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Nim

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description Nim Overview

Nim is a mathematical strategy game in which two players alternately remove one or more objects from a single pile among several piles. Under the standard normal-play rule, the player taking the final object wins, and optimal play can be determined by computing the binary exclusive-or, or nim-sum, of the pile sizes. Charles L. Bouton published a complete analysis in 1901, making Nim a foundational example in combinatorial game theory.

help Nim FAQ

How do you win the mathematical game of Nim?

Under the standard normal-play rule, the player who takes the final object from the piles wins the game. To guarantee a win, a player must leave the opponent in a losing position by calculating the binary XOR (exclusive OR) sum of the objects in all piles.

What is the binary XOR strategy used in Nim?

Optimal play requires converting the number of objects in each pile into binary numbers and calculating their exclusive OR (XOR) sum. If the resulting Nim-sum is not zero, the player whose turn it is can always make a move that leaves a Nim-sum of zero for their opponent.

What are the basic rules for playing Nim?

Nim is played with several piles of objects where two players take turns removing items. On a single turn, a player must remove one or more objects from exactly one single pile.

Can the first player always win a game of Nim?

In the standard setup where the initial Nim-sum is not zero, the first player can mathematically force a win. However, if the initial Nim-sum is exactly zero, the second player holds the winning advantage.

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