Maths Perplexors: Ages 12-13 by Teacher Superstore

RIC-6070 2.85/1164

Maths perplexors (Ages 12–13) Published by R.I.C. Publications® 2009 under licence to © 2007 MindWare Holdings Inc. Copyright © 2007 MindWare Holdings Inc. This version copyright © R.I.C. Publications® 2009

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Introduction

Contents

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

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

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

Dog days .......................................... 1 Farm fitting ....................................... 2 Getting petrol ................................... 3 Vegetable stew ................................. 4 Fair eating ......................................... 5 Vertical schooling ............................. 6 Hoot’s there? .................................... 7 What’s cooking? ............................... 8 That’s class ....................................... 9 Fair contests .................................... 10 Bests in baking ............................... 11 Fishing eagles ................................. 12 Bear with me .................................. 13 Whale tales .................................... 14 Fruit files ........................................ 15 Hidden nuts .................................... 16 Hits just a game .............................. 17 A day at the beach .......................... 18 Just for the farm of it ....................... 19 To bee or not to bee ........................ 20 Farm figures .................................... 21 Lucky numbers ............................... 22 Oh, brother! ................................... 23 You auto know this ......................... 24 Flower children .............................. 25 Something to crow about ................ 26 Good knight ................................... 27 Who’s on first? ................................ 28 Lighthouse School .......................... 29 Your vote counts ............................. 30 Gaining yards ................................. 31 Hooked on fishing .......................... 32 Herd around the town .................... 33 Eating lizards .................................. 34 Rug makers ..................................... 35 Cycling cicadas .............................. 36 Dancing hippos .............................. 37 Towns that work ............................. 38 Sandcastles ..................................... 39 How have you bean doing? ............ 40 Basketball anyone? ......................... 41 Travelling for days ........................... 42 Happy birthday ............................... 43 Thanksgiving feast .......................... 44 I ate it on the street ......................... 45 Hopping cows ................................ 46 It’s all in the pasta ........................... 47 Sports day fun ................................. 48 Marooned ....................................... 49 You auto have fun ........................... 50 Answers .................................... 51–53

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

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

Lessons

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

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There are many ways in which these puzzles can be used in a classroom. The following are examples only, not an exhaustive list. Homework This is not a ‘more of the same’ activity; it is an opportunity for students to consolidate and expand on what they have learnt in the classroom.

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

Small-group problem-solving Thinking and talking mathematically are two vital skills. By working on the logic puzzles in pairs or small groups, thinking and talking about the problem, students can share and strengthen these skills. Whole-class challenges Teacher assistance may be required with some students; modelling is an effective strategy. ‘Extras’ This is mainly a fun activity/challenge for the more mathematically able or advanced students.

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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 recent day they ate 40, 20, and 10 flies for dinner. Based on the clues, match the geckos with their ages and fly ‘consumptions’.

1. Multiply Greg’s age by 10 and the answer is the number of flies he ate for dinner. 2. Gail ate twice as many flies as the oldest gecko.

Greg 8 years old 4 years old 2 years old

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Gordon

8 years old 4 years old 2 years old

40 flies 20 flies 10 flies

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40 flies 20 flies 10 flies

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

Greg

Gail

Gordon

8 years old 4 years old 2 years old

40 flies 20 flies 10 flies

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

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

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8 years old 4 years old 2 years old

40 flies 20 flies 10 flies

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

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Dog days The clues

Spot, Fido and Duke were three dogs of varying sizes. They weighed 27, 18 and 9 kilograms. They spent their days doing exactly the same things, but no dog spent the same amount of time doing any one thing as any other dog. They spent 10, 8 and 6 hours sleeping. They spent 10, 8 and 6 hours barking. They spent 10, 8 and 6 hours scratching. Based on the clues, match the dogs with their weights and how they each spent their 24-hour day.

1. Subtract Spot’s weight from Fido’s weight to determine Duke’s weight. 2. Spot and Fido spent a combined total of 18 hours sleeping. 3. Spot and Duke spent a combined total of 18 hours barking. 4. Duke scratched more than Fido, and the lightest dog slept the least.

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The story

Spot

Fido

Duke

27 kg 18 kg 9 kg

10 hrs sleeping 8 hrs sleeping 6 hrs sleeping

10 hrs barking 8 hrs barking 6 hrs barking

10 hrs scratching 8 hrs scratching 6 hrs scratching

27 kg 18 kg 9 kg

10 hrs sleeping 8 hrs sleeping 6 hrs sleeping

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Maths perplexors

Farm fitting The clues

Farmers Brown, Smith and Jones all had farms of exactly 2100 acres. Each farm had a 600-acre plot, a 500-acre plot, a 400-acre plot, a 300-acre plot, a 200-acre plot, and a 100-acre plot. The farmers all grew the same crops of corn, beans, carrots, wheat, tomatoes and squash. Of course, no farmer devoted the same acreage of land to any one crop as any other farmer in using their entire 2100 acres of land. Based on the clues, match the farmers with the acreage they each devoted to the six crops.

1. Farmers Brown and Smith grew a combined total of 1000 acres of corn. 2. Farmers Smith and Jones grew a combined total of 500 acres of beans. 3. Farmers Brown and Jones grew a combined total of 1000 acres of carrots. 4. Farmers Brown and Smith grew a combined total of 500 acres of wheat. 5. Farmers Smith and Jones grew a combined total of 900 acres of corn. 6. Farmers Brown and Smith grew a combined total of 300 acres of beans.

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Brown

Smith

600 corn 500 corn 400 corn

300 beans 200 beans 100 beans

300 wheat 200 wheat 100 wheat

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600 carrots 500 carrots 400 carrots

300 squash 200 squash 100 squash

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600 corn 500 corn 400 corn

600 carrots 500 carrots 400 carrots

600 tomatoes 500 tomatoes 400 tomatoes

Jones

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300 beans 200 beans 100 beans

600 carrots 500 carrots 400 carrots

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300 beans 200 beans 100 beans

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300 wheat 200 wheat 100 wheat

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600 tomatoes 500 tomatoes 400 tomatoes

300 squash 200 squash 100 squash

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Getting petrol The clues

Billy, Betty, Bobbi and Burt were in a petrol station filling their cars with petrol. They were 40, 30, 25 and 20 years old. They weighed 150, 114, 75 and 57 kilograms. Their cars took 76, 72, 68 and 57 litres of petrol. In the year 2007, their cars were 20, 17, 15 and 10 years old. Based on the clues, match the names with their ages, weights, litres of petrol and the ages of their cars in 2007.

1. In 2007, the 1987 truck took the most petrol, the 1990 coupe took the least petrol, and the 1997 van took exactly 4000 mL more petrol than the 1992 sedan. 2. The youngest driver took exactly 15 000 mL fewer litres of petrol than the oldest driver who drove the newest car. 3. The lightest driver’s weight was one-half the weight of the oldest driver. 4. Divide Billy’s car age by two to discover Burt’s car age as of 2007. 5. Bobbi was exactly 10 years younger than Burt. 6. Multiply the youngest driver’s weight by two to find the weight of the driver of the 1987 truck. 7. Multiply Billy’s age by three to determine Betty’s weight.

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Billy

Betty

Bobbi

40 years old 30 years old 25 years old 20 years old

150 kg 114 kg 75 kg 57 kg

76 L 72 L 68 L 57 L

20 yrs car 17 yrs car 15 yrs car 10 yrs car

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20 yrs car 17 yrs car 15 yrs car 10 yrs car

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40 years old 30 years old 25 years old 20 years old

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150 kg 114 kg 75 kg 57 kg

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76 L 72 L 68 L 57 L

20 yrs car 17 yrs car 15 yrs car 10 yrs car

Maths perplexors

Vegetable stew The clues

Carl, Callie, Charli and Craig were comparing their favourite recipes for vegetable stew. They used the same four vegetables in their stews but each used a different amount of each vegetable in their recipes. They used 30, 27, 24 and 20 carrots. They used 17, 15, 13 and 12 potatoes. They used 40, 35, 34 and 26 tomatoes. They used 60, 54, 48 and 40 onions. Based on the clues, match the names with the number of carrots, potatoes, tomatoes and onions they each used in their recipes.

1. Callie’s recipe called for two tomatoes and three onions for each carrot in her stew. 2. Carl and Callie had a combined total of 25 potatoes in their recipes. 3. Carl and Craig had a combined total of 88 onions in their recipes. 4. Carl and Callie used a combined total of 50 carrots and 100 onions in their recipes. 5. Craig used three more carrots than Charli, and Charli used two fewer potatoes than Craig. 6. The person who used the fewest potatoes used the most carrots. 7. Multiply Craig’s potato number by two to discover Charli’s tomato number and, of course, Carl’s recipe did not call for the fewest tomatoes.

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Carl

Charli

17 potatoes 15 potatoes 13 potatoes 12 potatoes

40 tomatoes 35 tomatoes 34 tomatoes 26 tomatoes

60 onions 54 onions 48 onions 40 onions

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30 carrots 27 carrots 24 carrots 20 carrots

60 onions 54 onions 48 onions 40 onions

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30 carrots 27 carrots 24 carrots 20 carrots

17 potatoes 15 potatoes 13 potatoes 12 potatoes

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30 carrots 27 carrots 24 carrots 20 carrots

Callie

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40 tomatoes 35 tomatoes 34 tomatoes 26 tomatoes

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60 onions 54 onions 48 onions 40 onions

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Fair eating The clues

Joan, John, Jake and Jane entered four eating contests at their local country fair. They ate 24, 22, 21 and 18 pies. They ate 50, 48, 44 and 38 hot dogs. They ate 100, 96, 88 and 80 tacos. They ate 20, 15, 14 and 10 burgers. Based on the clues, match the names with the number of pies, hot dogs, tacos and burgers they ate that day.

1. Each one of the eaters ate the most of one of the four food items, and each one also ate the least of one of the four food items. 2. Joan and Jane ate a combined total of 39 pies and 196 tacos. 3. Joan and John ate a combined total of 98 hot dogs and 25 burgers. 4. Jane did not eat the least hot dogs, and John did not eat the most pies.

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Joan

John

Jake

24 pies 22 pies 21 pies 18 pies

50 hot dogs 48 hot dogs 44 hot dogs 38 hot dogs

100 tacos 96 tacos 88 tacos 80 tacos

20 burgers 15 burgers 14 burgers 10 burgers

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Jane

24 pies 22 pies 21 pies 18 pies

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100 tacos 96 tacos 88 tacos 80 tacos

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20 burgers 15 burgers 14 burgers 10 burgers

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Vertical schooling The clues

Grace, Greg, Gail and Gordon were the Years 1, 2, 3 and 4 teachers at the Bates High School. The school was a little unusual because it had a first, second, third and fourth floor with each class having its own floor. The classes had 16, 15, 13 and 12 girls, and 17, 14, 11 and 10 boys in them. Based on the clues, match the teachers with the years they taught, the floors they were on, and the number of girls and boys in their classes.

1. None of the year numbers matched the floor numbers. 2. Greg complained about the noise Grace’s class made in the room directly above him, and Gail complained about the noise Gordon’s class made in the room directly above her. 3. Gordon was not on the top floor. 4. Gail’s class was the only one with more boys than girls in it, and Grace and Greg did not teach Years 1 or 2. 5. Year 2 had the most girls. 6. Grace and Greg had a combined total of 25 girls in their classes. 7. Grace did have more girls in her class than Greg, but Greg had more boys in his class than Grace.

Greg

Gail

Year 1 Year 2 Year 3 Year 4

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

16 girls 15 girls 13 girls 12 girls

17 boys 14 boys 11 boys 10 boys

Year 1 Year 2 Year 3 Year 4

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17 boys 14 boys 11 boys 10 boys

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Gordon

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Year 1 Year 2 Year 3 Year 4

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

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Grace

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16 girls 15 girls 13 girls 12 girls

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17 boys 14 boys 11 boys 10 boys

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Hoot’s there? The clues

Four owls, named Oscar, Olivia, Ollie and Opal, lived in the Glenview Forest. They were 10, 6, 4 and 2 years old. They lived in trees that were 120, 100, 60 and 50 cm in diameter. One recent day, they competed against each other in two contests. The first contest was to see who could catch the most mice in an hour, and they caught 28, 24, 14 and 12 mice in an hour. The second contest was to see who could hoot the most times in a minute, and they hooted 78, 70, 39 and 35 hoots in a minute. Based on the clues, match the owls with their ages, tree sizes, mice caught and hoots per minute.

1. If you subtracted Olivia’s age from Oscar’s age, the answer would be Ollie’s age. 2. Ollie’s tree diameter was the same as Oscar’s tree radius, and Olivia’s tree radius was the same as Opal’s tree diameter. 3. Ollie caught twice as many mice as Olivia, and Oscar caught half as many mice as Opal. 4. Opal made half as many hoots as Olivia, and Oscar made twice as many hoots as Ollie. 5. Oscar was younger than Opal. 6. The youngest owl lived in the smallest tree, caught the most mice, and was the worst at hooting.

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Oscar

Olivia

Ollie

Opal

10 years old 6 years old 4 years old 2 years old

120 cm 100 cm 60 cm 50 cm

28 mice 24 mice 14 mice 12 mice

10 years old 6 years old 4 years old 2 years old

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78 hoots 70 hoots 39 hoots 35 hoots

Maths perplexors

What’s cooking? The clues

The towns of Glenview, Northbrook, Northfield and Deerfield recently recorded what their town monkeys did with their weekly shipment of 1000 bananas apiece. The monkeys used 100, 200, 300 and 400 bananas to make pies. The monkeys used 100, 200, 300 and 400 bananas to make bread. The monkeys used 100, 200, 300 and 400 bananas to make cakes. The monkeys used 100, 200, 300 and 400 bananas to make pudding. Based on the clues, match the towns with the number of bananas their monkeys used to make pies, breads, cakes and puddings.

1. Glenview and Deerfield used a combined total of 300 bananas to make pies, and they used a combined total of 300 bananas to make pudding. 2. Subtract Northbrook’s pie number from Northfield’s pie number to reveal Deerfield’s pie number. 3. Add Northbrook’s bread number to Northfield’s bread number to discover Deerfield’s bread number. 4. Multiply Northfield’s cake number by two to find Northfield’s bread number.

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Glenview

Northbrook

Northfield

100 pies 200 pies 300 pies 400 pies

100 bread 200 bread 300 bread 400 bread

100 cakes 200 cakes 300 cakes 400 cakes

100 pudding 200 pudding 300 pudding 400 pudding

100 pies 200 pies 300 pies 400 pies

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Deerfield

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100 bread 200 bread 300 bread 400 bread 100 cakes 200 cakes 300 cakes 400 cakes

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100 bread 200 bread 300 bread 400 bread

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100 pudding 200 pudding 300 pudding 400 pudding

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That’s class The clues

Allie, Ben, Carol, Dick and Eliot taught Years 1, 2, 3, 4 and 5 at Pleasant Valley Primary. They had 22, 21, 20, 17 and 15 boys in their classes, and 19, 18, 14, 13 and 10 girls in their classes. Based on the clues, match the teachers with their years, and the number of boys and girls in their classes.

1. Carol and Dick would rather teach Years 1, 2 or 3 in preference to the years they taught. 2. Eliot wanted to teach Years 2 or 3 in preference to the year he taught. 3. Ben taught one year level higher than Eliot, and Carol taught one year level lower than Dick. 4. Years 4 and 5 had more girls than boys in them. 5. Multiply the Year 3’s girl number by two to discover the Year 1’s boy number. 6. Year 5 did not have the least boys or the most girls. 7. Year 2 had a total of 34 students.

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Allie

Ben

Carol

Dick

Year 1 Year 2 Year 3 Year 4 Year 5

22 boys 21 boys 20 boys 17 boys 15 boys

19 girls 18 girls 14 girls 13 girls 10 girls

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Eliot

Maths perplexors

Fair contests The clues

Arlene, Arthur, Betty, Byron and Cassie went to a country fair and entered three contests. In the watermelon seed-spitting contest they spit seeds 13, 11.7, 10.4, 9.1 and 7.6 metres. In the pie-eating contest they ate 20, 18, 17, 15 and 10 pies. In the sheep-calling contest they called 47, 45, 40, 38 and 30 sheep. Based on the clues, match the names with their results in the three contests.

1. Between the two of them, Arlene and Arthur had the lowest score in each of the three contests and, between the two of them, Byron and Cassie had the top score in each of the three contests. 2. Arthur spit his seed exactly 130 cm less than Byron, and Cassie spit her seed exactly 130 cm less than Betty. 3. Byron ate exactly one pie fewer than Arlene, and Cassie called exactly two fewer sheep than Arthur.

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Arlene

Arthur

Betty

Byron

13 m 11.7 m 10.4 m 9.1 m 7.6 m

20 pies 18 pies 17 pies 15 pies 10 pies

47 sheep 45 sheep 40 sheep 38 sheep 30 sheep

13 m 11.7 m 10.4 m 9.1 m 7.6 m

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47 sheep 45 sheep 40 sheep 38 sheep 30 sheep

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20 pies 18 pies 17 pies 15 pies 10 pies

Cassie

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Bests in baking The clues

David, Evie, Frank, Gilda and Hilda were five retired bakers. Recalling their glory years, they recalled the best days they ever had in baking biscuits, doughnuts and pies. They also fondly remembered the biggest wedding cakes they had ever made. They baked 600, 540, 516, 492 and 468 biscuits on their best days. They baked 720, 696, 672, 600 and 588 doughnuts on their best days. They baked 360, 348, 336, 300 and 240 pies on their best days. Their biggest wedding cakes had been 120, 100, 60, 50 and 30 cm in diameter. Based on the clues, match the bakers with their best days production of biscuits, doughnuts and pies, and with their biggest wedding cakes.

1. Hilda’s wedding cake radius was the same as David’s cake diameter, Evie’s cake diameter was the same as Gilda’s cake radius, and Frank’s cake diameter was the same as David’s cake radius. 2. Gilda and Hilda’s combined baking total was 45 dozen pies, 99 dozen doughnuts, and 80 dozen biscuits. 3. David and Evie’s combined baking total was 95 dozen biscuits, 118 dozen doughnuts and 59 dozen pies. 4. Multiply Hilda’s cake radius number by 10 to determine the number of doughnuts she baked, and multiply Gilda’s cake radius number by 6 to identify the number of pies she baked. 5. Gilda baked exactly two dozen fewer biscuits than Frank, Evie baked exactly five dozen more pies than Gilda, and David baked exactly 10 dozen more doughnuts than Hilda. 6. Evie baked more biscuits than David.

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©R I . C.Pu bl i cat i on Evie. Frank Gildas •f orr evi ew pur posesonl y•

David

600 biscuits 540 biscuits 516 biscuits 492 biscuits 468 biscuits

720 doughnuts 696 doughnuts 672 doughnuts 600 doughnuts 588 doughnuts

360 pies 348 pies 336 pies 300 pies 240 pies

120 cm 100 cm 60 cm 50 cm 30 cm

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600 biscuits 540 biscuits 516 biscuits 492 biscuits 468 biscuits

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120 cm 100 cm 60 cm 50 cm 30 cm

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600 biscuits 540 biscuits 516 biscuits 492 biscuits 468 biscuits

Hilda

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Fishing eagles The clues

Randy, Spike, Tug, Val and Winnie were five eagles living near a river. They lived in trees that were 46.5, 43, 40.5, 38 and 35.5 metres tall. One recent day, scientists studied them as they fished all day. The eagles caught 52, 50, 46, 45 and 40 carp. They caught 67, 63, 60, 47 and 46 bass. They caught 47, 46, 35, 33 and 27 perch. Based on the clues, match the eagles with their trees, and the number of carp, bass and perch they caught that day.

1. Val and Winnie both caught more perch than carp, and Randy and Spike both caught more carp than bass. 2. Val caught exactly five fewer carp than Spike, and Tug caught exactly 20 fewer perch than Val. 3. Val’s tree was exactly 250 cm taller than Winnie’s tree, and Spike’s tree was exactly 250 cm taller than Randy’s tree. 4. Randy’s tree was 250 cm taller than Val’s tree. 5. Tug caught the most of one species of fish. 6. Spike caught four more carp than bass, Winnie caught 20 more bass than carp, and Spike caught exactly 6 more perch than Tug.

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Randy

Spike

Tug

Val

46.5 m 43 m 40.5 m 38 m 35.5 m

52 carp 50 carp 46 carp 45 carp 40 carp

67 bass 63 bass 60 bass 47 bass 46 bass

47 perch 46 perch 35 perch 33 perch 27 perch

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Winnie

46.5 m 43 m 40.5 m 38 m 35.5 m

67 bass 63 bass 60 bass 47 bass 46 bass

47 perch 46 perch 35 perch 33 perch 27 perch

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52 carp 50 carp 46 carp 45 carp 40 carp

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52 carp 50 carp 46 carp 45 carp 40 carp

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67 bass 63 bass 60 bass 47 bass 46 bass

47 perch 46 perch 35 perch 33 perch 27 perch

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Bear with me The clues

Ben, Bev, Di, Dee and Dora were five bears who lived together in the forest. Their favourite topic of conversation was food, and they talked about the best times they had enjoyed eating various things. They talked about the biggest salmon they had ever eaten; the various salmon weighed 13, 12, 11, 10.5 and 9 kilograms. They had eaten 840, 800, 750, 720 and 700 berries at one time. They had found and eaten 6, 5.5, 5, 4.5 and 4 kg of wild bee honey at one time. Over their lifetimes, they had stolen and eaten 425, 400, 375, 300 and 250 picnic baskets. Based on the clues, match the bears with their biggest salmon, berry consumption, honey consumption and picnic basket totals.

1. Dee’s salmon weighed exactly 2500 grams less than Di’s salmon, Ben’s salmon weighed exactly 2500 grams less than Dee’s salmon, and Dora did not catch the smallest salmon. 2. Multiply Ben’s honey number by 60 to find Bev’s berry number, and multiply Di’s honey number by 60 to reveal Dee’s berry number. 3. Ben and Dora did not eat the fewest berries, in fact, Ben ate more berries than both Dee and Dora. 4. Di and Dee ate a combined total of 22 kg of honey, and Bev and Dee ate a combined total of 23 kg of honey. 5. Dora’s picnic basket number was one-half Ben’s berry number, and Di’s picnic basket number was one-half Dora’s berry number. 6. Bev ate exactly 50 more picnic baskets than Ben.

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Ben

Bev

Dee

15 kg salmon 12.5 kg salmon 11 kg salmon 10 kg salmon 7.5 kg salmon

840 berries 800 berries 750 berries 720 berries 700 berries

14 kg honey 13 kg honey 12 kg honey 10 kg honey 8 kg honey

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840 berries 800 berries 750 berries 720 berries 700 berries

14 kg honey 13 kg honey 12 kg honey 10 kg honey 8 kg honey

425 baskets 400 baskets 375 baskets 300 baskets 250 baskets

w ww

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Dora

Maths perplexors

| 13

Whale tales The clues

Muffy, Fluffy, Boots, Duke and Moby were five whales living together in the Atlantic Ocean. They were 40, 38, 36, 35 and 30 years old. They weighed 100, 90, 80, 75 and 60 tonnes. The deepest dive they had made was to 4000, 3000, 2500, 1500 and 1000 metres. The most squid they had ever eaten at one meal was 500, 480, 460, 400 and 250 squid. Based on the clues, match the whales with their ages, weights, deepest dives and squid consumed at one meal.

1. Of the three oldest whales, one weighed the most, one dove the deepest, and one ate the most squid at one meal. 2. Muffy and Fluffy’s combined age was 65 years, their combined weight was 135 tonnes, their combined diving depth was 2.5 km, and their combined squideating total was 650 squid. 3. The oldest whale ate twice as many squid as the youngest whale. 4. Boots did not weigh the most and he did not dive the deepest, and Moby was exactly two years younger than Duke. 5. Fluffy dove deeper and ate more squid than Muffy. 6. Duke weighed exactly 10 000 Kg less than Moby, and Fluffy weighed exactly 20 000 Kg less than Boots. 7. Duke ate fewer squid than Moby, and Moby dove deeper than Boots.

40 years old 38 years old 36 years old 35 years old 30 years old

FluffyR. Bootsu Duke © I . C.P bl i cat i ons Moby •f orr evi ew pur posesonl y•

w ww

100 tonnes 90 tonnes 80 tonnes 75 tonnes 60 tonnes 4000 m 3000 m 2500 m 1500 m 1000 m 500 squid 480 squid 460 squid 400 squid 250 squid

14 | Maths perplexors

40 years old 38 years old 36 years old 35 years old 30 years old

100 tonnes 90 tonnes 80 tonnes 75 tonnes 60 tonnes

4000 m 3000 m 2500 m 1500 m 1000 m

500 squid 480 squid 460 squid 400 squid 250 squid

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40 years old 38 years old 36 years old 35 years old 30 years old

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Muffy

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Teac he r

The story

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100 tonnes 90 tonnes 80 tonnes 75 tonnes 60 tonnes

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Fruit files The clues

David, Elsie, Frank, Gail and Hilda were five gardeners who were very proud of their fruit trees. They each had an apple tree, a peach tree, a pear tree and a lemon tree in their gardens. One season, they decided to record the amount of fruit each tree produced and compare the results. Their trees produced 1500, 1450, 1400, 1300 and 1250 apples. Their trees produced 800, 750, 725, 700 and 600 peaches. Their trees produced 500, 450, 425, 400 and 375 pears. Their trees produced 300, 275, 250, 200 and 175 lemons. Based on the clues, match the gardeners with the amount of fruit their trees produced.

1. David, Elsie, Frank and Gail each owned one tree that produced the most fruit, and Frank and Gail each owned two trees that produced the least fruit. 2. David’s apple tree produced exactly 50 more apples than Frank’s apple tree, and Gail’s apple tree produced exactly 50 more apples than Hilda’s apple tree. 3. Gail’s lemon tree produced more lemons than Frank’s lemon tree. 4. David and Elsie’s peach trees produced a combined total of 1550 peaches, and David and Hilda’s lemon trees produced a combined total of 500 lemons. 5. Elsie’s lemon tree produced exactly 25 more lemons than Gail’s lemon tree, and Hilda’s peach tree produced exactly 25 more peaches than Frank’s peach tree. 6. Hilda grew more apples than Elsie. 7. David grew more pears than Hilda, and Elsie grew more pears than David.

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The story

©R . I . C.Pu bl i cat i on s Elsie Frank Gail •f orr evi ew pur posesonl y•

David

Hilda

1500 apples 1450 apples 1400 apples 1300 apples 1250 apples

800 peaches 750 peaches 725 peaches 700 peaches 600 peaches

500 pears 450 pears 425 pears 400 pears 375 pears

300 lemons 275 lemons 250 lemons 200 lemons 175 lemons

. te

300 lemons 275 lemons 250 lemons 200 lemons 175 lemons

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m . u

1500 apples 1450 apples 1400 apples 1300 apples 1250 apples

w ww

1500 apples 1450 apples 1400 apples 1300 apples 1250 apples

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Maths perplexors

| 15

Hidden nuts The clues

Alvin, Bunky, Carl, David and Eliot were five squirrels who all had super secret private collections of nuts that they kept hidden from each other. They had 20, 19, 18, 15 and 14 acorns hidden away. They had 17, 16, 13, 12 and 11 pecans hidden away. They had 10, 9, 8, 5 and 4 almonds hidden away. They had 7, 6, 3, 2 and 1 walnuts hidden away. Based on the clues, match the squirrels with their secret collections of acorns, pecans, almonds and walnuts.

1. Carl and David each had more walnuts than almonds in their collections, and Alvin and Bunky each had more pecans than acorns in their collections. 2. Bunky and David had a combined total of 10 walnuts in their collections, and they had a combined total of 15 almonds in their collections. 3. Alvin and Carl had a combined total of 35 acorns in their collections, and they had a combined total of 30 pecans in their collections. 4. Carl and Eliot had a combined total of 39 acorns in their collections and a combined total of 25 pecans in their collections. 5. Bunky and Eliot had a combined total of 18 almonds in their collections and a combined total of five walnuts in their collections.

20 acorns 19 acorns 18 acorns 15 acorns 14 acorns

Bunky

Carl

David

20 acorns 19 acorns 18 acorns 15 acorns 14 acorns

17 pecans 16 pecans 13 pecans 12 pecans 11 pecans

10 almonds 9 almonds 8 almonds 5 almonds 4 almonds

7 walnuts 6 walnuts 3 walnuts 2 walnuts 1 walnut

Eliot

w ww

17 pecans 16 pecans 13 pecans 12 pecans 11 pecans

10 almonds 9 almonds 8 almonds 5 almonds 4 almonds 7 walnuts 6 walnuts 3 walnuts 2 walnuts 1 walnut

16 | Maths perplexors

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20 acorns 19 acorns 18 acorns 15 acorns 14 acorns

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17 pecans 16 pecans 13 pecans 12 pecans 11 pecans

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Alvin

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Teac he r

The story

10 almonds 9 almonds 8 almonds 5 almonds 4 almonds 7 walnuts 6 walnuts 3 walnuts 2 walnuts 1 walnut

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Hits just a game The clues

Jack, Inez, Jill, Kelly and Laura played baseball for their school team. At the end of the season, they compared their batting performances. They had batted 104, 102, 92, 90 and 83 times. They had made 40, 38, 37, 35 and 30 hits. They had received 20, 19, 15, 10 and 9 walks. They had made 50, 45, 44, 40 and 39 outs. Based on the clues, match the players with their batting numbers, hit numbers, walk numbers and out numbers.

1. Jill had batted two more times than Kelly, and Laura had batted two more times than Jack. 2. Jack had five more hits than Jill, and Jill had five more hits than Inez. 3. Laura had batted fewer times than Kelly, but Laura had more hits than Kelly. 4. Jill made exactly five more outs than Kelly, Inez made exactly five more outs than Laura, and Kelly made exactly five more outs than Jack.

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Jack

Inez

Jill

Kelly

Laura

104 at bat 102 at bat 92 at bat 90 at bat 83 at bat

40 hits 38 hits 37 hits 35 hits 30 hits

20 walks 19 walks 15 walks 10 walks 9 walks

50 outs 45 outs 44 outs 40 outs 39 outs

w ww 50 outs 45 outs 44 outs 40 outs 39 outs

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| 17

A day at the beach The clues

Jake, Kathy, Linc, Mark and Nellie decided to spend the day at the beach. They all brought beach balls that were 112, 106, 56, 53 and 28 cm in diameter. They wisely brought sunscreen with them with sun protection factor (SPF) levels of 100, 95, 90, 88 and 83. While swimming, they saw 57, 52, 47, 40 and 35 sharks swimming with them. While enjoying their day on the sand, they were bitten by sand fleas 500, 450, 440, 400 and 390 times. Based on the clues, match the names with their beach ball diameters, SPF levels, sharks and flea bites.

1. The radius of Linc’s beach ball was the same as Kathy’s diameter, the diameter of Jake’s beach ball was the same as Mark’s radius and, of course, the diameter of Nellie’s beach ball was the same as Kathy’s radius. 2. Nellie’s SPF number was exactly five less than Mark’s SPF number, Linc’s SPF number was exactly five less than Kathy’s SPF number and, of course, Kathy’s SPF number was exactly five less than Jake’s SPF number. 3. Jake saw exactly five fewer sharks than Kathy, Linc saw exactly five fewer sharks than Mark and, of course, Nellie saw exactly five fewer sharks than Jake. 4. Jake received exactly 50 fewer flea bites than Mark, Nellie received exactly 50 fewer flea bites than Linc and, of course, Kathy received exactly 50 fewer flea bites than Nellie.

112 cm ball 106 cm ball 56 cm ball 53 cm ball 28 cm ball

Kathy Linc Mark © R. I . C.P ubl i cat i ons Nellie •f orr evi ew pur posesonl y•

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100 SPF 95 SPF 90 SPF 88 SPF 83 SPF

57 sharks 52 sharks 47 sharks 40 sharks 35 sharks 500 bites 450 bites 440 bites 400 bites 390 bites

18 | Maths perplexors

112 cm ball 106 cm ball 56 cm ball 53 cm ball 28 cm ball

100 SPF 95 SPF 90 SPF 88 SPF 83 SPF

57 sharks 52 sharks 47 sharks 40 sharks 35 sharks

500 bites 450 bites 440 bites 400 bites 390 bites

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112 cm ball 106 cm ball 56 cm ball 53 cm ball 28 cm ball

m . u

Jake

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Teac he r

The story

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100 SPF 95 SPF 90 SPF 88 SPF 83 SPF

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Just for the farm of it The clues

Mike, Nell, Oscar, Paula and Ruth were five farmers who were always trying to outdo each other in various agricultural activities. They were 55, 50, 45, 40 and 35 years old. In their pumpkin-growing contest, they grew pumpkins that were 279, 252, 140, 126 and 63 cm in diameter. In their pig-flying contest, they trained their pigs to fly 548, 539, 535, 530 and 521 metres. In their milk-production contest, they had cows that produced 53, 49, 45, 37 and 29 litres of milk in a day. Based on the clues, match the farmers with their ages, pumpkin diameters, pig-flying distances and milk-production totals.

1. The three youngest farmers each won one contest, but each also had the lowest number in one of the three contests. 2. Nell’s pig flew exactly 9 m less than Oscar’s pig, Paula’s pig flew exactly 9 m less than Mike’s pig and, of course, Oscar’s pig flew exactly 9 m less than Paula’s pig. 3. Oscar was five years younger than Nell, and Nell was five years younger than Mike. 4. Oscar’s pumpkin diameter was the same as Ruth’s radius, and Ruth’s diameter was the same as Mike’s radius. 5. Paula was older than Ruth and her cow produced exactly 4000 mL more milk than Ruth’s cow.

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The story

Mike

Nell

Oscar

Paula

Ruth

55 years old 50 years old 45 years old 40 years old 35 years old

279 cm 252 cm 140 cm 126 cm 63 cm

548 m pig 539 m pig 535 m pig 530 m pig 521 m pig

53 L 49 L 45 L 37 L 29 L

w ww 548 m pig 539 m pig 535 m pig 530 m pig 521 m pig

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53 L 49 L 45 L 37 L 29 L

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| 19

To bee or not to bee The clues

Jim, Kate, Lulu, Moe and Nancy were students at Bates Primary School. They were in the Years 2, 3, 4, 5 and 6. None of them won the annual school spelling bee, but they all spelled an amazing number of words before being eliminated. They spelled 675, 650, 625, 620 and 595 words correctly. Their classes had 18, 17, 16, 13 and 12 boys, and 15, 14, 11, 10 and 9 girls in them. Based on the clues, match the students with their school years, words spelled correctly, and the number of boys and girls in their classes.

1. Years 5 and 6 classes had more girls than boys in them. 2. The Year 4 class had a total of 25 students. 3. The Year 2 class had a total of 27 students. 4. The Year 2 student spelled exactly 25 fewer words than the Year 3 student, the Year 5 student spelled exactly 25 fewer words than the Year 2 student, and the Year 6 student spelled exactly 25 fewer words than the Year 4 student. 5. Jim was exactly one year higher than Kate, Nancy was exactly one year higher than Jim, Moe was exactly one year higher than Nancy, and Lulu was exactly one year higher than Moe. 6. The Year 4 student did not spell the most words correctly. 7. The Year 3 class had exactly five more boys than the Year 6 class, but it had exactly three fewer girls than the Year 6 class.

Year 2 Year 3 Year 4 Year 5 Year 6

w ww

675 words 650 words 625 words 620 words 595 words 18 boys 17 boys 16 boys 13 boys 12 boys 15 girls 14 girls 11 girls 10 girls 9 girls

20 | Maths perplexors

Year 2 Year 3 Year 4 Year 5 Year 6

675 words 650 words 625 words 620 words 595 words

18 boys 17 boys 16 boys 13 boys 12 boys

15 girls 14 girls 11 girls 10 girls 9 girls

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Year 2 Year 3 Year 4 Year 5 Year 6

m . u

Jim

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Teac he r

The story

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675 words 650 words 625 words 620 words 595 words

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Farm figures The clues

Alex, Betty, Carl, Dana and Ellie all owned farms of exactly 4000 acres. Each farm had a 1000-acre plot, a 900acre plot, an 800-acre plot, a 700-acre plot and a 600-acre plot. The farmers all grew exactly the same crops of cotton, wheat, corn, beans and beets. Based on the clues, match the farmers with the acres they each devoted to the five crops.

1. Alex and Ellie planted a combined total of 1900 acres of cotton. 2. Alex and Dana planted a combined total of 1900 acres of wheat. 3. Betty and Dana planted a combined total of 1900 acres of corn. 4. Betty and Carl planted a combined total of 1900 acres of beans. 5. Betty and Carl planted a combined total of 1800 acres of beets. 6. Alex and Betty planted a combined total of 1400 acres of beets. 7. Betty and Dana planted a combined total of 1500 acres of cotton. 8. Carl and Dana planted a combined total of 1600 acres of wheat.

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Alex

Betty

Carl

Dana

Ellie

1000 cotton 900 cotton 800 cotton 700 cotton 600 cotton

1000 wheat 900 wheat 800 wheat 700 wheat 600 wheat

1000 corn 900 corn 800 corn 700 corn 600 corn

1000 beans 900 beans 800 beans 700 beans 600 beans

1000 beets 900 beets 800 beets 700 beets 600 beets

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1000 beans 900 beans 800 beans 700 beans 600 beans 1000 beets 900 beets 800 beets 700 beets 600 beets

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| 21

Lucky numbers The clues

Five pigs, named Pinky, Tollie, Buddy, Slim and Jonas, all had the same five lucky numbers of 25, 20, 15, 10 and 5. The superstitious pigs insisted on wearing all five numbers every day with each of those numbers appearing on a different item of clothing. However, it was bad luck if any pig wore the same number on the same item of clothing as another pig on the same day. The pigs followed a schedule that allowed them to wear all five lucky numbers every day on their five items of clothing without any pig wearing the same number on the same item of clothing as another pig. Based on the clues, figure out their number and clothing schedule for one day.

1. Buddy and Slim wore no number higher than 10 on their hats or shirts that day. 2. Pinky and Tollie wore no number higher than 10 on their coats that day. 3. Slim’s hat number was one-half the size of Tollie’s hat number. 4. Multiply Slim’s shirt number by five to find Jonas’ shirt number. 5. Subtract Buddy’s coat number from Jonas’s coat number to identify Tollie’s coat number. 6. Subtract Buddy’s tie number from Tollie’s tie number to reveal Pinky’s tie number.

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The story

Pinky

Tollie

Buddy

Slim

25 hat 20 hat 15 hat 10 hat 5 hat

25 shirt 20 shirt 15 shirt 10 shirt 5 shirt

25 coat 20 coat 15 coat 10 coat 5 coat

25 tie 20 tie 15 tie 10 tie 5 tie

25 pants 20 pants 15 pants 10 pants 5 pants

25 hat 20 hat 15 hat 10 hat 5 hat

w ww

25 coat 20 coat 15 coat 10 coat 5 coat

22 | Maths perplexors

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25 shirt 20 shirt 15 shirt 10 shirt 5 shirt

m . u

25 shirt 20 shirt 15 shirt 10 shirt 5 shirt

Jonas

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25 coat 20 coat 15 coat 10 coat 5 coat

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Oh, brother! The clues

Ricky, Sam, Tom, Vic and Will were five brothers living on different floors of the same five story apartment building. They were 40, 38, 36, 35 and 33 years old. The brothers collected model cars, coins and stamps. They collected 800, 770, 740, 720 and 690 model cars. They collected 1000, 950, 930, 905 and 880 coins. They collected 620, 600, 560, 540 and 500 stamps. Based on the clues, match the brothers with the floor they lived on, their ages, and their model car, coin and stamp collections.

1. The floor numbers never matched the birth order numbers; i.e: the first born did not live on the 1st floor, and so on. 2. The oldest brother and the youngest brother did not have the most cars, coins or stamps, but at least they did not have the fewest cars, coins and stamps either. 3. Will was two years younger than Tom, Sam was two years younger than Will, and Vic was two years older than Ricky. 4. Each of the three middle brothers in age had the largest of one of the three collections and each also had the smallest of one of the three collections. 5. Vic lived one floor above Will but Vic was not living on the top floor, and Tom lived one floor above Sam. 6. Sam had exactly 30 more cars than Tom, Tom had exactly 30 more cars than Ricky and Vic had more cars than Will. 7. Sam did not have the fewest stamps and had more stamps than Tom but fewer than Ricky. 8. Tom had more coins than Ricky but fewer than Will.

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©R I . C.PuTom bl i cat i on Sam. Vics •f orr evi ew pur posesonl y•

Ricky

Will

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

40 years old 38 years old 36 years old 35 years old 33 years old

800 cars 770 cars 740 cars 720 cars 690 cars

1000 coins 950 coins 930 coins 905 coins 880 coins

620 stamps 600 stamps 560 stamps 540 stamps 500 stamps

800 cars 770 cars 740 cars 720 cars 690 cars

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

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

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

Maths perplexors

| 23

You auto know this The clues

Bertha, Bonnie, Bert, Bret and Bill were five rally car drivers. The numbers on their cars were 99, 89, 79, 75 and 60. They had been racing for 20, 18, 16, 15 and 13 years. Over their years in racing they had finished in first place 47, 45, 40, 39 and 35 times. They had finished in second place 90, 80, 78, 70 and 60 times. They had finished in third place 160, 140, 120, 100 and 90 times. Based on the clues, match the racers with their rally car numbers, racing years, and first, second and third place finishes.

1. Car 99 was driven by the driver with the least experience, and that driver finished in second place twice as many times as first place and in third place twice as many times as in second place. 2. Car 60 was driven by the driver with the most experience, and that driver finished in third place twice as many times as in second place. 3. Car 89 was driven by the driver who had five years less experience than the driver of the car with the lowest number, and Car 89’s driver had finished in second place twice as many times as in first place. 4. Bonnie finished in third place twice as many times as in second place, Bret finished in third place twice as many times as in second place, and Bert finished in third place twice as many times as in second place. 5. Bonnie finished in third place 20 fewer times than Bert and 20 more times than Bret. 6. Bill’s car number was exactly 10 less than Bert’s car number, and Bonnie’s car number was 10 less than Bill’s car number. 7. Multiply Bret’s first place number by two to determine Bonnie’s second place number. 8. Bertha had more experience than Bonnie, Bonnie won more races than Bertha, and Bertha finished the same number of times in second and third places.

Bertha

Car 99 Car 89 Car 79 Car 75 Car 60

20 years 18 years 16 years 15 years 13 years

1st 47 1st 45 1st 40 1st 39 1st 35

2nd 90 2nd 80 2nd 78 2nd 70 2nd 60

3rd 160 3rd 140 3rd 120 3rd 100 3rd 90

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20 years 18 years 16 years 15 years 13 years 1st 47 1st 45 1st 40 1st 39 1st 35

24 | Maths perplexors

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Car 99 Car 89 Car 79 Car 75 Car 60

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Car 99 Car 89 Car 79 Car 75 Car 60

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20 years 18 years 16 years 15 years 13 years

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Flower children The clues

Bates Primary School’s property line was exactly 750 feet in length. The property line was divided into five identical 46-m strips. Each of these 46-m strips was composed of a 15-m section, a 12-m section, a 9-m section, a 6-m section and a 3-m section. Each 46-m length was assigned to the Years 1, 2, 3, 4 and 5, and they planted roses, tulips, lilies, daisies and peonies on the five sections of their assigned 46-m strip of land. Of course, no class was allowed to plant the same flower in the same sized section as any other class. Based on the clues, see if you can figure out how each class planted each section of their 46 m strips this year.

1. Years 1 and 5 planted a combined total of 27 m of roses, Years 2 and 5 planted a combined total of 27 m of tulips, Years 1 and 4 planted a combined total of 27 m of lilies, and the 2nd and 3rd years planted a combined total of 27 m of daisies. 2. Year 3 planted more peonies than Year 4. 3. Years 3 and 4 planted a combined total of 9 m of roses and 9 m of tulips. 4. Year 2 planted more lilies than Year 5, and Year 4 planted more roses than Year 3.

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Year 1

Year 2

Year 3

Year 4

Year 5

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

15 m tulips 12 m tulips 9 m tulips 6 m tulips 3 m tulips

15 m lilies 12 m lilies 9 m lilies 6 m lilies 3 m lilies

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

15 m peonies 12 m peonies 9 m peonies 6 m peonies 3 m peonies

w ww 15 m lilies 12 m lilies 9 m lilies 6 m lilies 3 m lilies

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| 25

Something to crow about The clues

Hecky, Cawful, Bing, Moose and Dirk were five crows living together on different branches of a 30 metrehigh tree. These branches were 27, 24, 21, 18 and 15 m high. The crows were 12, 10, 8, 7 and 5 years old. In a contest to see who could fly the fastest, the crows flew 50, 48, 46, 45 and 42 kph. In a cawing contest to see who could caw the most times in a minute, they cawed 100, 96, 90, 84 and 80 caws in a minute. In a grub-eating contest, they ate 200, 180, 168, 160 and 150 grubs in an hour. Based on the clues, match the crows with their branches, ages, speed, cawing and grub-eating totals.

1. The oldest crow did not live on the highest branch, the next oldest crow did not live on the next branch down from the highest branch, and so on through the ages of the crows. 2. Multiply Hecky’s age by six to find his kph number, and multiply Dirk’s age by six to discover his kph number. 3. Multiply Hecky’s kph number by two to determine his number of caws, and multiply Dirk’s kph number by two to identify his number of caws. 4. Multiply Cawful’s kph number by two to find his caws number, and multiply Moose’s kph number by two to reveal his caws number. 5. Multiply Cawful’s caw number by two to attain his number of grubs, and multiply Moose’s caw number by two to acquire his number of grubs. 6. Bing was exactly two years older than Moose, and the 10-year-old crow won all three contests. 7. Dirk was older than Hecky, Dirk flew faster than Hecky, Bing ate exactly 10 more grubs than Dirk, and Cawful’s tree height added to Dirk’s tree height would be 33 m. 8. Add Bing’s tree height number and Moose’s tree height number to get the answer 51 m.

Hecky

27 m 24 m 21 m 18 m 15 m

12 years old 10 years old 8 years old 7 years old 5 years old

50 kph 48 kph 46 kph 45 kph 42 kph

100 caws 96 caws 90 caws 84 caws 80 caws

200 grubs 180 grubs 168 grubs 160 grubs 150 grubs

200 grubs 180 grubs 168 grub 160 grubs 150 grubs

200 grubs 180 grubs 168 grubs 160 grubs 150 grubs

w ww

12 years old 10 years old 8 years old 7 years old 5 years old 50 kph 48 kph 46 kph 45 kph 42 kph

26 | Maths perplexors

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27 m 24 m 21 m 18 m 15 m

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27 m 24 m 21 m 18 m 15 m

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12 years old 10 years old 8 years old 7 years old 5 years old 50 kph 48 kph 46 kph 45 kph 42 kph

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Good knight The clues

Derek, David, Donald, Drew and Daniel were five retired knights. One recent day they got together and compared careers. They had fought 500, 480, 470, 460 and 420 jousts. They had rescued 250, 235, 220, 205 and 190 damsels. They had slain 50, 47, 45, 42 and 39 dragons. They had gone on 240, 235, 230, 220 and 215 quests. In doing all this, the knights had worn out 85, 83, 78, 71 and 64 horses. Based on the clues, match the knights with their jousts, damsels, dragons, quests and horses.

1. Between the three of them, David, Donald and Daniel had the highest number in each of the five categories. 2. David and Drew never had the lowest number in any of the five categories. 3. Multiply Donald’s damsel number by two to discover his number of jousts, and multiply Drew’s damsel number by two to find his number of jousts. 4. Multiply Daniel’s number of quests by two to reveal his number of jousts, and multiply David’s number of quests by two to obtain his number of jousts. 5. Drew fought exactly 10 more jousts than David, and Derek went on more quests than Donald. 6. Multiply Drew’s dragon number by five to uncover his number of quests. 7. David and Daniel did not slay the most dragons, and Derek did not slay the fewest dragons. 8. Daniel slew exactly three fewer dragons than Derek, and David rescued exactly 15 fewer damsels than Derek. 9. Derek and Daniel each wore out more than 64 horses, Drew wore out exactly seven more horses than Donald and exactly seven fewer horses than Daniel.

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©R . I . C.Pu bl i cat i on David Donald Drews •f orr evi ew pur posesonl y•

Derek

Daniel

500 jousts 480 jousts 470 jousts 460 jousts 420 jousts

250 damsels 235 damsels 220 damsels 205 damsels 190 damsels

50 dragons 47 dragons 45 dragons 42 dragons 39 dragons

240 quests 235 quests 230 quests 220 quests 215 quests

85 horses 83 horses 78 horses 71 horses 64 horses

50 dragons 47 dragons 45 dragons 42 dragons 39 dragons

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500 jousts 480 jousts 470 jousts 460 jousts 420 jousts

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500 jousts 480 jousts 470 jousts 460 jousts 420 jousts

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500 jousts 480 jousts 470 jousts 460 jousts 420 jousts

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| 27

Who’s on first? The clues

Jill, James, Jane, Jack and Joan were brothers and sisters in the same family. They were 13, 14, 15, 16 and 18 years old. They rode bikes that were numbered 1, 2, 3, 4 and 5 to a snack shop. At the snack shop, they stood in single file to place their orders and, naturally enough, they were first, second, third, fourth and fifth in line. When it was their turn to order, they ordered 1, 2, 3, 4 and 5 hot dogs, and ice-creams with 1, 2, 3, 4 and 5 scoops. Based on the clues, match the names with their ages, bike numbers, places in line, hot dog orders and ice-cream scoops.

1. The first born did not ride Bike 1, was not first in line, did not order one hot dog, and did not order one scoop of ice-cream. The second born did not ride Bike 2, was not second in line, did not order two hot dogs, and did not order two scoops of icecream. The same rule is true for the third, fourth and fifth born children. 2. Jill was two years older than Joan, James was two years older than Jack, and Jane was two years older than James. 3. Joan’s bike number was twice the size of Jack’s bike number, Jill’s bike number was twice the size of Joan’s bike number, and Jane’s bike number was smaller than James’s bike number. 4. While waiting in line, James poked Jack in the back, and Jill poked Jane in the back. 5. Jane and Joan ordered a combined total of eight hot dogs, and Jack ordered more hot dogs than James. 6. James and Jane ordered a combined total of 5 scoops of icecream, and Jack and Joan ordered a combined total of nine scoops of ice-cream.

Jill

JamesR. Janeu Jack © I . C.P bl i cat i ons Joan •f orr evi ew pur posesonl y• 13 years old 14 years old 15 years old 16 years old 18 years old

13 years old 14 years old 15 years old 16 years old 18 years old

Bike 1 Bike 2 Bike 3 Bike 4 Bike 5

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

1 hot dog 2 hot dogs 3 hot dogs 4 hot dogs 5 hot dogs

1 scoop 2 scoops 3 scoops 4 scoops 5 scoops

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Bike 1 Bike 2 Bike 3 Bike 4 Bike 5

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

28 | Maths perplexors

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13 years old 14 years old 15 years old 16 years old 18 years old

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

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Lighthouse School The clues

Sharon, Stanley, Susan, Sam and Sara were the teachers for Years 1, 2, 3, 4 and 5 at the world famous Lighthouse School. The school was famous because it consisted of five storeys with a different class being located on each of the five floors of the lighthouse. The teachers had been teaching for 42, 40, 21, 20 and 10 years. Their classes had 21, 19, 17, 16 and 15 boys, and 23, 22, 20, 18 and 14 girls. Based on the clues, match the teachers with their school years, floors, years of experience, and boys and girls in their classes.

1. The floor levels and year levels were never the same. Year 1 was not on the first floor, and so on. 2. Sam taught twice as long as Susan, Sara taught twice as long as Sharon, and Susan taught twice as long as Stanley. 3. The two teachers with a combined total of 82 years experience had more boys than girls in each of their classes. 4. Susan had 40 students in her classroom, Stanley had 38 students in his classroom, and Sam had 35 students in his classroom. 5. Sam and Sara taught on the highest two floors. 6. Year 1 was not on the fifth floor and it had the most boys. 7. The 5th year had the most girls and was located on the first floor. 8. Sharon was on a higher floor than Stanley but taught a lower year level than Stanley, and Sara taught a higher grade than Stanley.

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Sharon

Stanley

Susan

Sam

Sara

Year 1 Year 2 Year 3 Year 4 Year 5

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

42 years 40 years 21 years 20 years 10 years

21 boys 19 boys 17 boys 16 boys 15 boys

23 girls 22 girls 20 girls 18 girls 14 girls

w ww 21 boys 19 boys 17 boys 16 boys 15 boys

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23 girls 22 girls 20 girls 18 girls 14 girls

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| 29

Your vote counts The clues

Randy, Stacy, Troy, Inez and Rory were the five candidates running for the office of mayor of Glenview. They made 1000, 900, 700, 600 and 500 speeches. They made 1800, 1400, 1200, 800 and 300 promises. They kissed 90, 70, 60, 50 and 40 babies. They shook 900, 600, 400, 350 and 300 hands. In the election, they received 3140, 2570, 2400, 2260 and 1690 votes. Based on the clues, match the candidates with their speeches, promises, kisses, handshakes and votes.

1. Each candidate received one vote for every speech, promise, kiss and handshake they made during the campaign for mayor. 2. Randy, Stacy, Troy and Inez were each at the top of one of the four categories of speeches, promises, kisses and handshakes, but each was also at the bottom of one of those four categories and, of course, one of them won the election and one of them received the fewest votes. 3. Randy and Rory made a combined total of 1100 speeches, and Troy and Inez made a combined total of 1900 speeches. 4. Inez and Rory kissed a combined total of 90 babies and made a combined total of 3200 promises. 5. Stacy and Inez kissed a combined total of 130 babies. 6. Multiply Stacy’s promise total by four to find Troy’s promise total. 7. Troy kissed more babies than Randy, Randy shook as many hands as Stacy and Troy combined and, of course, Inez shook more hands than Rory.

Stacy

Troy

Inez

1000 speeches 900 speeches 700 speeches 600 speeches 500 speeches

1800 promises 1400 promises 1200 promises 800 promises 300 promises

90 kisses 70 kisses 60 kisses 50 kisses 40 kisses

900 shakes 600 shakes 400 shakes 350 shakes 300 shakes

3140 votes 2570 votes 2400 votes 2260 votes 1690 votes

1000 speeches 900 speeches 700 speeches 600 speeches 500 speeches

Rory

w ww

1800 promises 1400 promises 1200 promises 800 promises 300 promises 90 kisses 70 kisses 60 kisses 50 kisses 40 kisses

30 | Maths perplexors

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1000 speeches 900 speeches 700 speeches 600 speeches 500 speeches 1800 promises 1400 promises 1200 promises 800 promises 300 promises

m . u

Randy

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90 kisses 70 kisses 60 kisses 50 kisses 40 kisses

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Gaining yards The clues

Fred, Gail, Hank, Jill and Ken all played Gridiron for the local amateur team. Because they played an American game, distances were judged in yards. They all played for five years and they all gained exactly 4000 yards in that time. In the first year they gained 1000, 900, 800, 700 and 600 yards. They gained exactly the same number of yards in the second, third, fourth and fifth years. Of course, none of the players gained the same number of yards in more than one year. Based on the clues, match the players with the yards they gained in each of the five years they played.

1. Fred and Ken gained a combined total of 1900 yards in the first year, Fred and Gail gained a combined total of 1900 yards in the second year, Jill and Ken gained a combined total of 1900 yards in the third year, Gail and Hank gained a combined total of 1900 yards in the fourth year and, of course, Fred and Gail gained a combined total of 1800 yards in the first year. 2. In the first year, Jill gained more yards than Hank, and in the second year Jill gained fewer yards than she gained in the first year. 3. Ken gained fewer yards in the fifth year than he gained in the fourth year.

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Fred

Gail

Hank

Jill

Ken

1st 1000 yds 1st 900 yds 1st 800 yds 1st 700 yds 1st 600 yds

2nd 1000 yds 2nd 900 yds 2nd 800 yds 2nd 700 yds 2nd 600 yds

3rd 1000 yds 3rd 900 yds 3rd 800 yds 3rd 700 yds 3rd 600 yds

4th 1000 yds 4th 900 yds 4th 800 yds 4th 700 yds 4th 600 yds

5th 1000 yds 5th 900 yds 5th 800 yds 5th 700 yds 5th 600 yds

w ww

. te

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| 31

Hooked on fishing The clues

Sharon, Sally, Saul, Shawn and Sarah were five avid anglers. They kept careful records of their catches for the year and recently compared their catches for the season. They caught 750, 725, 700, 650 and 625 perch. They caught 1500, 1450, 1400, 1300 and 1200 bass. They caught 350, 325, 300, 270 and 250 trout. They caught 95, 90, 85, 70 and 65 salmon. They caught 200, 190, 170, 160 and 150 catfish. Based on the clues, match the anglers with their fishing totals for each species of fish they caught.

1. Each of the five anglers caught the most of one species of fish, and each of them caught the fewest of one species of fish. 2. Sharon caught exactly 25 fewer perch than Sally, Shawn caught exactly 25 fewer perch than Saul, Shawn caught exactly 100 more perch than Sharon and, of course, Saul caught exactly 100 more perch than Sally. 3. Sarah caught exactly 25 fewer trout than Sharon, and Shawn caught exactly 25 fewer trout than Sarah. 4. Multiply Sally’s trout number by six to discover her bass number. 5. Sarah caught more catfish than Shawn and more bass than Shawn as well. 6. Saul caught exactly 100 more bass than Sarah. 7. Multiply Sally’s salmon number by two to reveal Shawn’s catfish number. 8. Sharon caught more catfish than Sally, and Saul caught more salmon than Sharon.

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The story

Sharon

Sally

Saul

Shawn

Sarah

750 perch 725 perch 700 perch 650 perch 625 perch

1500 bass 1450 bass 1400 bass 1300 bass 1200 bass

350 trout 325 trout 300 trout 270 trout 250 trout

95 salmon 90 salmon 85 salmon 70 salmon 65 salmon

200 catfish 190 catfish 170 catfish 160 catfish 150 catfish

750 perch 725 perch 700 perch 650 perch 625 perch

350 trout 325 trout 300 trout 270 trout 250 trout

32 | Maths perplexors

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1500 bass 1450 bass 1400 bass 1300 bass 1200 bass

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1500 bass 1450 bass 1400 bass 1300 bass 1200 bass

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350 trout 325 trout 300 trout 270 trout 250 trout

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Herd around the town The clues

The towns of Alton, Balton, Carleton, Dayton and Elton were very proud of their town herds of goats, horses, bison, elk and sheep. They had 500, 400, 300, 200 and 100 goats. They had 1000, 900, 800, 700 and 600 horses. They had 1500, 1400, 1300, 1200 and 1100 bison. They had 2000, 1900, 1800, 1700 and 1600 elk. They had 2500, 2400, 2300, 2200 and 2100 sheep. Based on the clues, match the towns with the sizes of their herds.

1. If Alton did not have the largest herd, then Balton had the largest herd, and if Carleton did not have the smallest herd, then Dayton had the smallest herd. 2. Dayton and Elton had a combined total of 700 goats, Alton and Carleton had a combined total of 1700 horses, and Balton and Elton also had a combined total of 1700 horses. 3. Balton did not have the most goats or horses. 4. Multiply Elton’s goat number by three to find its horse total. 5. Balton and Elton’s combined bison total was 2900, Carleton and Elton’s combined bison total was 2700, and Balton and Dayton’s combined elk total was 3900. 6. Elton had fewer elk than Alton. 7. Alton and Elton’s combined total of sheep was 4900, and Dayton and Elton’s combined total of sheep was 4700.

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Alton

Balton

Carleton

Dayton

Elton

500 goats 400 goats 300 goats 200 goats 100 goats

1000 horses 900 horses 800 horses 700 horses 600 horses

1500 bison 1400 bison 1300 bison 1200 bison 1100 bison

2000 elk 1900 elk 1800 elk 1700 elk 1600 elk

2500 sheep 2400 sheep 2300 sheep 2200 sheep 2100 sheep

w ww 1500 bison 1400 bison 1300 bison 1200 bison 1100 bison

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2000 elk 1900 elk 1800 elk 1700 elk 1600 elk 2500 sheep 2400 sheep 2300 sheep 2200 sheep 2100 sheep www.ricpublications.com.au

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| 33

Eating lizards The clues

Five lizards, named Larry, Liza, Lucy, Lenny and Luke, decided to record their daily consumption of flies, roaches, ants, gnats and bees and compare the results. They ate 95, 90, 80, 75 and 70 flies. They ate 56, 50, 44, 30 and 24 roaches. They ate 200, 180, 160, 150 and 125 ants. They ate 425, 400, 375, 300 and 275 gnats. They ate 45, 40, 35, 25 and 20 bees. Based on the clues, match the lizards with the number of flies, roaches, ants, gnats and bees they consumed.

1. When Larry did not have the highest number in any category then Liza had the highest number, but when Larry and Liza did not have the highest number then Lucy certainly did. 2. If Lenny did not have the lowest number in any category then Luke had the lowest number. 3. Luke ate exactly 10 more flies than Lucy, Larry ate exactly six fewer roaches than Lucy, and Luke ate exactly six fewer roaches than Larry. 4. Larry did not eat the most ants, Liza ate exactly 20 fewer ants than Larry, and Luke ate more ants than Lenny. 5. Luke ate exactly 25 fewer gnats than Larry, and Luke ate exactly 25 more gnats than Lucy. 6. Liza did not eat the most bees, and Lucy ate exactly 10 fewer bees than Liza. 7. Larry did not eat the most flies and Lenny did not eat the fewest bees.

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Larry

Liza

Lucy

Lenny

Luke

95 flies 90 flies 80 flies 75 flies 70 flies

56 roaches 50 roaches 44 roaches 30 roaches 24 roaches

200 ants 180 ants 160 ants 150 ants 125 ants

425 gnats 400 gnats 375 gnats 300 gnats 275 gnats

45 bees 40 bees 35 bees 25 bees 20 bees

95 flies 90 flies 80 flies 75 flies 70 flies

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w ww

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56 roaches 50 roaches 44 roaches 30 roaches 24 roaches

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200 ants 180 ants 160 ants 150 ants 125 ants

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Rug makers The clues

Ivan, Inez, Inga, Igor and Irene were five rug makers who owned shops next to each other on Main Street. One recent day, they each sold one rectangular rug and one round rug. The rectangular carpets were 600, 540, 480, 420 and 360 cm in length, and 300, 240, 180, 120 and 60 cm in width. The circular rugs were 180, 150, 120, 90 and 60 cm in diameter. Their shops on Main Street were numbered 1, 2, 3, 4 and 5 from east to west. Based on the clues, match the rug makers with the lengths, widths and areas of their rectangular carpets, the diameters of their circular carpets, and their address numbers on Main Street.

1. Ivan’s width was one-half Igor’s length, Inez’s width was one-half Irene’s length, and Inga’s width was one-half Inez’s length. 2. Irene’s rug was exactly 120 cm longer than Igor’s rug, and Inga’s rug was exactly 60 cm wider than Inez’s rug. 3. Inga’s rug was longer than Ivan’s rug, and Irene’s rug was wider than Igor’s rug. 4. The radius of Inga’s circular rug was the same as Irene’s diameter, and Igor’s diameter was the same as Ivan’s radius. 5. Inez’s diameter was larger than Ivan’s diameter. 6. Inez’s neighbours to the east were Inga and Irene, and her neighbours to the west were Igor and Ivan. 7. Igor’s address number was twice as large as Inga’s address number.

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Ivan

Inez

Inga

Igor

Irene

600 cm long 540 cm long 480 cm long 420 cm long 360 cm long

300 cm wide 240 cm wide 180 cm wide 120 cm wide 60 cm wide

16.2 m2 14.4 m2 7.56 m2 5.76 m2 2.16 m2

180 cm D 150 cm D 120 cm D 90 cm D 60 cm D

1 Main St 2 Main St 3 Main St 4 Main St 5 Main St

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180 cm D 150 cm D 120 cm D 90 cm D 60 cm D 1 Main St 2 Main St 3 Main St 4 Main St 5 Main St

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| 35

Cycling cicadas The clues

Carol, Connie, Cora, Callie and Clara were five female cicadas. They belonged to different cycles and arrived every 17, 15, 12, 10 and 8 years. They all arrived in May but on different days. They arrived on 30, 25, 20, 15 and 12 May. They stayed for 240, 192, 168, 120 and 96 hours. During that time, they laid 1000, 950, 925, 900 and 850 eggs. They spent their time on trees that were 360, 288, 180, 144 and 72 cm in diameter. Based on the clues, match the cicadas with their cycles, dates, hours, eggs and trees.

1. Carol’s cycle was two years longer than Connie’s cycle, Clara’s cycle was two years longer than Carol’s cycle and, of course, Cora’s cycle was two years longer than Callie’s cycle. 2. Connie arrived later in May than Carol, Carol arrived later in May than Callie, Callie arrived later in May than Cora, and Cora arrived later in May than Clara. 3. Carol lived twice as many hours as Connie, Cora lived twice as many hours as Callie, and Connie lived exactly one day longer than Callie. 4. Cora laid exactly 50 more eggs than Carol, Carol laid exactly 50 more eggs than Connie, and Callie laid exactly 50 more eggs than Cora. 5. Clara’s radius was the same as Cora’s diameter, Callie’s radius was the same as Connie’s diameter, and Carol’s diameter was the same as Connie’s radius.

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Carol

Connie

Cora

Callie

Clara

17 yr cycle 15 yr cycle 12 yr cycle 10 yr cycle 8 yr cycle

30 May 25 May 20 May 15 May 12 May

240 hours 192 hours 168 hours 120 hours 96 hours

1000 eggs 950 eggs 925 eggs 900 eggs 850 eggs

360 cm 288 cm 180 cm 144 cm 72 cm

17 yr cycle 15 yr cycle 12 yr cycle 10 yr cycle 8 yr cycle

240 hours 192 hours 168 hours 120 hours 96 hours

36 | Maths perplexors

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30 May 25 May 20 May 15 May 12 May

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30 May 25 May 20 May 15 May 12 May

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240 hours 192 hours 168 hours 120 hours 96 hours

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Dancing hippos The clues

Henry, Hilda, Harriet, Hank and Hannah were five hippos who had devoted their lives to becoming ballet dancers. They were 35, 32, 29, 25 and 22 years old. They used 36,33,30,18 and 15 metres of material to make their latest ballet costume. They practised dancing 18, 16, 13, 11 and 9 hours a day. They weighed 2000, 1900, 1800, 1750 and 1650 kilograms. Before each performance, they ate 75, 70, 68, 66 and 61 fish to keep up their strength. Based on the clues, match the hippos with their ages, feet of material, practise hours, weights and fish consumed.

1. Neither of the two oldest hippos used 36 metres, practised 18 hours, weighed 2000 kg or ate 75 fish, and none of the three youngest hippos used 15 metres, practised 9 hours, weighed 1650 kg or ate 61 fish. 2. Henry, Hilda and Harriet did not use 15 metres, Hilda, Harriet and Hannah did not practise nine hours, and Hilda, Harriet and Hank did not eat 61 fish. 3. Harriet, Hank and Hannah did not use 36 metres, did not practise 18 hours, and did not weigh 2000 kg. 4. Hilda, Hank and Hannah did not eat 75 fish. 5. Harriet was three years younger than Hilda, and Hannah was three years younger than Hank. 6. Hilda used 3 metres more material than Henry, and Henry used 3 metres more than Hannah. 7. Hilda practiced two hours less than Harriet, Hilda weighed 100 kg less than Henry, and Hannah weighed 100 kg less than Hilda. 8. Henry ate exactly five more fish than Hannah, and Hank ate more fish than Hilda.

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©R . I . C.Pu bl i cat i on Hilda Harriet Hanks Hannah •f orr evi ew pur posesonl y•

Henry

35 years old 32 years old 29 years old 25 years old 22 years old

36 metres 33 metres 30 metres 18 metres 15 metres

18 hours 16 hours 13 hours 11 hours 9 hours

2000 kg 1900 kg 1800 kg 1750 kg 1650 kg

75 fish 70 fish 68 fish 66 fish 61 fish

18 hours 16 hours 13 hours 11 hours 9 hours

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2000 kg 1900 kg 1800 kg 1750 kg 1650 kg 75 fish 70 fish 68 fish 66 fish 61 fish www.ricpublications.com.au

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35 years old 32 years old 29 years old 25 years old 22 years old

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35 years old 32 years old 29 years old 25 years old 22 years old

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35 years old 32 years old 29 years old 25 years old 22 years old

Maths perplexors

| 37

Towns that work The clues

The towns of Alton, Balton, Carleton, Dayton and Elton conducted a survey of their citizens to see how they earned their livings. They had 100, 90, 80, 60 and 50 citizens working as police officers. They had 85, 83, 81, 78 and 76 doctors. They had 185, 173, 161, 138 and 125 lawyers. They had 105, 95, 85, 65 and 55 teachers. They had 40, 37, 35, 32 and 29 pilots. Based on the clues, match the towns with the number of police officers, doctors, lawyers, teachers and pilots each town had living there.

1. When Alton did not have the lowest number for any occupation Balton always did, and when Carleton or Dayton did not have the highest number for any occupation Elton always did. 2. Alton and Carleton had a combined total of 190 police officers. 3. Elton had more police officers than doctors, Carleton had two more doctors than Alton and two less than Dayton. 4. Alton had more lawyers than Carleton, but Carleton had more lawyers than Elton. 5. Carleton had exactly 10 more teachers than Elton, Dayton had exactly 20 more teachers than Alton and, of course, Carleton had exactly 20 more teachers than Dayton. 6. Carleton had two fewer pilots than Balton. 7. Dayton does not have the most pilots.

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Alton

Balton

Carleton

Dayton

Elton

100 police 90 police 80 police 60 police 50 police

85 doctors 83 doctors 81 doctors 78 doctors 76 doctors

185 lawyers 173 lawyers 161 lawyers 138 lawyers 125 lawyers

105 teachers 95 teachers 85 teachers 65 teachers 55 teachers

40 pilots 37 pilots 35 pilots 32 pilots 29 pilots

100 police 90 police 80 police 60 police 50 police

185 lawyers 173 lawyers 161 lawyers 138 lawyers 125 lawyers

38 | Maths perplexors

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85 doctors 83 doctors 81 doctors 78 doctors 76 doctors

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85 doctors 83 doctors 81 doctors 78 doctors 76 doctors

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R.I.C. Publications®

185 lawyers 173 lawyers 161 lawyers 138 lawyers 125 lawyers

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Sandcastles The clues

Bela, Sandy, Byron, Belle and Baxter were the captains of sandcastle building teams. They headed teams numbered 100, 97, 94, 90 and 87. Their teams consisted of 20, 16, 13, 12 and 8 members. The total number of hours each team worked on their castles was 160, 128, 91, 72 and 64 hours. The castles were 900, 720, 630, 540 and 450 centimetres high. All the castles were round and had diameters of 9, 7.5, 6, 4.5 and 3 metres. Based on the clues, match the team captains with their team numbers, team members, team working hours, castle heights and castle diameters.

1. Team 100 had the fewest members, Team 87 had the most members, and Team 97 spent the most hours building their sandcastle. 2. Bela’s team number was three less than Byron’s team number, Belle’s team number was three less than Baxter’s team number and, of course, Bela’s team did not have the most members. 3. Byron’s team had more members than Sandy’s team, and each member of Byron’s team worked 10 hours compared to each member of Sandy’s team, who worked 8 hours each. 4. Baxter had fewer members on his team than Bela had on her team. 5. One member of Bela’s team worked no hours at all, but the rest of the team all worked 6 hours each, and Belle’s team worked more hours than Baxter’s team. 6. Team 90’s castle was 180 cm higher than Team 100’s castle, and Team 87’s castle was 180 cm higher than Team 97’s castle. 7. Belle’s team did not build the highest castle, and Team 94 did not build the highest castle either. 8. Team 94’s radius was the same as Team 90’s diameter, Team 87’s diameter was the same as Team 97’s radius, and Sandy’s diameter was exactly 150 cm smaller than Bela’s diameter.

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©R . I . C.Pu bl i cat i on Sandy Byron Belles •f orr evi ew pur posesonl y•

Bela

Baxter

Team 100 Team 97 Team 94 Team 90 Team 87

20 members 16 members 13 members 12 members 8 members

160 hours 128 hours 91 hours 72 hours 64 hours

900 cm high 720 cm high 630 cm high 540 cm high 450 cm high

9 metres D 7.5 metres D 6 metres D 4.5 metres D 3 metres D

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Team 100 Team 97 Team 94 Team 90 Team 87

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Team 100 Team 97 Team 94 Team 90 Team 87

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Team 100 Team 97 Team 94 Team 90 Team 87

Maths perplexors

| 39

How have you bean doing? The clues

Peter, Spike, Max, Duke and Baldy were five rabbits who liked to collect jelly beans. Each rabbit had amassed a total of exactly 5000 jelly beans. They had 1400, 1200, 1100, 800 and 500 red jelly beans. They had 1400, 1200, 1100, 800 and 500 blue jelly beans. They had 1400, 1200, 1100, 800 and 500 green jelly beans. They had 1400, 1200, 1100, 800 and 500 yellow jelly beans. They had 1400, 1200, 1100, 800 and 500 pink jelly beans. Based on the clues, match the rabbits with the number of red, blue, green, yellow and pink jelly beans they each had in their 5000 jelly bean collections.

1. The number of jelly beans in each rabbit’s collection was different for every colour. If a rabbit had 500 red jelly beans, he did not have 500 blue, green, yellow or pink jelly beans, and so on. 2. Peter and Spike had a combined total of 1300 red jelly beans, Max and Duke had a combined total of 1300 blue jelly beans, Spike and Max had a combined total of 1300 green jelly beans, Duke and Baldy had a combined total of 1300 yellow jelly beans, and Peter and Baldy had a combined total of 1300 pink jelly beans. 3. Duke had a combined total of 2000 red and yellow jelly beans, and Peter had a combined total of 2000 red and yellow jelly beans. 4. Spike did not have the largest number of yellow jelly beans, and Duke did not have the largest number of pink jelly beans.

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Peter

Spike

Max

Duke

Baldy

1400 red 1200 red 1100 red 800 red 500 red

1400 blue 1200 blue 1100 blue 800 blue 500 blue

1400 green 1200 green 1100 green 800 green 500 green

1400 yellow 1200 yellow 1100 yellow 800 yellow 500 yellow

1400 pink 1200 pink 1100 pink 800 pink 500 pink

1400 red 1200 red 1100 red 800 red 500 red

1400 green 1200 green 1100 green 800 green 500 green

40 | Maths perplexors

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1400 blue 1200 blue 1100 blue 800 blue 500 blue

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1400 blue 1200 blue 1100 blue 800 blue 500 blue

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1400 green 1200 green 1100 green 800 green 500 green

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Basketball anyone? The clues

Moose, Shorty, Alex, Scott and Biff were the starting five on the Bates High School basketball team. They wore the numbers 88, 70, 44, 35 and 22 on their uniforms. They were 210, 180, 150, 120 and 90 cm tall. During the season, they had scored 600, 575, 550, 500 and 475 points. They had committed 50, 47, 40, 37 and 34 fouls. They had made 96, 92, 90, 88 and 45 free throws. Based on the clues, match the players with their uniform numbers, heights, points, fouls and free throws.

1. Shorty’s uniform number was twice Biff’s number, Moose’s uniform number was one-half the size of Scott’s uniform number, and Alex’s uniform number was twice the size of Shorty’s number. 2. The two smallest uniform numbers belonged to the two shortest players. 3. The shortest player scored the most points and made the most free throws. 4. Alex scored exactly 25 fewer points than Moose, Shorty scored exactly 25 fewer points than Biff, and Scott scored exactly 25 fewer points than Alex. 5. Biff was exactly 30 cm shorter than Scott, Alex made exactly two fewer free throws than Shorty, and Scott made exactly two fewer free throws than Alex. 6. Moose was one-half the size of Alex. 7. Divide Biff’s points number by his foul number and the answer is 10. 8. Shorty committed exactly three fewer fouls than Alex, and the shortest player committed the fewest fouls.

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Scott

uniform 88 uniform 70 uniform 44 uniform 35 uniform 22

210 cm 180 cm 150 cm 120 cm 90 cm

600 points 575 points 550 points 500 points 475 points

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50 fouls 47 fouls 40 fouls 37 fouls 34 fouls 96 free throws 92 free throws 90 free throws 88 free throws 45 free throws

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m . u

Shorty

w ww

Moose

o c . che e r o t r s super

Biff

600 points 575 points 550 points 500 points 475 points

50 fouls 47 fouls 40 fouls 37 fouls 34 fouls

96 free throws 92 free throws 90 free throws 88 free throws 45 free throws

R.I.C. Publications®

Maths perplexors

| 41

Travelling for days The clues

Aaron, Betty, Carol, Diane and Eddie travelled to India, Korea, China, Japan and Russia. They spent 25, 23, 21, 10 and 9 days in India. They spent 18, 17, 16, 12 and 11 days in Korea. They spent 15, 10, 5, 4 and 2 days in China. They spent 19, 14, 13, 7 and 6 days in Japan. They spent 24, 20, 8, 3 and 1 day in Russia. Based on the clues, match the names with the number of days they spent in each country.

1. Carol, Diane and Eddie spent more days in India than Korea, and Betty spent twice as much time in Korea as she spent in India. 2. Diane and Eddie both spent more days in China than they spent in Japan. 3. Carol spent one-third as much time in China as Eddie, and Betty spent twice as much time in China as Aaron. 4. Multiply Carol’s China time by five to discover her India time, and multiply Betty’s China time by four to find Carol’s Korea time. 5. Diane and Eddie spent a combined total of 23 days in Korea, and Aaron and Betty spent a combined total of 33 days in Japan. 6. Add Carol’s Japan days to Diane’s Japan days to uncover Eddie’s Japan days. 7. Multiply Diane’s Japan number by three to determine Eddie’s India number, Betty spent more time in Japan than Aaron, and Diane spent more time in Korea than Eddie. 8. Aaron travelled 67 days total, Betty 70 days total, Carol 55 days total and Diane 53 days total.

Betty

Carol

Diane

25 India 23 India 21 India 10 India 9 India

18 Korea 17 Korea 16 Korea 12 Korea 11 Korea

15 China 10 China 5 China 4 China 2 China

19 Japan 14 Japan 13 Japan 7 Japan 6 Japan

24 Russia 20 Russia 8 Russia 3 Russia 1 Russia

25 India 23 India 21 India 10 India 9 India

Eddie

w ww

18 Korea 17 Korea 16 Korea 12 Korea 11 Korea

15 China 10 China 5 China 4 China 2 China

42 | Maths perplexors

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m . u

Aaron

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

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Teac he r

The story

o c . che e r o t r s super

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15 China 10 China 5 China 4 China 2 China

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Happy birthday The clues

Chad, Chet, Dora, Dani and Ray all had birthday parties. They were 56, 50, 44, 38 and 32 years old. At their parties, they had 80, 76, 72, 68 and 64 guests. The parties lasted for 8, 7, 6, 5 and 4 hours. The parties cost $2000, $1500, $1000, $750 and $375. The birthday cakes were 150, 120, 75, 60 and 30 cm in diameter. Based on the clues, match the names with their ages, guests, party lengths, costs and cakes.

1. The oldest spent the most and had the smallest cake, and the youngest spent the least and had the largest cake. 2. The 50 year old had the most guests and spent one-half as much as the oldest person. 3. Chad spent one-half as much as Dani, Chet spent one-half as much as Chad and, of course, Dora was exactly six years younger than Ray. 4. Dani’s cake radius was the same as Ray’s cake diameter, and Dani’s cake diameter was the same as Dora’s cake radius. 5. Multiply Chet’s party hours by eight to determine the number of guests at his party and, of course, Dani was exactly six years older than Chad. 6. Multiply Chad’s party hours by 19 to find his number of guests. 7. Ray had more guests than Dani, Dani’s party lasted exactly two hours less than Chet’s party, and Ray’s party lasted two hours less than Dora’s party.

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

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Teac he r

The story

Chad

Chet

Dora

Dani

Ray

56 years old 50 years old 44 years old 38 years old 32 years old

80 guests 76 guests 72 guests 68 guests 64 guests

8 hours 7 hours 6 hours 5 hours 4 hours

$2000 $1500 $1000 $750 $375

150 cm 120 cm 75 cm 60 cm 30 cm

w ww

. te

$2000 $1500 $1000 $750 $375 150 cm 120 cm 75 cm 60 cm 30 cm

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o c . che e r o t r s super

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Maths perplexors

| 43

Thanksgiving feast The clues

Bertha, Clara, Daphne, Elsie and Frances were five American mothers who liked to host Thanksgiving dinner. They had 40, 38, 36, 34 and 32 guests for dinner. They roasted turkeys that weighed 34, 32, 28, 25 and 22 pounds. They cooked 50, 49, 47, 40 and 32 individual sweet potatoes. They baked 27, 24, 21, 20 and 16 pumpkin pies. They prepared 72, 69, 65, 64 and 57 individual ears of corn for the dinner. Based on the clues, match the mothers with their guests, turkeys, sweet potatoes, pies and ears of corn.

1. The mother with the fewest guests planned on each guest eating exactly 16 ounces of turkey, one sweet potato, one-half of a pumpkin pie, and two ears of corn in order for all the food to be eaten. 2. The mother with the most guests planned on each guest eating one sweet potato and one-half of a pumpkin pie each. 3. Elsie had more guests than Frances, Frances had more guests than Daphne, Bertha had more guests than Elsie, and Daphne had more guests than Clara. 4. The mother who roasted the smallest turkey made the most sweet potatoes and pies. 5. Bertha’s turkey weighed 48 ounces less than Elsie’s turkey, Daphne baked exactly three fewer pies than Elsie, and Elsie made more sweet potatoes than Daphne. 6. Daphne made more ears of corn than Clara, Frances made more ears of corn than Daphne, and Elsie made more ears of corn than Frances.

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

ew i ev Pr

Teac he r

The story

1 pound = 16 ounces

Bertha

40 guests 38 guests 36 guests 34 guests 32 guests

34 lb. turkey 32 lb. turkey 28 lb. turkey 25 lb. turkey 22 lb. turkey

50 potatoes 49 potatoes 47 potatoes 40 potatoes 32 potatoes

27 pies 24 pies 21 pies 20 pies 16 pies

72 corn 69 corn 65 corn 64 corn 57 corn

w ww

34 lb. turkey 32 lb. turkey 28 lb. turkey 25 lb. turkey 22 lb. turkey 50 potatoes 49 potatoes 47 potatoes 40 potatoes 32 potatoes

44 | Maths perplexors

. te

m . u

40 guests 38 guests 36 guests 34 guests 32 guests

ClaraR. Daphne Elsie © I . C. Publ i cat i ons Frances •f orr evi ew pur posesonl y•

o c . che e r o t r s super

R.I.C. Publications®

50 potatoes 49 potatoes 47 potatoes 40 potatoes 32 potatoes

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I ate it on the street The clues

Laura, Mike, Nellie, Oscar and Patty were street food vendors in the town of Hamilton. They sold the same five food items of apples, bananas, doughnuts, samosas and hot dogs. One recent day, they compared their sales for the day. They sold 90, 87, 86, 82 and 79 apples. They sold 127, 120, 113, 106 and 100 bananas. They sold 270, 258, 237, 226 and 200 doughnuts. They sold 360, 348, 316, 300 and 280 samosas. They sold 450, 435, 395, 350 and 300 hot dogs. Based on the clues, match the vendors with their sales of all five food items.

1. Each vendor sold the most of one of the five food items, and each vendor sold the least of one of the five food items. 2. Oscar and Patty sold a combined total of 580 samosas and 650 hot dogs. 3. Patty sold exactly seven fewer bananas than Nellie, Laura sold exactly seven fewer bananas than Oscar, and Oscar sold exactly seven fewer bananas than Patty. 4. Nellie and Patty sold a combined total of 426 doughnuts, and Mike and Nellie sold a combined total of 885 hot dogs. 5. Oscar sold equal numbers of samosas and hot dogs. 6. Multiply Mike’s apple number by four to determine his samosa number. 7. Oscar sold exactly three more apples than Laura, and Mike sold more doughnuts than Laura.

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

ew i ev Pr

Teac he r

The story

Laura

Mike

Nellie

Oscar

Patty

90 apples 87 apples 86 apples 82 apples 79 apples

127 bananas 120 bananas 113 bananas 106 bananas 100 bananas

270 doughnuts 258 doughnuts 237 doughnuts 226 doughnuts 200 doughnuts

360 samosas 348 samosas 316 samosas 300 samosas 280 samosas

450 hot dogs 435 hot dogs 395 hot dogs 350 hot dogs 300 hot dogs

450 hot dog 435 hot dogs 395 hot dogs 350 hot dogs 300 hot dogs

450 hot dogs 435 hot dogs 395 hot dogs 350 hot dogs 300 hot dogs

w ww

. te

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Maths perplexors

| 45

Hopping cows The clues

Pamela, Harriet, Hannah, Hilda and Clara were five cows belonging to Farmer Jones. They were always devising contests and competing against each other. In the hopping on one hoof contest, they hopped 275, 265, 255, 250 and 240 hops in a minute. In the field goal kicking contest, they kicked field goals of 77, 75, 70, 65 and 60 metres. In the milk production contest, they produced 92, 80, 68, 60 and 48 litres of milk in a day. In the swatting flies with their tails contest, they swatted 523, 500, 477, 454 and 400 flies in an hour. In the bales of hay-eating contest, they ate 17, 16, 15, 14 and 12 bales of hay in a day. Based on the clues, match the cows with their results in the contests.

1. Pamela, Harriet and Hannah each won at least one contest and had none of the worst scores, and Hilda and Clara won no contests and each had at least one of the worst scores. 2. Pamela hopped exactly 10 more hops than Hilda, and Harriet hopped exactly 10 hops less than Clara. 3. Hilda’s field goal kick was 500 cm less than Hannah’s kick, and Hannah’s field goal kick was exactly 500 cm less than Pamela’s field goal kick. 4. Hannah produced exactly 8000 more millilitres of milk than Hilda. 5. Harriet ate more bales of hay than Hilda but fewer bales of hay than Hannah. 6. Hannah swatted exactly 23 more flies than Harriet, and Hilda swatted exactly 23 more flies than Hannah. 7. The cow that won the hopping contest did not win another contest, and the cow that won the field goal kicking contest did not win another contest. 8. Hilda did not eat the fewest bales and Clara’s field goal kick was shorter than Hilda’s.

Pamela

275 hops 265 hops 255 hops 250 hops 240 hops

77 m kick 75 m kick 70 m kick 65 m kick 60 m kick

92 L 80 L 68 L 60 L 48 L

523 flies 500 flies 477 flies 454 flies 400 flies

17 bales 16 bales 15 bales 14 bales 12 bales

w ww

77 m kick 75 m kick 70 m kick 65 m kick 60 m kick 92 L 80 L 68 L 60 L 48 L

46 | Maths perplexors

. te

275 hops 265 hops 255 hops 250 hops 240 hops

m . u

275 hops 265 hops 255 hops 250 hops 240 hops

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

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Teac he r

The story

o c . che e r o t r s super

R.I.C. Publications®

77 m kick 75 m kick 70 m kick 65 m kick 60 m kick 92 L 80 L 68 L 60 L 48 L

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It’s all in the pasta The clues

Jake, Kathy, Laurel, Marty and Nigel all owned Italian restaurants. They kept records of their most popular types of pasta and compared the results. They sold 875, 865, 855, 850 and 840 plates of penne. They sold 780, 770, 760, 750 and 730 plates of linguine. They sold 415, 400, 385, 370 and 345 plates of rotini pasta. They sold 2100, 1750, 1560, 830 and 800 plates of spaghetti. They sold 1660, 1600, 1500, 1460 and 1400 plates of ravioli. Based on the clues, match the owners with the number of different types of pasta they sold in a week.

1. Each of the five owners sold the most of one type of pasta, and Marty and Nigel were the only two owners who sold the least of any type of pasta. 2. Jake, Kathy and Laurel did not sell the most plates of linguine and rotini, and each of these three sold more plates of spaghetti than they sold of ravioli. 3. Kathy sold exactly 60 fewer plates of ravioli than Jake, Jake sold exactly 10 fewer plates of penne than Laurel, and Kathy sold exactly 10 fewer plates of penne than Jake. 4. Nigel did not sell the most linguine, Jake sold exactly 10 fewer plates of linguine than Kathy, and Laurel sold exactly 10 fewer plates of linguine than Marty. 5. Laurel sold exactly 15 fewer plates of rotini than Jake, and Kathy sold exactly 15 fewer plates of rotini than Nigel. 6. Marty sold exactly 10 more plates of penne than he sold of spaghetti. 7. Laurel sold exactly 100 fewer plates of ravioli than Kathy, but Laurel sold exactly 100 more plates of ravioli than Marty and, of course, Jake sold more spaghetti than Laurel.

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

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Teac he r

The story

©R . I . C.Pu bl i cat i on Kathy Laurel Martys •f orr evi ew pur posesonl y•

Jake

Nigel

875 penne 865 penne 855 penne 850 penne 840 penne

780 linguine 770 linguine 760 linguine 750 linguine 730 linguine

415 rotini 400 rotini 385 rotini 370 rotini 345 rotini

2100 spaghetti 1750 spaghetti 1560 spaghetti 830 spaghetti 800 spaghetti

1660 ravioli 1600 ravioli 1500 ravioli 1460 ravioli 1400 ravioli

. te

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o c . che e r o t r s super

R.I.C. Publications®

875 penne 865 penne 855 penne 850 penne 840 penne

m . u

875 penne 865 penne 855 penne 850 penne 840 penne

w ww

875 penne 865 penne 855 penne 850 penne 840 penne

Maths perplexors

| 47

Sports day fun The clues

Dick, Elsie, Fanny, Greta and Hank were the five finalists in the Bates Primary School sports carnival and biscuit-eating contest. They raced the 100 meters and finished in 16, 15, 14, 13 and 12 seconds. They triple jumped 16, 15, 14, 13 and 12 metres. They long jumped 600, 570, 540, 510 and 480 cm. They threw a discus 28, 26, 24, 20 and 18 metres. They ate 27, 25, 24, 23 and 21 biscuits in a minute. Based on the clues, match the finalists with their racing times, vaulting heights, jumping lengths, throwing distances and biscuit-eating totals.

1. Each of the five finalists scored the best in one of the five categories, and each scored the worst in one of the five events. 2. Fanny was the only finalist whose triple jump distance was the same as her seconds in the 100-metre race. 3. Elsie raced exactly one second faster than Greta, Greta raced exactly one second faster than Hank, and Hank raced exactly one second faster than Dick. 4. Fanny triple jumped exactly one metre less than Hank, Hank triple jumped exactly three metres less than Greta, and Hank triple jumped two metres less than Dick. 5. Hank long jumped exactly 1.2 m farther than Greta, and Hank threw the discus exactly 200 cm farther than Greta as well. 6. Dick ate exactly two more biscuits than Greta, and Dick long jumped exactly 60 cm farther than Greta. 7. Elsie long jumped exactly 60 cm farther than Fanny.

Dick

ElsieR. Fannyu Greta © I . C.P bl i cat i ons Hank •f orr evi ew pur posesonl y• 16 seconds 15 seconds 14 seconds 13 seconds 12 seconds

16 seconds 15 seconds 14 seconds 13 seconds 12 seconds

16 m triple jump 15 m triple jump 14 m triple jump 13 m triple jump 12 m triple jump

600 cm jump 570 cm jump 540 cm jump 510 cm jump 480 cm jump

28 m discus 26 m discus 24 m discus 20 m discus 18 m discus

27 biscuits 25 biscuits 24 biscuits 23 biscuits 21 biscuits

w ww

16 m triple jump 15 m triple jump 14 m triple jump 13 m triple jump 12 m triple jump 600 cm jump 570 cm jump 540 cm jump 510 cm jump 480 cm jump

48 | Maths perplexors

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16 seconds 15 seconds 14 seconds 13 seconds 12 seconds

m . u

16 seconds 15 seconds 14 seconds 13 seconds 12 seconds

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Teac he r

The story

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Marooned The clues

Ruth, Sarah, Tom, Vicky and Walter were marooned together on a 2000-hectare island. After some discussion, they divided the 2000 hectares into 600, 500, 400, 300 and 200-hectare sections and agreed to live on their own sections. While living on their sections, they gathered 600, 500, 400, 300 and 200 coconuts. They gathered 600, 500, 400, 300 and 200 clams. They gathered 600, 500, 400, 300 and 200 crabs. They gathered 600, 500, 400, 300 and 200 oysters. When they added up all the numbers for each person the answer was 2000 for each person. Based on the clues, match the names with their hectares, coconuts, clams, crabs and oysters.

1. Each person marooned on the island managed to use all five numbers exactly one time. If a person lived on 200 hectares, he or she did not have 200 coconuts, clams, crabs or oysters, and so on. 2. Multiply Sarah’s hectares by two to discover Walter’s hectares, and multiply Ruth’s hectares by two to find Tom’s hectares. 3. Vicky had a combined total of 900 coconuts and clams, and Walter had more acres than Tom. 4. Tom had a combined total of 700 clams and crabs, Ruth had a combined total of 800 crabs and oysters, Sarah had a combined total of 600 coconuts and clams, and Walter had a combined total of 500 clams and crabs.

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

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Teac he r

The story

Ruth

Sarah

Tom

Vicky

Walter

600 acres 500 acres 400 acres 300 acres 200 acres

600 coconuts 500 coconuts 400 coconuts 300 coconuts 200 coconuts

600 clams 500 clams 400 clams 300 clams 200 clams

600 crabs 500 crabs 400 crabs 300 crabs 200 crabs

600 oysters 500 oysters 400 oysters 300 oysters 200 oysters

w ww

. te

600 crabs 500 crabs 400 crabs 300 crabs 200 crabs 600 oysters 500 oysters 400 oysters 300 oysters 200 oysters

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m . u

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Maths perplexors

| 49

You auto have fun The clues

Audrey, Drake, Glenda, Kyle and June sold used cars for a living. In one recent year, they sold 500, 490, 470, 460 and 450 sports cars. They sold 990, 980, 960, 950 and 940 trucks. They sold 757, 753, 749, 745 and 700 vans. They sold 672, 650, 628, 606 and 600 coupés. They sold 350, 335, 320, 305 and 300 sedans. Based on the clues, match the names with the number of sports cars, trucks, vans, coupés and sedans they sold that year.

1. Each sales person sold the most of one kind of car, and each sales person also sold the fewest of another kind of car. 2. Glenda and June sold a combined total of 990 sports cars, Audrey and Drake sold a combined total of 1890 trucks, Audrey and Glenda sold a combined total of 1510 vans, and Glenda and Kyle sold a combined total of 1206 coupés. 3. Multiply Glenda’s sports car sales by two to find her truck sales. 4. Audrey and Drake sold a combined total of 685 sedans. 5. Neither June nor Glenda sold 300 sedans, and Drake sold exactly 15 more sedans than Glenda. 6. Audrey sold more trucks than Drake, and Audrey sold more coupés than June. 7. Kyle sold more sports cars than Drake, but Drake sold more vans than Kyle.

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

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Teac he r

The story

Audrey

Drake

Glenda

Kyle

June

500 sports 490 sports 470 sports 460 sports 450 sports

990 trucks 980 trucks 960 trucks 950 trucks 940 trucks

757 vans 753 vans 749 vans 745 vans 700 vans

672 coupés 650 coupés 628 coupés 606 coupés 600 coupés

350 sedans 335 sedans 320 sedans 305 sedans 300 sedans

500 sports 490 sports 470 sports 460 sports 450 sports

m . u

w ww

50 | Maths perplexors

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990 trucks 980 trucks 960 trucks 950 trucks 940 trucks

o c . che e r o t r s super

R.I.C. Publications®

757 vans 753 vans 749 vans 745 vans 700 vans

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Answers 1. Dog days

10. Fair contests

Spot

Fido

Duke

Arlene

Arthur

Betty

Byron

Cassie

18 kg 8 hrs sleeping 10 hrs barking 6 hrs scratching

27 kg 10 hrs sleeping 6 hrs barking 8 hrs scratching

9 kg 6 hrs sleeping 8 hrs barking 10 hrs scratching

7.6 m 18 pies 30 sheep

11.7 m 10 pies 40 sheep

10.4 m 15 pies 45 sheep

13 m 17 pies 47 sheep

9.1 m 20 pies 38 sheep

2. Farm fitting

11. Bests in baking David

Evie

Frank

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

Gilda

Hilda

492 biscuits

468 biscuits

Smith

Jones

540 biscuits

600 corn 100 beans 400 carrots 200 wheat 500 tomatoes 300 squash

400 corn 200 beans 500 carrots 300 wheat 600 tomatoes 100 squash

500 corn 300 beans 600 carrots 100 wheat 400 tomatoes 200 squash

720 doughnuts 696 doughnuts 672 doughnuts 588 doughnuts 600 doughnuts

3. Getting petrol Billy

Betty

25 years old 150 kg 76 L 20 yrs car

20 years old 75 kg 57 L 17 yrs car

Bobbi

Burt

30 years old 57 kg 68 L 15 yrs car

40 years old 114 kg 72 L 10 yrs car

4. Vegetable stew Carl

Callie

Charli

Craig

30 carrots 12 potatoes 35 tomatoes 40 onions

20 carrots 13 potatoes 40 tomatoes 60 onions

24 carrots 15 potatoes 34 tomatoes 54 onions

27 carrots 17 potatoes 26 tomatoes 48 onions

516 biscuits

348 pies

360 pies

336 pies

300 pies

240 pies

60 cm

50 cm

30 cm

100 cm

120 cm

12. Fishing eagles Randy

Spike

Tug

Val

Winnie

40.5 m 52 carp 47 bass 35 perch

43 m 50 carp 46 bass 33 perch

46.5 m 46 carp 67 bass 27 perch

38 m 45 carp 63 bass 47 perch

35.5 m 40 carp 60 bass 46 perch

13. Bear with me Ben

Bev

10 kg salmon 800 berries 14 kg honey 250 baskets

7.5 kg salmon 840 berries 13 kg honey 300 baskets

15 kg salmon 700 berries 12 kg honey 375 baskets

Dee

12.5 kg salmon 720 berries 10 kg honey 425 baskets

Joan 21 pies 48 hot dogs 100 tacos 10 burgers

John

Jake

Jane

22 pies 50 hot dogs 80 tacos 15 burgers

24 pies 38 hot dogs 88 tacos 14 burgers

18 pies 44 hot dogs 96 tacos 20 burgers

6. Vertical schooling Gail

Gordon

Year 4 3rd floor 12 girls 11 boys

Year 2 1st floor 16 girls 17 boys

Year 1 2nd floor 15 girls 14 boys

w ww

Greg

Year 3 4th floor 13 girls 10 boys

. te

7. Hoot’s there?

Olivia

Ollie

Opal

6 yrs old 100 cm 12 mice 70 hoots

4 yrs old 120 cm 14 mice 78 hoots

2 yrs old 50 cm 28 mice 35 hoots

10 yrs old 60 cm 24 mice 39 hoots

8. What’s cooking? Glenview

Northbrook

Northfield

Deerfield

200 pies 400 bread 300 cakes 100 pudding

300 pies 100 bread 200 cakes 400 pudding

400 pies 200 bread 100 cakes 300 pudding

100 pies 300 bread 400 cakes 200 pudding

9. That’s class Allie

Ben

Carol

Dick

Eliot

Year 3 22 boys 10 girls

Year 2 21 boys 13 girls

Year 4 15 boys 19 girls

Year 5 17 boys 18 girls

Year 1 20 boys 14 girls

R.I.C. Publications®

Dora 11 kg salmon 750 berries 8 kg honey 400 baskets

Muffy

Fluffy

Boots

Duke

Moby

30 yrs old 75 tonnes 1000 m 250 squid

35 yrs old 60 tonnes 1500 m 400 squid

40 yrs old 80 tonnes 2500 m 500 squid

38 yrs old 90 tonnes 4000 m 460 squid

36 yrs old 100 tonnes 3000 m 480 squid

15. Fruit files David

Elsie

Frank

Gail

Hilda

1300 apples 750 peaches 425 pears 300 lemons

1400 apples 800 peaches 450 pears 275 lemons

1250 apples 700 peaches 500 pears 175 lemons

1500 apples 600 peaches 375 pears 250 lemons

1450 apples 725 peaches 400 pears 200 lemons

16. Hidden nuts Alvin

Bunky

Carl

David

Eliot

15 acorns 17 pecans 9 almonds 1 walnut

14 acorns 16 pecans 10 almonds 3 walnuts

20 acorns 13 pecans 4 almonds 6 walnuts

18 acorns 11 pecans 5 almonds 7 walnuts

19 acorns 12 pecans 8 almonds 2 walnuts

o c . che e r o t r s super

Oscar

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14. Whale tales

m . u

5. Fair eating

Grace

600 biscuits

ew i ev Pr

Teac he r

Brown

17. Hits just a game Jack

Inez

Jill

Kelly

Laura

90 at bat 40 hits 10 walks 40 outs

83 at bat 30 hits 9 walks 44 outs

104 at bat 35 hits 19 walks 50 outs

102 at bat 37 hits 20 walks 45 outs

92 at bat 38 hits 15 walks 39 outs

18. A day at the beach Jake

Kathy

Linc

Mark

Nellie

53 cm ball 100 SPF 52 sharks 390 bites

56 cm ball 95 SPF 57 sharks 400 bites

112 cm ball 90 SPF 35 sharks 500 bite

106 cm ball 88 SPF 40 sharks 440 bites

28 cm ball 83 SPF 47 sharks 450 bites

Maths perplexors

| 51

Answers 19. Just for the farm of it

27. Good knight

Mike

Nell

Oscar

Paula

Ruth

Derek

David

Donald

Drew

Daniel

45 yrs old 252 cm 548 m pig 29 L

40 yrs old 279 cm 521 m pig 37 L

35 yrs old 63 cm 530 m pig 53 L

55 yrs old 140 cm 539 m pig 49 L

50 yrs old 126 cm 535 m pig 45 L

420 jousts 220 damsels 42 dragons 220 quests 83 horses

460 jousts 205 damsels 45 dragons 230 quests 85 horses

500 jousts 250 damsels 50 dragons 215 quests 64 horses

470 jousts 235 damsels 47 dragons 235 quests 71 horses

480 jousts 190 damsels 39 dragons 240 quests 78 horses

20. To bee or not to bee Jim

Kate

Lulu

Year 3 675 words 18 boys 11 girls

Year 2 650 words 17 boys 10 girls

Year 6 595 words 13 boys 14 girls

21. Farm figures

28. Who’s on first?

Year 5 625 words 12 boys 15 girls

Year 4 620 words 16 boys 9 girls

Jill

James

Jane

Jack

Joan

15 yrs old Bike 4 5th in line 4 hot dogs 1 scoop

16 yrs old Bike 5 3rd in line 1 hot dog 3 scoops

18 yrs old Bike 3 4th in line 5 hot dogs 2 scoops

14 yrs old Bike 1 2nd in line 2 hot dogs 5 scoops

13 yrs old Bike 2 1st in line 3 hot dogs 4 scoops

Carl

700 cotton 600 wheat 900 corn 1000 beans 800 beets

600 cotton 700 wheat 800 corn 900 beans 1000 beets

Dana

Ellie

800 cotton 900 wheat 1000 corn 600 beans 700 beets

1000 cotton 800 wheat 600 corn 700 beans 900 beets

22. Lucky numbers 25 hat 20 shirt 10 coat 5 tie 15 pants

Tollie

Buddy

Slim

Jonas

20 hat 15 shirt 5 coat 25 tie 10 pants

5 hat 10 shirt 15 coat 20 tie 25 pants

10 hat 5 shirt 25 coat 15 tie 20 pants

15 hat 25 shirt 20 coat 10 tie 5 pants

23. Oh, brother!

Sharon

Stanley

Susan

Year 2 3rd floor 21 years 15 boys 20 girls

Year 3 2nd floor 10 years 16 boys 22 girls

Year 5 1st floor 20 years 17 boys 23 girls

30. Your vote counts

Sam

Sara

Year 1 4th floor 40 years 21 boys 14 girls

Year 4 5th floor 42 years 19 boys 18 girls

Randy

Stacy

Troy

Inez

Rory

500 speeches

700 speeches

1000 speeches 900 speeches

800 promises

300 promises

1200 promises 1800 promises 1400 promises

600 speeches

Ricky

Sam

3rd floor 33 yrs old 740 cars 905 coins 600 stamps

4th floor 36 yrs old 800 cars 880 coins 560 stamps

Tom

Vic

Will

5th floor 40 yrs old 770 cars 930 coins 540 stamps

2nd floor 35 yrs old 720 cars 1000 coins 500 stamps

1st floor 38 yrs old 690 cars 950 coins 620 stamps

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24. You auto know this Bertha

Bonnie

Bert

Bret

Bill

Car 75 18 years 1st 45 2nd 90 3rd 90

Car 79 16 years 1st 47 2nd 70 3rd 140

Car 99 13 years 1st 40 2nd 80 3rd 160

Car 60 20 years 1st 35 2nd 60 3rd 120

Car 89 15 years 1st 39 2nd 78 3rd 100

25. Flower children

. te

90 kisses

70 kisses

40 kisses

50 kisses

900 shakes

600 shakes

300 shakes

400 shakes

350 shakes

2260 votes

1690 votes

2570 votes

3140 votes

2400 votes

Fred

Gail

Hank

Jill

Ken

1st 1000 yds 2nd 900 yds 3rd 700 yds 4th 600 yds 5th 800 yds

1st 800 yds 2nd 1000 yds 3rd 600 yds 4th 900 yds 5th 700 yds

1st 600 yds 2nd 700 yds 3rd 800 yds 4th 1000 yds 5th 900 yds

1st 700 yds 2nd 600 yds 3rd 900 yds 4th 800 yds 5th 1000 yds

1st 900 yds 2nd 800 yds 3rd 1000 yds 4th 700 yds 5th 600 yds

32. Hooked on fishing Sharon

Sally

Saul

Shawn

Sarah

625 perch 1450 bass 350 trout 70 salmon 190 catfish

650 perch 1500 bass 250 trout 85 salmon 160 catfish

750 perch 1400 bass 270 trout 90 salmon 150 catfish

725 perch 1200 bass 300 trout 95 salmon 170 catfish

700 perch 1300 bass 325 trout 65 salmon 200 catfish

o c . che e r o t r s super

Year 1

Year 2

Year 3

Year 4

Year 5

15 m roses 9 m tulips 12 m lilies 3 m daisies 6 m peonies

9 m roses 12 m tulips 6 m lilies 15 m daisies 3 m peonies

3 m roses 6 m tulips 9 m lilies 12 m daisies 15 m peonies

6 m roses 3 m tulips 15 m lilies 9 m daisies 12 m peonies

12 m roses 15 m tulips 3 m lilies 6 m daisies 9 m peonies

26. Something to crow about Hecky

Cawful

Bing

Moose

Dirk

21 m 7 yrs old 42 kph 84 caws 168 grubs

18 m 5 yrs old 45 kph 90 caws 180 grubs

24 m 12 yrs old 46 kph 80 caws 160 grubs

27 m 10 yrs old 50 kph 100 caws 200 grubs

15 m 8 yrs old 48 kph 96 caws 150 grubs

52 | Maths perplexors

60 kisses

m . u

Pinky

29. Lighthouse School

ew i ev Pr

900 cotton 1000 wheat 700 corn 800 beans 600 beets

Nancy

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

Betty

Teac he r

Alex

Moe

33. Herd around the town Alton

Balton

Carleton

Dayton

Elton

500 goats 1000 horses 1200 bison 1800 elk 2500 sheep

200 goats 800 horses 1500 bison 2000 elk 2200 sheep

100 goats 700 horses 1300 bison 1600 elk 2100 sheep

400 goats 600 horses 1100 bison 1900 elk 2300 sheep

300 goats 900 horses 1400 bison 1700 elk 2400 sheep

34. Eating lizards Larry 75 flies 50 roaches 180 ants 425 gnats 45 bees

Liza 95 flies 30 roaches 160 ant 300 gnats 35 bees

Lucy 80 flies 56 roaches 200 ants 375 gnats 25 bees

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Lenny 70 flies 24 roaches 125 ants 275 gnats 40 bees

Luke 90 flies 44 roaches 150 ants 400 gnats 20 bees

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Answers 35. Rug makers

43 Happy birthday

Ivan

Inez

Inga

Igor

Irene

Chad

Chet

Dora

Dani

Ray

420 cm long 180 cm 7.56 m2 120 cm D 5 Main St

600 cm long 240 cm 14.4 m2 150 cm D 3 Main St

540 cm long 300 cm 16.2 m2 180 cm D 2 Main St

360 cm long 60 cm wide 2.16 m2 60 cm D 4 Main St

480 cm long 120 cm wide 5.76 m2 90 cm D 1 Main St

38 yrs old 76 guests 4 hours $750 75 cm

32 yrs old 64 guests 8 hours $375 150 cm

50 yrs old 80 guests 7 hours $1000 120 cm

44 yrs old 68 guests 6 hours $1500 60 cm

56 yrs old 72 guests 5 hours $2000 30 cm

36. Cycling cicadas

44. Thanksgiving feast

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

Connie

Cora

Callie

Clara

Bertha

Clara

Daphne

Elsie

Frances

10 yr cycle 25 May 240 hours 900 eggs 72 cm

8 yr cycle 30 May 120 hours 850 eggs 144 cm

17 yr cycle 15 May 192 hours 950 eggs 180 cm

15 yr cycle 20 May 96 hours 1000 eggs 288 cm

12 yr cycle 12 May 168 hours 925 eggs 360 cm

40 guests 25 lb. turkey 40 potatoes 20 pies 57 corn

32 guests 32 lb. turkey 32 potatoes 16 pies 64 corn

34 guests 34 lb. turkey 47 potatoes 21 pies 65 corn

38 guests 28 lb. turkey 49 potatoes 24 pies 72 corn

36 guests 22 lb. turkey 50 potatoes 27 pies 69 corn

37. Dancing hippos

45. I ate it on the street

ew i ev Pr

Teac he r

Carol

Henry

Hilda

Harriet

Hank

Hannah

Laura

Mike

Nellie

Oscar

29 yrs old 33 m 18 hours 2000 kg 66 fish

25 yrs old 36 m 11 hours 1900 kg 68 fish

22 yrs old 18 m 13 hours 1750 kg 75 fish

35 yrs old 15 m 9 hours 1650 kg 70 fish

32 yrs old 30 m 16 hours 1800 kg 61 fish

79 apples

87 apples

86 apples

82 apples

90 apples

106 bananas

100 bananas

127 bananas

113 bananas

120 bananas

38. Towns that work

Patty

237 doughnuts 258 doughnuts 200 doughnuts 270 doughnuts 226 doughnuts 360 samosas

348 samosas

316 samosas

300 samosas

280 samosas

395 hot dogs

450 hot dogs

435 hot dogs

300 hot dogs

350 hot dogs

46. Hopping cows

Alton

Balton

Carleton

Dayton

Elton

Pamela

Harriet

Hannah

Hilda

Clara

90 police 81 doctors 173 lawyers 65 teachers 29 pilots

50 police 76 doctors 125 lawyers 55 teachers 37 pilots

100 police 83 doctors 161 lawyers 105 teachers 35 pilots

60 police 85 doctors 185 lawyers 85 teachers 32 pilots

80 police 78 doctors 138 lawyers 95 teachers 40 pilots

250 hops 75 m kick 92 L 523 flies 17 bales

255 hops 77 m kick 80 L 454 flies 15 bales

275 hops 70 m kick 68 L 477 flies 16 bales

240 hops 65 m kick 60 L 500 flies 14 bales

265 hops 60 m kick 48 L 400 flies 12 bales

39. Sandcastles

Belle

Baxter

Jake

Kathy

Laurel

Marty

Nigel

Team 100 8 members 64 hours 720 cm high 7.5m D

Team 97 16 members 160 hours 450 cm high 6m D

Team 87 20 members 128 hours 630 cm high 3m D

Team 90 12 members 91 hours 900 cm high 4.5 m D

865 penne

855 penne

875 penne

840 penne

850 penne

750 linguine

760 linguine

770 linguine

780 linguine

730 linguine

385 rotini

400 rotini

370 rotini

345 rotini

415 rotini

1750 spaghetti

2100 spaghetti 1560 spaghetti

830 spaghetti

800 spaghetti

1660 ravioli

1600 ravioli

1400 ravioli

1460 ravioli

Max

Duke

Baldy

Dick

Elsie

Fanny

Greta

Hank

1100 red 800 blue 500 green 1400 yellow 1200 pink

1200 red 500 blue 1400 green 800 yellow 1100 pink

1400 red 1100 blue 1200 green 500 yellow 800 pink

16 seconds 15 m triple 540 cm jump 28 m discus 25 biscuits

13 seconds 14 m triple 570 cm jump 18 m discus 27 biscuits

12 seconds 12 m triple 510 cm jump 20 m discus 24 biscuits

14 seconds 16 m triple 480 cm jump 24 m discus 23 biscuits

15 seconds 13 m triple 600 cm jump 26 m discus 21 biscuits

Scott

Biff

Ruth

Sarah

Tom

Vicky

Walter

200 acres 400 coconuts 600 clams 500 crabs 300 oysters

300 acres 200 coconuts 400 clams 600 crabs 500 oysters

400 acres 300 coconuts 500 clams 200 crabs 600 oysters

500 acres 600 coconuts 300 clams 400 crabs 200 oysters

600 acres 500 coconuts 200 clams 300 crabs 400 oysters

40. How have you bean doing? Peter

800 red 1400 blue 1100 green 1200 yellow 500 pink

Spike

1500 ravioli

48. Sports day fun

. te

500 red 1200 blue 800 green 1100 yellow 1400 pink

41. Basketball anyone?

m . u

Sandy

Team 94 13 members 72 hours 540 cm high 9m D

w ww

Bela

o c . che e r o t r s super 49. Marooned

Moose

Shorty

Alex

uniform 35

uniform 44

uniform 88

uniform 70

uniform 22

90 cm

210 cm

180 cm

150 cm

120 cm

600 points

475 points

575 points

550 points

500 points

34 fouls

37 fouls

40 fouls

47 fouls

50 fouls

96 free throws

92 free throws

90 free throws

88 free throws 45 free throws

42. Travelling for days

50. You auto have fun

Aaron

Betty

Carol

Diane

Eddie

Audrey

Drake

Glenda

Kyle

June

10 India 17 Korea 2 China 14 Japan 24 Russia

9 India 18 Korea 4 China 19 Japan 20 Russia

25 India 16 Korea 5 China 6 Japan 3 Russia

23 India 12 Korea 10 China 7 Japan 1 Russia

21 India 11 Korea 15 China 13 Japan 8 Russia

450 sports 950 trucks 753 vans 650 coupés 350 sedans

460 sports 940 trucks 749 vans 672 coupés 335 sedans

490 sports 980 trucks 757 vans 600 coupés 320 sedans

470 sports 990 trucks 745 vans 606 coupés 300 sedans

500 sports 960 trucks 700 vans 628 coupés 305 sedans

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Maths perplexors

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