Chocolate Bar

Half-eaten chocolate

Half-eaten chocolate

You have a bar of chocolate as above. The bottom left piece is dark chocolate and no one likes dark chocolate, right?

Your mother wants you to share the chocolate with your brother, so you come up with an idea. Each turn one person can pick a piece and gets to eat everything to its right and above. The person who ate the dark chocolate loses. You are to play the first move, what is the sum of all piece that can guarantees you a win?

Assume that your brother plays optimally.


  • If you choose the \(9^{\text{th}}\) piece, you get to eat the piece \(5,6,9,10,11,12,13\).

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