First thing to notice: Order of your moves doesn't count. This is a wonderfully freeing observation, because it radically reduces the number of factors to consider.

Are you going to flip a coin the last row or not? It certainly seems to cry out for it, because then you get four tails for free. Let's say you do. Then you are going to need to fix the penny above the one you flipped. (If you flip penny 14, then penny 10 needs to be fixed). If you flip another in that column, then you have ruined your pretty last row. So one way to start this problem is to flip a penny in the last row, and then try not to flip any more in the last row or the column above the one you flipped.

In other words, we play around a lot.

The shortest solution is seven moves, and one answer is 2, 4, 7, 10, 11, 12, 13. I would like to see a proof that this solution is unique.

When Al Brodax was casting voices for the cartoon film Yellow Submarine, he found a guy in a bar whose voice was perfect for the George Harrison character. He offered the man the role, and the offer was accepted. The man was a deserter from the British Army. One day he was hiding out from the police, the next day he was in a studio taping cartoon voices, hanging around with a bunch of animators and flower children, and meeting various Beatles and other famous people. Shortly before he was done, the police found and arrested him.

You have just read the solution to this problem. Why not try the current Challenge now?

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