Break It Up!

[From the Fourth Annual Iowa Collegiate Mathematics Competition. Written by Paul Zeitz. Slight modifications by Sam Rebelsky.]

Two people take turns breaking up a rectangular chocolate bar which starts as 6x8 squares in size. Players alternate turns. For a turn, a player takes one of the pieces of chocolate consisting of two or more squares and breaks it into two pieces. Breaks can only be made along a division between the squres and each break must be a straight line. The last player who can (legally) break the chocolate wins (and gets to eat the chocolate bar). Is there a winning strategy for the first or second player?

For example, you can turn the original bar into a 6x2 piece and a 6x6 piece. You can turn this latter piece into a 2x6 piece and a 4x6 piece. You can also turn the original bar into two 4x6 pieces, two 3x8 pieces, and so on and so forth.

What about the general case, when the starting bar is MxN?


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