10178

# The Secret of Nim

Explore the mathematical background of the game of Nim and learn how to play the optimal strategy.

### DETAILS

The crucial factor for an optimal (winning) strategy is the nim-value. For details of how to calculate it, see Nim-Value. The circle-plus symbol used in this Demonstration indicates the operation of calculating the nim-value.
Snapshot 1: if at any point in the game, the nim-value is zero for a given player, the position is safe, which means that player can win with correct play
Snapshot 2: otherwise, the position is unsafe and the player will always lose if the other player plays correctly
Snapshot 3: to achieve a safe position, find a heap whose size is less than the min-value of with the nim-value of all the heaps; reduce that heap to , resulting in a nim-value of zero

### PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.