October 2026 Problem of the Month

America turned 250 years old this year, so we will celebrate by playing the Game of 250.

You and your opponent alternate picking numbers from 1 to 10, and a running total is kept.

If the object of the game is to be the player who makes the total exactly 250, and you go first, what number should you pick to guarantee a win for yourself?

Solution to the Problem:

Here is the solution:

The answer is 8.

250 is 8 more than a multiple of eleven, so pick 8 as your starting number.
Then, no matter what your opponent chooses, you say 11 minus that number.
On your twenty-third turn, you will cause the score to hit 250 exactly.