Question

In Determinant Tic-Tac-Toe, Player 1 enters a 1 in an empty 3 × 3 matrix. Player 0 counters with a 0 in a vacant position, and play continues in turn until the 3 × 3 matrix is completed with five 1’s and four 0’s. Player 0 wins if the determinant is 0 and player 1 wins otherwise.

If Player 1 goes first and enters a 1 in the middle square, is there a strategy that can give player 2 a guaranteed win?

Answer 1

Answer:

In Determinant Tic-Tac-Toe, Player 1 enters a 1 in an empty 3 × 3 matrix. Player 0 counters with a 0 in a vacant position, and play continues in turn until the 3 × 3 matrix is completed with five 1’s and four 0’s. Player 0 wins if the determinant is 0 and player 1 wins otherwise.

(a) If Player 1 goes first and enters a 1 in the middle square, is there a strategy that can give player 2 a guaranteed win?

And (b) (extra) If a method exists, will it work for an (n × n) grid, where n > 3?

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