# Secrets behind the Nim game

Jennifer Kirubai Victor Christ Dass, (2006) Secrets behind the Nim game. Universiti Malaysia Sabah. (Unpublished)

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## Abstract

This dissertation discusses the nim game in detail. Nim game is a traditional two-person game where players alternatively take turns in removing counters (objects) from the piles of counters. The purposes of this study are to identify different ways in winning the nim game mathematically, to modify the standard nim game and also use game trees in winning the nim game. The number of counters use to play this game in this research vary from one to thirty and the number of piles are within the range from one to four. In determining the winning ways for the nim game, a few methods are used. namely the binary concept, XOR (bitwise-exclusive-or) and game trees. Binary concept includes changing decimal numbers to binary numbers and the other way round. XOR is a concept where binary numbers are added without carry. This concept is used to determine the winning position of the game. Modifications are done to the standard nim game in order to make it a game of chance. In this dissertation, the nim game is firstly modified by blocking certain moves and secondly by modifying the coin game. These modifications allow equal chances of both the players to win the game. Finally, game trees are illustrations formed to represent the nim game with small amount of piles and counters. The winner of the game is the last player who removes the counter except for one variation discussed which is the misere nim. In conclusion, all the objectives of this dissertation have been achieved. These include obtaining different winning methods mathematically for the nim game, successfully modifying the nim game to obtain a game of chance and finally winning the nim game through game trees.

Item Type: Academic Exercise Nim game, Traditional game, Mathematics concept ?? QA273-280 ?? SCHOOL > School of Science and Technology Unnamed user with email storage.bpmlib@ums.edu.my 25 Jan 2012 04:12 23 Oct 2017 00:34 http://eprints.ums.edu.my/id/eprint/3349