Nim Game

To play the version of the game of Nim pictured below, click here. (Here is another interactive applet for Nim.) Nim is an ancient game. There are many ways to play. In some versions the person who takes the last object (or number) is the winner and in other versions that person is the loser. It is thought to have originated in China; the earliest references to Nim in Europe date to the 1400's. It is often played with whatever objects are at hand (pebbles, toothpicks, matches, coins), but it can also be played verbally, without objects, as desribed below.




In order to play Nim verbally, find a partner and choose a number that you will count up to. You also need to choose the maximum amount of numbers you can count off at a time. For example, let's say you and I are playing, and we decide to count to 21. We also decide we can say up to three numbers at a time. I might start by saying: "1, 2, 3," and you might then say "4, 5." I might follow up with "6," and you might say: "7, 8, 9." We could continue in this way until we got to 21, and the person to say "21" loses the game.

This is a great game for a road trip, and there is a very straightforward strategy for winning every time (no matter what the ending number or the maximum amount of numbers chosen). Can you figure out the strategy??