# Slice

Discrete Mathematics Level 4

The game Slice is played using a $$m \times n$$ rectangular piece of paper as a board. Players alternate turns, on each turn they choose a rectangle and cut it into two rectangles, each with integer side lengths. The last player who is able to cut a rectangle is the winner. If $$1 \leq m \leq 20$$ and $$1 \leq n \leq 20$$, for how many of the $$400$$ different starting games does the first player have a winning strategy, no matter how the second player plays?

Details and assumptions

For a $$1 \times 1$$ board, the second player is a winner.

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