The Sprague–Grundy function of the real game Euclid
نویسندگان
چکیده
منابع مشابه
The Sprague-Grundy function of the real game Euclid
The game Euclid, introduced and named by Cole and Davie, is played with a pair of nonnegative integers. The two players move alternatively, each subtracting a positive integer multiple of one of the integers from the other integer without making the result negative. The player who reduces one of the integers to zero wins. Unfortunately, the name Euclid has also been used for a subtle variation ...
متن کاملThe Sprague-Grundy function of the game Euclid
We show that the Sprague-Grundy function of the game Euclid is given by g(x, y) = b|y/x− x/y|c for x, y ≥ 1.
متن کاملOn Calculating the Sprague-grundy Function for the Game Euclid
The two-person nim-type game Euclid, E, is played on a board. A position (a, b), or equivalently (b, a), consists of a pair of positive integers. Players alternate moves, a move consisting of decreasing the larger number in the current position by any positive multiple of the smaller number, as long as the result remains positive. The first player unable to make a move loses. Some background in...
متن کاملThe game of 3-Euclid
In this paper we study 3-Euclid, a modification of the game Euclid to three dimensions. In 3-Euclid, a position is a triplet of positive integers, written as (a, b, c). A legal move is to replace the current position with one in which any integer has been reduced by an integral multiple of some other integer. The only restriction on this subtraction is that the result must stay positive.We solv...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2011
ISSN: 0012-365X
DOI: 10.1016/j.disc.2010.12.011