You and I have 12 pennies, arranged in a row, heads up.

We take turns. On each turn, the player can flip either (A) one coin or (B) two coins that are adjacent to each other. The player can choose on his turn which of these do, and which coin or coins to flip.

Once a coin has been flipped, it can’t be flipped again.

(Example: I start by flipping coin 5. Now it’s your turn; you can then, for instance, flip coin 12, or coins 9 and 10, or coins 3 and 4. But you can’t reflip coin 5, and you can’t flip coins 4 and 6, because they aren’t adjacent.)

The goal is to be the one to flip the last coin or coins, leaving the coins all tails.

What’s the winning strategy, and who’s the winner — the person who goes first, or the person who goes second?

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