A Home for Mathematics in Literature - The Problems
The Curious Incident of the Dog in the Night-Time, written by Mark Haddon, is a national bestseller that brings life to some of the mathematical stumpers and tricks that a MATHCOUNTS audience would enjoy! Christopher Boone is the main character, and he allows the reader to read over his shoulder as he writes a murder mystery. His love for mathematics is obvious from the start… the first chapter is Chapter 2, the next is Chapter 3, followed by Chapters 5, 7, 11, 13, and so. He later explains his fascination with prime numbers. "Prime numbers are what is left when you have taken all of the patterns away. I think prime numbers are like life. They are very logical but you could never work out the rules, even if you spend all your time thinking about them." One problem that Christopher did not need to spend much time thinking about was a question posed to him by one of his father’s friends, "What’s 251 times 864?" Christopher quickly answers 216,864 and explains how he easily came up with this: "You multiply 864 ´ 1000, which is 864,000. Then you divide it by 4, which is 216,000 and that’s 250 ´ 864. Then you just add another 864 onto it to get 251 ´ 864. And that’s 216,864." Using similar logic, what is the product 501 ´ 422?
At the end of the book, Christopher shares with the reader a problem that is on one of his math tests. He is asked to prove: "A triangle with sides that can be written in the from n2 + 1, n2 – 1 and 2n (where n > 1) is a right triangle." Can you prove that a triangle with sides that measure 9, 40 and 41 is a right triangle? If you can, perhaps you can attempt Christopher’s math problem, too!
Christopher shares a well-known math problem with the reader. Perhaps you have already struggled with this problem in the past. On the old MATHCOUNTS Web site, there were quite a few strings about this problem on the forums. See what you think about The Monty Hall Problem, as Christopher refers to it:
You are on a game show. On this game show the idea is to win a car as a prize. The game show host shows you three doors. He says that there is a car behind one of the doors and there are goats behind the other two doors. He asks you to pick a door. You pick a door but the door is not opened. Then the game show host opens one of the doors you didn’t pick to show a goat (because he knows what is behind the doors). Then he says that you have one final chance to change your mind before the doors are opened and you get a car or a goat. So he asks you if you want to change your mind and pick the other unopened door instead. What should you do?