The Secret of Nim

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

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

Contributed by: Ralf Becker (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

The crucial factor for an optimal (winning) strategy is the nim-value. For details of how to calculate it, see Nim-Value (Wolfram MathWorld). 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



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send