radios 10 radios

20 computers 15 computers 10 computers

20 computers 15 computers 10 computers

20 computers 15 computers 10 computers

35 DVD players 30 DVD players 25 DVD players

35 DVD players 30 DVD players 25 DVD players

35 DVD players 30 DVD players 25 DVD players

35 mobile phones 30 mobile phones 25 mobile phones

35 mobile phones 30 mobile phones 25 mobile phones

35 cameras 30 cameras 25 cameras

35 cameras 30 cameras 25 cameras

35 mobile phones 30 mobile phones 25 mobile phones

35 cameras 30 cameras 25 cameras

42 | Maths perplexors

Vi ew in

g

sa

Thomas

Prim-Ed Publishing

Theda

www.prim-ed.com


43

Go buy the book

The story

The clues 1. Zelda sold the most of exactly two types of books, and Zelda sold the fewest of exactly two types of books, but Zack and Zoe did exactly the same thing. 2. Zelda and Zack sold a combined total of exactly 260 westerns. 3. Zelda sold exactly 5 more romance novels than Zack, but Zack sold exactly 5 more mysteries than Zelda. 4. Zack sold exactly 5 more books of poetry than Zoe. 5. Zelda sold exactly 50 more fantasy novels than Zoe, but Zoe sold more books of poetry than Zelda. 6. Zack sold more fantasy novels than Zelda, and Zack also sold more romance novels than Zoe.

m pl

e

Zelda, Zack and Zoe were three bookshop owners who met at a convention. They compared their sales of the six most popular types of books with the previous month. They had sold 150, 140 and 120 western novels. They had sold 390, 385 and 380 romance novels. They had sold 550, 545 and 540 mystery novels. They had sold 255, 250 and 245 science fiction novels. They had sold 75, 70 and 65 books of poetry. They had sold 1100, 1050 and 1000 fantasy novels. Based on the clues, match the owners with the number of western novels, romance novels, mystery novels, science fiction novels, books of poetry, and fantasy novels they sold.

Zelda

150 western 140 western 120 western

Zoe

150 western 140 western 120 western

150 western 140 western 120 western

390 romance 385 romance 380 romance

390 romance 385 romance 380 romance

sa

Zack

390 romance 385 romance 380 romance

550 mystery 545 mystery 540 mystery

550 mystery 545 mystery 540 mystery

550 mystery 545 mystery 540 mystery

255 science fiction 250 science fiction 245 science fiction

255 science fiction 250 science fiction 245 science fiction

255 science fiction 250 science fiction 245 science fiction

Vi ew in

g

75 poetry 70 poetry 65 poetry

75 poetry 70 poetry 65 poetry

75 poetry 70 poetry 65 poetry

1100 fantasy 1050 fantasy 1000 fantasy

1100 fantasy 1050 fantasy 1000 fantasy

1100 fantasy 1050 fantasy 1000 fantasy

www.prim-ed.com

Prim-Ed Publishing

Maths perplexors

| 43


It‘s a dog‘s life

The story

1 hr scratching 2 hrs scratching 3 hrs scratching

1. Buddy and Bowser scratched for a combined total of exactly 5 hours each day. 2. Bowser and Barkly spent a combined total of 5 hours eating and 3 hours digging. 3. Buddy chewed exactly 4 more hours than he scratched. 4. Bowser spent twice as much time barking as he did scratching. 5. Buddy spent more time chewing than Barkly.

Bowser

Barkly

1 hr scratching 2 hrs scratching 3 hrs scratching

1 hr scratching 2 hrs scratching 3 hrs scratching

1 hr eating 2 hrs eating 3 hrs eating

1 hr eating 2 hrs eating 3 hrs eating

1 hr digging 2 hrs digging 3 hrs digging

1 hr digging 2 hrs digging 3 hrs digging

4 hrs chewing 6 hrs chewing 8 hrs chewing

4 hrs chewing 6 hrs chewing 8 hrs chewing

sa

Buddy

The clues

m pl

For no good reason, scientists decided to follow three dogs around for one 24-hour day and record everything they did during that time. The dogs were named Buddy, Bowser and Barkly. The scientists discovered that the three dogs all did exactly the same six doggy things, but none of the dogs did these things for the same amount of time as any other dog. The dogs scratched themselves for 1, 2 and 3 hours. The dogs ate for 1, 2 and 3 hours. The dogs enjoyed digging for 1, 2 and 3 hours. The dogs chewed stuff for 4, 6 and 8 hours. The dogs barked at nothing for 4, 6 and 8 hours. The dogs slept for 4, 6 and 8 hours. Based on the clues, match the dogs with the amount of time they scratched, ate, dug, chewed, barked and slept.

e

44

1 hr eating 2 hrs eating 3 hrs eating

1 hr digging 2 hrs digging 3 hrs digging

4 hrs chewing 6 hrs chewing 8 hrs chewing

4 hrs barking 6 hrs barking 8 hrs barking

4 hrs barking 6 hrs barking 8 hrs barking

4 hrs barking 6 hrs barking 8 hrs barking

4 hrs sleeping 6 hrs sleeping 8 hrs sleeping

4 hrs sleeping 6 hrs sleeping 8 hrs sleeping

4 hrs sleeping 6 hrs sleeping 8 hrs sleeping

44 | Maths perplexors

Vi ew in

g

Prim-Ed Publishing

www.prim-ed.com


45

Camel crossing

e

Chad

Carmen

15 years old 12 years old 10 years old

15 years old 12 years old 10 years old

Vi ew in

15 years old 12 years old 10 years old

1. The youngest camel drank the most water, travelled the fewest days, and ended the trip across the desert with only 8 monkeys left on its back. 2. The oldest camel drank the least water, travelled the most days, and ended the trip across the desert with 10 monkeys on its back. 3. Carol and Chad were paid a combined total of 25 coconuts and travelled a combined total of 22 days. 4. Carol was older than Chad and, of course, Carmen got paid more coconuts than Carol.

g

Carol

The clues

sa

Carol, Chad and Carmen were three camels, aged 15, 12 and 10 years old, who agreed to carry three groups of monkeys across the desert for payment in coconuts. The monkeys were in groups of 15, 12 and 10. Alas, the ride was bumpy and some of the monkeys fell off the backs of all three camels, so the camels ended up with fewer monkeys than they started with. The camels lost 5, 3 and 2 monkeys. Before they crossed the desert, the camels drank 10, 12 and 15 litres of water to prepare themselves for the long journey. The trips across the desert took 15, 12 and 10 days and, of course, the camels were paid 15, 12 and 10 coconuts. Based on the clues, match the camels with their ages, the number of monkeys they started out with, the number of monkeys they lost, the litres of water they drank, the days of their trips, and their payment in coconuts.

m pl

The story

15 monkeys 12 monkeys 10 monkeys

15 monkeys 12 monkeys 10 monkeys

15 monkeys 12 monkeys 10 monkeys

5 monkeys lost 3 monkeys lost 2 monkeys lost

5 monkeys lost 3 monkeys lost 2 monkeys lost

5 monkeys lost 3 monkeys lost 2 monkeys lost

15 litres 12 litres 10 litres

15 litres 12 litres 10 litres

15 litres 12 litres 10 litres

15-day trip 12-day trip 10-day trip

15-day trip 12-day trip 10-day trip

15-day trip 12-day trip 10-day trip

15 coconuts 12 coconuts 10 coconuts

15 coconuts 12 coconuts 10 coconuts

15 coconuts 12 coconuts 10 coconuts

www.prim-ed.com

Prim-Ed Publishing

Maths perplexors

| 45


Pet shop sales

The story

Walt, Wilma and Willard each owned a pet shop in the pleasant town of Gooferville. It was their custom to meet once a month and compare sales of various types of pets with the previous month. The owner who sold the most pets had the privilege of buying the other two owners their lunches. In the previous month, they sold 300, 250 and 200 hamsters. They sold 300, 250 and 200 rabbits. They sold 300, 250 and 200 puppies. They sold 275, 225 and 175 goldfish. They sold 275, 225 and 175 kittens. They sold 275, 225 and 175 birds. Based on the clues, match the pet shop owners with their sales of hamsters, rabbits, puppies, goldfish, kittens and birds.

1. Walt sold the most of three types of pets, and Willard also sold the most of three types of pets. 2. Walt sold the fewest of three types of pets, and Willard also sold the fewest of three types of pets. 3. If you added together Wilma’s sales of hamsters and puppies, the answer would be exactly 100 larger than Willard’s combined hamster and puppy sales total. 4. Walt sold more kittens than Wilma.

Wilma

m pl

Walt

The clues

e

46

Willard

300 hamsters 250 hamsters 200 hamsters

300 hamsters 250 hamsters 200 hamsters

300 hamsters 250 hamsters 200 hamsters

300 rabbits 250 rabbits 200 rabbits

300 rabbits 250 rabbits 200 rabbits

300 rabbits 250 rabbits 200 rabbits

300 puppies 250 puppies 200 puppies

275 goldfish 225 goldfish 175 goldfish

Vi ew in

g

sa

300 puppies 250 puppies 200 puppies

300 puppies 250 puppies 200 puppies

275 goldfish 225 goldfish 175 goldfish

275 goldfish 225 goldfish 175 goldfish

275 kittens 225 kittens 175 kittens

275 kittens 225 kittens 175 kittens

275 kittens 225 kittens 175 kittens

275 birds 225 birds 175 birds

275 birds 225 birds 175 birds

275 birds 225 birds 175 birds

46 | Maths perplexors

Prim-Ed Publishing

www.prim-ed.com


47

It‘s in the cards

The story

The clues 1. Before they lost any cards, shells and marbles, each of the three collectors had collected the most of one type of the items collected. 2. After she lost her football cards, Jane still had a respectable 450 cards left. 3. After she lost her marbles, Jolene still had 400 marbles left in her marble collection, and after she lost some seashells she still had 400 seashells left. 4. Before he lost some of his seashells, Jack had collected more seashells than Jolene. 5. After she lost some football cards, Jolene only had 250 cards left in her collection. 6. After she lost her marbles, Jane only had 300 marbles left in her marble collection. 7. Of course, Jack lost more seashells than Jane.

m pl

e

Jane, Jack and Jolene enjoyed collecting football cards, seashells and marbles. At the peak of their collections, they had collected an amazing 500, 450 and 400 cards. They had collected an astonishing 500, 450 and 400 seashells. They had collected an unbelievable 500, 450 and 400 marbles. Sadly, through a series of unhappy circumstances, they all lost some cards, seashells and marbles. They lost 150, 100 and 50 cards. They lost 150, 100 and 50 seashells. They lost 150, 100 and 50 marbles. Based on the clues, match the collectors with the size of their collections before they lost any cards, seashells and marbles, and with their losses of cards, seashells and marbles.

Jack

sa

Jane

500 cards 450 cards 400 cards

500 seashells 450 seashells 400 seashells

500 seashells 450 seashells 400 seashells

500 seashells 450 seashells 400 seashells

500 marbles 450 marbles 400 marbles

500 marbles 450 marbles 400 marbles

500 marbles 450 marbles 400 marbles

150 lost cards 100 lost cards 50 lost cards

150 lost cards 100 lost cards 50 lost cards

150 lost cards 100 lost cards 50 lost cards

150 lost shells 100 lost shells 50 lost shells

150 lost shells 100 lost shells 50 lost shells

150 lost shells 100 lost shells 50 lost shells

150 lost marbles 100 lost marbles 50 lost marbles

150 lost marbles 100 lost marbles 50 lost marbles

Vi ew in

g

500 cards 450 cards 400 cards

Jolene

150 lost marbles 100 lost marbles 50 lost marbles

www.prim-ed.com

Prim-Ed Publishing

500 cards 450 cards 400 cards

Maths perplexors

| 47


48

Check your toytals

Bertha, Bonnie and Billy were managers of separate shops for the Acme Toy Corporation. As part of their duties they had to submit a monthly report of toy sales to corporate headquarters, giving exact sales figures for the six most popular items. One month, they sold 955, 950 and 945 dolls. They sold 1050, 1000 and 950 games. They sold 890, 880 and 870 yoyos. They sold 900, 885 and 850 jigsaw puzzles. They sold 860, 840 and 820 rubber balls. They sold 830, 810 and 790 spinning tops. Based on the clues, match the managers with their monthly sales figures for dolls, games, yoyos, puzzles, balls and tops.

1. Each manager sold the most of two types of toys, and each manager also sold the least of two types of toys. 2. Bonnie sold exactly 5 more dolls than Bertha and exactly 50 more games than Bertha. 3. Billy sold exactly 5 fewer dolls than Bertha and exactly 50 fewer games than Bertha. 4. Bonnie sold exactly 20 more balls than Bertha and exactly 20 more tops than Bertha.

Bonnie

m pl

Bertha

The clues

e

The story

Billy

955 dolls 950 dolls 945 dolls

955 dolls 950 dolls 945 dolls

1050 games 1000 games 950 games

1050 games 1000 games 950 games

1050 games 1000 games 950 games

890 yoyos 880 yoyos 870 yoyos

890 yoyos 880 yoyos 870 yoyos

890 yoyos 880 yoyos 870 yoyos

900 puzzles 885 puzzles 850 puzzles

900 puzzles 885 puzzles 850 puzzles

900 puzzles 885 puzzles 850 puzzles

860 balls 840 balls 820 balls

860 balls 840 balls 820 balls

860 balls 840 balls 820 balls

830 tops 810 tops 790 tops

830 tops 810 tops 790 tops

830 tops 810 tops 790 tops

48 | Maths perplexors

Vi ew in

g

sa

Prim-Ed Publishing

955 dolls 950 dolls 945 dolls

www.prim-ed.com


49

Classy flower power 1. Class 5 planted a combined total of 25 metres with roses and tulips. 2. Classes 5 and 6 planted a combined total of 35 metres with daisies. 3. Of course, Class 6 planted more roses than tulips. 4. Class 5 planted a combined total of 55 metres of pansies and petunias. 5. Class 7 planted a combined total of 55 metres of lilies and pansies and, of course, Class 7 planted more lilies than Class 6.

Class 6

Class 7

10 metres roses 15 metres roses 20 metres roses

10 metres roses 15 metres roses 20 metres roses

10 metres tulips 15 metres tulips 20 metres tulips

10 metres tulips 15 metres tulips 20 metres tulips

10 metres daisies 15 metres daisies 20 metres daisies

10 metres daisies 15 metres daisies 20 metres daisies

25 metres lilies 30 metres lilies 35 metres lilies

25 metres lilies 30 metres lilies 35 metres lilies

25 metres pansies 30 metres pansies 35 metres pansies

25 metres pansies 30 metres pansies 35 metres pansies

25 metres pansies 30 metres pansies 35 metres pansies

25 metres petunias 30 metres petunias 35 metres petunias

25 metres petunias 30 metres petunias 35 metres petunias

25 metres petunias 30 metres petunias 35 metres petunias

10 metres roses 15 metres roses 20 metres roses

Vi ew in

10 metres tulips 15 metres tulips 20 metres tulips

sa

Class 5

g

The clues

m pl

The pupils at Southlands School loved flowers and logic problems. Each year, the school had a tradition of planting six different types of flowers along its 405-metre boundary line. The school divided that 405 metres into three identical 135-metre parts. Each 48-metre part was divided into identical 10-, 15-, 20-, 25-, 30- and 35-metre sections. The sections were to be planted with roses, tulips, daisies, lilies, pansies and petunias. This year, the honour of planting the sections was assigned to Classes 5, 6 and 7. The logic part of the exercise was, the classes had to figure out a way to plant all six sections with all six types of flowers without any class planting the same type of flower in the same length section as another class. Based on the clues, see if you can figure out this year’s planting plan.

e

The story

10 metres daisies 15 metres daisies 20 metres daisies

25 metres lilies 30 metres lilies 35 metres lilies

www.prim-ed.com

Prim-Ed Publishing

Maths perplexors

| 49


50

Who is the dealer?

The Acme car dealership sold six different types of automobiles. Pauline, Peter and Peggy were the top three salespeople at the dealership. Last month, by an amazing coincidence, they all sold exactly 210 automobiles. They sold 30, 20 and 10 4WDs. They sold 30, 20 and 10 convertibles. They sold 30, 20 and 10 vans. They sold 60, 50 and 40 sports cars. They sold 60, 50 and 40 coupes. They sold 60, 50 and 40 luxury cars. Based on the clues, match the salespeople with the number of 4WDs, convertibles, vans, sports cars, coupes and luxury cars they sold to reach the 210 total they each sold for the month.

1. Peter sold a combined total of exactly 50 4WDs and convertibles and a combined total of exactly 100 coupes and luxury cars. 2. Pauline sold a combined total of exactly 40 4WDs and convertibles and a combined total of exactly 100 sports cars and coupes. 3. Pauline sold more 4WDs than Peter, and Peter sold more coupes than Peggy.

Peter

m pl

Pauline

The clues

30 4WDs 20 4WDs 10 4WDs

30 4WDs 20 4WDs 10 4WDs

30 convertibles 20 convertibles 10 convertibles

30 convertibles 20 convertibles 10 convertibles

30 vans 20 vans 10 vans

60 sports cars 50 sports cars 40 sports cars

60 coupes 50 coupes 40 coupes

60 luxury cars 50 luxury cars 40 luxury cars

g

sa

50 | Maths perplexors

e

The story

Peggy 30 4WDs 20 4WDs 10 4WDs 30 convertibles 20 convertibles 10 convertibles 30 vans 20 vans 10 vans

60 sports cars 50 sports cars 40 sports cars

60 sports cars 50 sports cars 40 sports cars

60 coupes 50 coupes 40 coupes

60 coupes 50 coupes 40 coupes

60 luxury cars 50 luxury cars 40 luxury cars

60 luxury cars 50 luxury cars 40 luxury cars

Vi ew in

30 vans 20 vans 10 vans

Prim-Ed Publishing

www.prim-ed.com


Answers 1. Bakers get the blues

12. Just dropping by

Nate

Nellie Nick Mary

Martha Mabel

10 pies 5 muffins

15 pies 10 muffins

30 cups 20 glasses 10 plates

5 pies 15 muffins

20 cups 10 glasses 30 plates

2. A croc pot?

13. You auto know

Sherman Alice Bert 20 baboons 4 lost

16 baboons 8 lost

12 baboons 6 lost

3. Beehive yourself! Buzz Bill Bob 150 flowers 25 stings

200 flowers 20 stings

Alex

Alice Anne

25 years 30 flat tyres 35 km/L

35 years 30 years 25 flat tyres 35 flat tyres 30 km/L 25 km/L

14. Sneeze the day!

100 flowers 10 stings

Nancy Nick Nora

Rita Rolanda

7 worms 11 eggs

9 worms 9 eggs

15. Coconuts downriver

5. Snap out of it! Shane Sidney

250 snaps 16 years old

300 snaps 12 years old

6. And the whinny is‌ Hiram Hank Hannah 70 apples 70 flies

65 apples 75 flies

g

75 apples 65 flies

7. Parrot party

Bonkly

Booker Boomer

25 coconuts 8 dropped 50 bananas

26 coconuts 12 dropped 40 bananas

28 coconuts 14 dropped 45 bananas

16. Cat in a hat

Bucky

Huckly Mouser

9 hats 7 vests 3 scarves

7 hats 9 vests 5 scarves

sa

275 snaps 14 years old

80 sneezes 75 coughs 155 tissues

m pl

11 worms 7 eggs

95 sneezes 96 coughs 130 tissues

e

Ruth

100 sneezes 80 coughs 180 tissues

4. A fair worming!

Sarah

10 cups 30 glasses 20 plates

11 hats 5 vests 7 scarves

17. Giraffe losers?

Peter Paul

Gail

Gordon Gilda

11 cups 23 cupcakes

13 cups 16 cups 25 cupcakes 22 cupcakes

3 m 27 lions 36 coins

2 m 33 lions 32 coins

Vi ew in

Polly

8. Happy webbing day

Sylvia

Sharon Shana

12 cm 10 flies

10 cm 9 flies

9. A carrot caper

9 cm 12 flies

Spike

Mike Rex

30 picked 10 dropped

25 picked 15 dropped

35 picked 5 dropped

10. Barking lots Biff

Byron Belle

5 postal workers 49 barks

9 postal workers 55 barks

13 postal workers 43 barks

11. Coffee lorries Peter

Pam Penny

18 wheels 320 km 10 cups

6 wheels 180 km 15 cups

www.prim-ed.com

12 wheels 240 km 20 cups

Prim-Ed Publishing

4m 30 lions 25 coins

18. A fair time Roger

Roland Ryan

14 bags peanuts 14 sandwiches 9 cups soft drink

16 bags peanuts 18 sandwiches 11 cups soft drink

18 bags peanuts 16 sandwiches 10 cups soft drink

19. Camping delights Jake

Jane Jill

15 bears 25 coyotes 6 snakes

20 bears 30 coyotes 4 snakes

10 bears 20 coyotes 8 snakes

20. A raft of thrills Henry

Hilda Harriet

10 years 17 passengers 5 overboard

8 years 20 passengers 3 overboard

14 years 12 passengers 7 overboard

21. Artful lodgers Cathy

Carol Chuck

23 landscapes 30 portraits 10 waterscapes 18 dogs

21 landscapes 20 portraits 15 waterscapes 16 dogs

25 landscapes 25 portraits 25 waterscapes 14 dogs

Maths perplexors

| 51


Answers 30. And the dinner is …

22. The defence rests Maxine

Melvin Maggie

Hector

Harriet Hester

5 years 95 cases 10 lost 20 days

10 years 100 cases 15 lost 10 days

250 sandwiches 150 pies 200 sausage rolls 150 soft drinks

200 sandwiches 250 pies 150 sausage rolls 200 soft drinks

15 years 90 cases 20 lost 15 days

150 sandwiches 200 pies 250 sausage rolls 250 soft drinks

31. Eating elephants

23. I suspect fowl play Gertie

Grace Greta

Dwayne Darla Daphne

50 singles 90 doubles 60 triples 48 home runs

75 singles 70 doubles 75 triples 54 home runs

450 cherry 400 apple 800 peach 500 pumpkin 350 blueberry

100 singles 80 doubles 55 triples 56 home runs

24. Climb every mountain David Darlene

14 years 11 mountains 13 countries 12 m fall

13 years 14 mountains 11 countries 14 m fall

32. Garden of eatin‘

11 years 13 mountains 14 countries 15 m fall

21 trout 22 bass 18 salmon 17 tuna

25 trout 20 bass 21 salmon 18 tuna

23 trout 19 bass 20 salmon 19 tuna

26. One 24-hour sty

27. Nuts we lost

8 hrs eating 10 hrs sleeping 6 hrs oinking 23 kg swill

10 hrs eating 6 hrs sleeping 8 hrs oinking 19 kg swill

Steve

Sheldon Shirley

65 walnuts hidden 60 almonds hidden 5 walnuts lost 6 almonds lost

75 walnuts hidden 69 almonds hidden 7 walnuts lost 10 almonds lost

70 walnuts hidden 72 almonds hidden 10 walnuts lost 12 almonds lost

28. In this corner Biff

Benny Boris

8 years 20 won 6 lost 10 noses

10 years 15 won 5 lost 16 noses

12 years 18 won 3 lost 14 noses

29. You‘re fired up! Frank

Farrah Felicity

25 years 100 women 96 men 90 babies

20 years 95 women 89 men 88 babies

52 | Maths perplexors

Gregory 50 tomatoes 49 cucumbers 50 potatoes 40 radishes 42 peppers

33. Did you trip?

Vi ew in

6 hrs eating 8 hrs sleeping 10 hrs oinking 27 kg swill

60 tomatoes 54 cucumbers 49 potatoes 45 radishes 39 peppers

Toula

Tammy Tori

32 countries 30 days travel 14 museums 15 parks 5 days sick

30 countries 28 days travel 15 museums 14 parks 6 days sick

28 countries 32 days travel 16 museums 16 parks 4 days sick

g

Snorts Pixie Trotter

Gail

55 tomatoes 59 cucumbers 48 potatoes 49 radishes 35 peppers

sa

Ivan Irene

George

m pl

25. The old fishing hole Inez

500 cherry 300 apple 600 peach 400 pumpkin 450 blueberry

e

Diane

400 cherry 350 apple 700 peach 600 pumpkin 400 blueberry

23 years 90 women 91 men 93 babies

34. Town talent Mopeville

Kookston Loopin

200 yodellers 450 jugglers 245 magicians 300 dancers 290 acrobats

180 yodellers 475 jugglers 250 magicians 285 dancers 280 acrobats

190 yodellers 500 jugglers 240 magicians 315 dancers 275 acrobats

35. Lost without you Bunky

Bjorn Bixby

475 shoes 650 gym shorts 195 glasses 196 pens 590 beanies

500 shoes 450 shoes 600 gym shorts 700 gym shorts 200 glasses 190 glasses 189 pens 187 pens 550 beanies 660 beanies

36. Anyone want a buggy ride? Clem

Charly Callie

1200 cockroaches 950 ants 800 bedbugs 785 fleas 615 ticks

1000 cockroaches 1150 ants 780 bedbugs 735 fleas 625 ticks

1100 cockroaches 1050 ants 795 bedbugs 750 fleas 620 ticks

37. A tough race Oscar

Olive Oona

490 speeches 980 promises 760 pledges 475 commitments 6400 votes

495 speeches 950 promises 750 pledges 500 commitments 6450 votes

Prim-Ed Publishing

480 speeches 990 promises 770 pledges 450 commitments 6500 votes www.prim-ed.com


Answers 45. Camel crossing

38. You ain‘t lion Mongo

Bongo Tongo

Carol

Chad Carmen

490 fleas 480 nits 475 ear mites 25 bald spots 15 hairballs

600 fleas 490 nits 485 ear mites 21 bald spots 14 hairballs

12 years old 12 monkeys 3 monkeys lost 12 litres 12 days 10 coconuts

10 years old 10 monkeys 2 monkeys lost 15 litres 10 days 15 coconuts

500 fleas 500 nits 480 ear mites 23 bald spots 13 hairballs

39. Tree fruitful

46. Pet shop sales

400 peaches 500 apples 300 lemons 400 limes 500 pears

300 peaches 400 apples 500 lemons 300 limes 400 pears

40. Charity drop Fred

Fran Faye

360 dish success 500 drink success 15 dish drop 25 drink drop 625 tips

380 dish success 525 drink success 10 dish drop 20 drink drop 650 tips

200 corn 400 beetroot 300 beans 500 peppers 600 onions 700 pumpkins

g

300 corn 200 beetroot 400 beans 600 peppers 700 onions 500 pumpkins

Vi ew in

400 corn 300 beetroot 200 beans 700 peppers 500 onions 600 pumpkins

42. A win-win-win situation

Thomas Teresa Theda 10 TVs 20 radios 15 computers 35 DVD players 30 mobile phones 25 cameras

15 TVs 10 radios 20 computers 30 DVD players 25 mobile phones 35 cameras

20 TVs 15 radios 10 computers 25 DVD players 35 mobile phones 30 cameras

43. Go buy the book Zelda

Zack Zoe

140 western 120 western 150 western 390 romance 385 romance 380 romance 540 mystery 545 mystery 550 mystery 255 science fiction 245 science fiction 250 science fiction 65 poetry 75 poetry 70 poetry 1050 fantasy 1100 fantasy 1000 fantasy

44. It‘s a dog‘s life Buddy

Bowser Barkly

2 hrs scratching 1 hr eating 3 hrs digging 6 hrs chewing 4 hrs barking 8 hrs sleeping

3 hrs scratching 2 hrs eating 1 hr digging 8 hrs chewing 6 hrs barking 4 hrs sleeping

www.prim-ed.com

250 hamsters 250 rabbits 250 puppies 225 goldfish 225 kittens 225 birds

200 hamsters 300 rabbits 200 puppies 275 goldfish 175 kittens 275 birds

47. It‘s in the cards Jane

Jack Jolene

500 cards 400 seashells 450 marbles 50 lost cards 100 lost shells 150 lost marbles

450 cards 500 seashells 400 marbles 100 lost cards 150 lost shells 50 lost marbles

sa

41. The farmers are plotting Brown Smith Jones

Wilma Willard

300 hamsters 200 rabbits 300 puppies 175 goldfish 275 kittens 175 birds

m pl

400 dish success 475 drink success 5 dish drop 15 drink drop 675 tips

Walt

e

Edward Elaine Elsie 500 peaches 300 apples 400 lemons 500 limes 300 pears

15 years old 15 monkeys 5 monkeys lost 10 litres 15 days 12 coconuts

400 cards 450 seashells 500 marbles 150 lost cards 50 lost shells 100 lost marbles

48. Check your toytals Bertha

Bonnie Billy

950 dolls 1000 games 890 yoyos 900 puzzles 820 balls 790 tops

955 dolls 1050 games 870 yoyos 850 puzzles 840 balls 810 tops

945 dolls 950 games 880 yoyos 885 puzzles 860 balls 830 tops

Class 5

Class 6

Class 7

10 m roses 15 m tulips 20 m daisies 35 m lilies 30 m pansies 25 m petunias

20 m roses 10 m tulips 15 m daisies 30 m lilies 35 m pansies 30 m petunias

15 m roses 20 m tulips 10 m daisies 25 m lilies 25 m pansies 35 m petunias

49. Classy flower power

50. Who is the dealer? Pauline Peter Peggy 30 4WDs 10 convertibles 20 vans 60 sports cars 40 coupes 50 luxury cars

20 4WDs 30 convertibles 10 vans 50 sports cars 60 coupes 40 luxury cars

10 4WDs 20 convertibles 30 vans 40 sports cars 50 coupes 60 luxury cars

1 hr scratching 3 hrs eating 2 hrs digging 4 hrs chewing 8 hrs barking 6 hrs sleeping

Prim-Ed Publishing

Maths perplexors

| 53


6066 Maths Perplexors ages 8-9