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Consider the following two players game:

Giving chessboard NxN, and single king placed on some square on the board. Each player in his turn, can move the king in each direction in the same way player can move king in regular chessboard game. But - the king can't return to square he was already in. Edit: the winner is the player who makes the last turn.

The question:

What is the winning strategy? Should I play first or second and what is the invariant condition?

What I discoverd so far:

if N=2 I want to be first. if N=3 and the king at first is in the middle sqaure (2,2), then I want to be second.

pelegbarsever
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  • To be clear, you lose the game if you can't make a move, yes? Also there's a good chance this simply depends on whether N is even or odd. – eyeballfrog Nov 22 '21 at 17:43
  • yes thank you, I forgot to mentioned this important detail. – pelegbarsever Nov 22 '21 at 18:00
  • What's the source of this question? If it's from a competition, then please confirm if the starting position can be chosen by the first player. if you came up with it, then be aware that there might not be a "nice" solution, even though a solution exists. (EG We know that chess has a pre-determined winner, but we don't know which one or how to play.) – Calvin Lin Nov 22 '21 at 18:26
  • Thank you for your comment. My professor gave me this question so I dont know its source, But there suppose to be reasonable solution. The first player can't chose the starting point. – pelegbarsever Nov 22 '21 at 18:52

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