Confused101's blog

Winner of the 2-player game.
By Confused101, history, 8 years ago, In English

Numbers 1....N are written in table (3 <= N <= 1000), at each step one player choose some number and mark it as visited, player wins if he can make 3 consecutive numbers visited in his turn. Who will win the game if both play optimally? game is 2-player game with alternating turns.

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8 years ago, # |
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It's obvious that if we mark some number x, an opponent instantly loses if he takes any number y : |x - y| ≤ 2.

Let's define f(n) the answer for table of "length" n. We know that f(3) = 1 (1st player wins on such board anyways). Trying all possible moves we can easily calculate f(n): by taking some number x (1 ≤ x ≤ n), we split the table into two parts of lengths max(0, x - 3) and max(0, n - x - 2), since there's no point of keeping neighbouring to x unavailable numbers on the table.

If you still have some difficulties, googling "sprague grundy theory" shuold help.

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