How does the game Nim work?

Nim is an ancient mathematical game played by two people who take turns removing objects from several piles. In the standard version, a player may remove any number of objects (at least one) from a single pile, and the player who removes the final object wins.12

Strategy and Binary Logic

The game is defined by "safe" and "unsafe" positions. A position is considered safe if the player who just moved has secured a winning state; otherwise, it is unsafe. To determine the status of a position, players convert the number of objects in each pile into binary notation. If the sum of each binary column is zero or an even number, the position is safe. A skillful player aims to move so that every position they leave for their opponent is a safe one.12

Because this strategy relies on binary arithmetic, it is highly suitable for computers. In 1940, physicist Edward Uhler Condon showcased the Nimatron, a machine capable of playing a perfect game of Nim, at the New York World’s Fair.12