Tic tac toe Part 1

Discrete Mathematics Level 3

Two players are about to play tic-tac-toe on a 4-by-4 grid. If Player 1 were to place a cross intelligently such that it blocks off as many winning paths as possible, what fraction of the number of winning paths are left?

Details and Assumptions

  • In a 4-by-4 tic-tac-toe game, forming a row of three still yields a win.

  • A winning path is a row that can yield a win. (i.e. Any row of three).

  • Diagonals are included in rows of three.

  • The fraction numerator and the denominator are coprime integers.


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