## Problem of the Month

### Forcing Nim

Let's play a game. We have a few piles of pennies: one pile has 3 pennies, one has 6, one has 10, and one has 12.

3-6-10-12

We'll take turns removing pennies. On your turn, you may take as many pennies as you want from any single pile. The twist: if you take just one penny from a pile, your opponent MUST take pennies from that same pile on his next turn. The first player to have no legal moves, loses.

For example: I could take 5 pennies from the third pile, leaving 3-6-5-12. Then you might take 1 penny from the fourth pile, leaving 3-6-5-11. I would then be forced to take from the fourth pile; maybe I take 2 pennies, leaving 3-6-5-9. And so on.

Starting from 3-6-10-12, would you want to go first or second? You don't need to give me the complete winning strategy; just say whether you want to go first or second, and why.

Send your answers to this puzzle to me (Joseph DiMuro) at joseph.dimuro@biola.edu by April 30, 2015.

## Why Choose Mathematics at Biola?

- Thorough in both educational quality and personal attention to students
- Faculty and students work together to make the study of mathematics a successful and enjoyable learning experience
- Involvement in the Putnam Exam; a nationwide contest for math students
- Experienced faculty who not only teach classes in which they are specialists, but work on research projects with individual students
- Small class sizes
- Readily accessible computing facilities