Now Black cannot make the symmetric move, because that would fence off two regions of four squares each. The only other piece that might legally fit in the central region is piece 7, which has already been used. So, the central region is unplayable by either side. That leaves the two end regions. Black cannot place piece 2 in either region without illegally fencing off one to four squares. So, White can win from here by employing the symmetric strategy against Black!
I received a more elegant solution to this puzzle from Claude Chaunier. In his solution, the symmetric strategy is stopped on the very last move! Black has no legal response at all, and the game is immediately over. If you would like to see his solution, just email me.
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