Theoni Pappas - Puzzles from Penrose the Mathematical Cat

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THE CHILDRENS MATHEMATICS CALENDARS

NUMBERS & OTHER MATH IDEAS COME ALIVE

Puzzles

from

Penrose

the mathematical cat

theoni pappas

Wide World Publishing Tetra

Copyright 2013 by Theoni Pappas.

All rights reserved.

No part of this work may be reproduced, copied or transmitted in any form or by any means without written permission from both the copyright owner and Wide World Publishing/Tetra. Without limiting the rights under the copyrights reserved above, no part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted, in any form or by any means (electronic, mechanical, photocopying, recording or otherwise), without written permission of both the copyright owner and the publisher of this book.

Publisher:

Wide World Publishing/Tetra

P.O. Box 476

San Carlos, CA 94070

web site: http://www.wideworldpublishing.com

First e-book format edition 2013 ISBN: 978-1-884550-71-3

TABLE of CONTENTS

When Theoni Pappas, Penroses mistress, first saw him, he was not only the runt of the litter, but a scaredy-cat that would dash away when anyone came near him. It took a bit of time for his mistress to make him feel safe and comfortable.

Penrose had no idea what was in store for him in his new home. In fact, when he learned his mistress was a mathematics person, he was certain his life would be very quiet and probably a bit boring around the house. He quickly learned to the contrary. Whenever he walked into her office, he would always find papers and books scattered around. He often noticed books opened to drawings, papers scribbled with strange symbols and formsall fascinating looking objects. In the beginning he had no idea what the equations and symbols he came across meant, but he began to realize they must be important to some people.

Penrose would often stretch out on his mistress papers, and as he studied them he began to discover new and exciting worlds of incredible ideas. Sure he came across lots of math problems, but somehow these were not always tedious computation problems.

He found problems that made him think in a new way. He knew he couldnt just guess a number answer he had to put on his logic hat. Discovering ideas and using logic is what Penrose learned to love about mathematics.

Penrose has made many friends and met many interesting creatures and peoplefrom his cat friends, Watson, Maya, Morris Snowpea, and Maurice to Mr. Abacus, Fibonacci rabbit, the fractal dragon, Tangramians, the math-reptiles, and Sorry Snowflake to name a few. From his many math adventures with these and other friends, Penrose began to collect puzzles he liked. He decided to share some of his favorite puzzles from his collection in this book. Some have been around a long time. Some may seem easy while others require much thought. He hopes you will enjoy tackling them.

When Penrose attended the Cats Galore Cat Show, he noticed that 1/2 of the cats were Siamese, 1/4 were Persian, 1/5 were Abbys, and 1 cat was a Tabby. How did he figure out how many cats were in the show without having to count them?

From my mistress work I learned about special properties of numbers. Do you know which numbers I am describing below?

(1)Divide me into any number and the number remains unchanged.

(2)I am even and I am a prime number.

(3)I cannot be divided into any number, yet every number can be divided into me.

(4)Add me to any number, and the number remains unchanged.

(5)Add a trillion of me and the sum is the same as adding just two of me.

It was Tuesday, when my mistress and I went to see her neighbors sons, Tom and Jerry at work. When it came time for Tom to go home, Jerry wouldnt let him. Why?

I figured out a way by moving only one glass of water that I could line up the glasses so that full ones and empty ones alternate. What did I do?

My cat friend Morris tried and tried to solve this puzzle, but he just couldnt do it.

Without lifting your pencil, connect the 9 dots with just 4 straight lines.

Move 3 red dots so the stack points downward

At first when I saw this problem I thought to myself, Why are letters mixed with the numbers? This was a tricky one until I started trying different possibilities.

(1) 24 toothpick-like sticks are joined to make this figure. Take away 8 toothpicks, and end up with just two squares.