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This problem is a brilliant demonstration of how complex games often hinge on a simple, deterministic rule. The key is recognizing the pattern in the sum of powers modulo a base number.
For this specific problem, when the power is 1 (i.e., 1, 2, 3, ..., n), the first player, "Player 1," wins if n % 8 != 0. Otherwise, "Player 2" wins. The solution lies in controlling the cumulative sum's remainder when divided by 8.
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Powers Game
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This problem is a brilliant demonstration of how complex games often hinge on a simple, deterministic rule. The key is recognizing the pattern in the sum of powers modulo a base number.
For this specific problem, when the power is 1 (i.e., 1, 2, 3, ..., n), the first player, "Player 1," wins if n % 8 != 0. Otherwise, "Player 2" wins. The solution lies in controlling the cumulative sum's remainder when divided by 8.