ANALISIS PERMAINAN EMPAT BILANGAN
Abstract
The four-number game starts from 4-tuple (a; b; c; d) of nonnegative numbers a, b, c, d. In this game, the next 4-tuple is (|a-b|; |b-c|; |c-d|; |d-a|) and similar rule of changes of the subsequent 4-tuples is imposed until the game reaches the zero 4-tuple (0, 0, 0, 0). The winner of this game is the one who chooses the initial 4-tuple leading to the longest game. In this paper analyzes the game length based on the following criteria imposed on the four numbers of the 4-tuple: nonnegative integers, nonnegative rationals and nonnegative reals. The results shows that every
four-number game with nonnegative integers or rational integers has nite length. Despite of this fact, for every positive integer m, there is an initial 4-tuple based on Tribonacci sequence that leads to four-number game with length greater than m. For the game with real integers, although the game generally has nite length, there are (innite number of) initial 4-tuples that leads to innite length games.
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