Nim

Variations

There are many variations of Nim, most of which can be analysed mathematically in a similar way to Nim.

Misère Nim

Misère Nim is identical to Nim, except that the player to take the last dot loses.

The Subtraction Game

The Subtraction Game starts with one or more heaps, like Nim, but there is a limit on the number of objects that each player may remove. For example, the game might start with a single heap of 10 objects, and each player is allowed to remove up to 3 objects.

Grundy's game

Grundy's game starts with a single heap, such as of 10 objects, and the players take turns in dividing the heap into two heaps of different sizes. Thus, a heap of six objects may be divided into heaps of 5+1 or 4+2, but not 3+3.

Other topics

Description

Strategy

History

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