After wasting 10 minutes I found the secret-- it's a secret button called "Abandon". Worked well for me and cruised right out of there. For puzzle people, have a blast. For the rest the button works best.

Or you could google a bit and read up the theory behind it and solve the puzzle:

http://mathworld.wolfram.com/LightsOutPuzzle.html
One thing the page does not mention is matrix algebra is valid over any field, not just R. And a set of integers modulo prime (2 in this case) is a field.

Also, let dead threads lie