Nim

Nim is a mathematical strategy game in which two players alternately remove objects from separate piles, and the player forced to take the last object either wins or loses depending on the chosen variant. The game's exact origin is uncertain, though similar counter-removal games have been played in various cultures for a long time, and the modern name and formal mathematical analysis of its winning strategy date to the early twentieth century, when it was shown to be fully solvable using the binary exclusive-or of the pile sizes. It is frequently used as a teaching example in combinatorial game theory.