15th ibmo - venezuela 2000/q5.
Source: Spanish Communities
April 15, 2006
inductionnumber theory unsolvednumber theory
Problem Statement
There are a buch of 2000 stones. Two players play alternatively, following the next rules:()On each turn, the player can take 1, 2, 3, 4 or 5 stones of the bunch.
() On each turn, the player has forbidden to take the exact same amount of stones that the other player took just before of him in the last play.The loser is the player who can't make a valid play. Determine which player has winning strategy and give such strategy.