May 2010
Problem of the Month

Game of Fifty

You and your opponent alternate picking numbers from 1 to 6, and a running total is kept.

If the object of the game is to be the player who makes the total exactly 50, and you go first, what number should you pick to guarantee a win for yourself and why?

Solution to the Problem:

Pick the number 1 as your starting number.

Fifty is 1 more than a multiple of 7, so you should pick 1 as your starting number.

Then, no matter what your opponent chooses, you say 7 minus that number.

On your eighth turn, you will cause the score to reach 50 exactly.

Click here for explanations of many other mathematical games.

Send any comments or questions to: David Pleacher