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Problem of the Week
Problem E and Solution
Taking Grapes


Quinn and Birgitta are playing a game using a bowl of grapes. The rules of the game are as follows:

The game starts with \(8\) grapes and Quinn goes first. Quinn has developed a winning strategy so that she is guaranteed to win this game, regardless of how many grapes Birgitta takes on her turns. Find all the possible first moves in Quinn’s winning strategy. Justify your answer.


Quinn has five options to begin with. She can remove \(1\), \(2\), \(3\), \(4\), or \(5\) grapes. Let’s look at each case.

Therefore, Quinn’s winning strategy starts by removing \(1\), \(2\), or \(4\) grapes.