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The perfect square game is played as follows: player 1 says a positive integer, then player 2 says a strictly smaller positive integer, and so on. The game ends when someone says 1; that player wins if and only if the sum of all numbers said is a perfect square. What is the sum of all n such that, if player 1 starts by saying n, player 1 has a winning strategy?

 Jun 15, 2020
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The sum of all n is 1 + 3 + 4 + 8 = 16.

 Jun 17, 2020

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