APPLICATION OF CONGRUENCE FROM NUMBER THEORY TO NIM GAMES

Abstract

Not only are numbers, formulas and symbols common in maths, but there are also games that can be learnt as an addition to the skills that refer to critical thinking. In mathematics, the simple application of games developed in number theory is a form of reflection related to mathematics. One of the applications of number theory that games are capable of is the NIM game. NIM game is an old traditional game that has a strategy in solving the game. In this game, which is carried out by two players, each player has his turn alternately to win it with the rules of this game. The success of winning the NIM game is that there are objects available and undergo the game with the concept (strategy) as a way to take the intended object. A player who takes the last object is the winner of the game. The following will describe 7 NIM games: NIM Maxima, NIM One-Four, NIM Three-Five, NIM One-Three-Four, NIM One-Three-Five, NIM One-Three-Five-Seven and NIM Two-Four-Nine-Eight. This NIM game is a form of application of mathematics in number theory that focuses on congruence theory as a way to determine the winning strategy in the NIM game.