The game Slice is played using a m×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≤m≤20 and 1≤n≤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 1×1 board, the second player is a winner
If m=2 and player 1 slices the rectangle into two long strips of width 1, there will always be an even number of slices left. Therefore, there are automatically at least 20 answers. Add 19 to that if you flip m and n and there are 39 answers that correspond to (m,n)=2.
its 300
Since the player not able to make a move loses, the first player wins if and only if is even
