Grundy’s Game
Grundy’s game
Grundy’s game is a two-player mathematical game of strategy. It was defined by P. Grundy in 1939 and is named after him. The game starts with a single heap of objects, and the two players take turns splitting the heap into two heaps of different sizes. The game can be analyzed using the Sprague-Grundy theorem, which requires the heap sizes in the game to be mapped onto equivalent nim heap sizes. This mapping is captured in the On-Line Encyclopedia of Integer Sequences as OEIS: A002188. Using this mapping, the strategy for playing the game Nim can also be used for Grundy’s game.
Why is Grundy’s game Popular?
Grundy’s game is significant because it is a simple yet challenging game that can be used to teach mathematical concepts such as game theory and the Sprague-Grundy theorem. It is also interesting because it can be reduced to the game of Nim, which is a well-known game in combinatorial game theory.
Game Components of Grundy’s game
A single heap of objects
Game Setup of Grundy’s game
The game starts with a single heap of objects.
Gameplay Mechanics of Grundy’s game
Players take turns splitting the heap into two heaps of different sizes.The game can be analyzed using the Sprague-Grundy theorem, which requires the heap sizes in the game to be mapped onto equivalent nim heap sizes.Using this mapping, the strategy for playing the game Nim can also be used for Grundy’s game.
Game Objective of Grundy’s game
The objective of the game is to force the other player to take the last object.
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