Maths Olympiad Prep

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Number theory Difficulty 4.8 AIME Find the answer

[ Winning and losing positions ]

The game starts with the number 60. On a turn, a player is allowed to decrease the current number by any of its divisors. The player who ends up with zero loses.

#

A number or a short expression. Spacing and $ signs are ignored.

Solution

In this game, the one who gets one wins. The first one wins. The winning positions are odd numbers.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.