Peculiar Eating Competition

Logic Level 2

Charlie and Alex are going to the chocolate factory. They purchase a chocolate bar that is divided into a $3 \times 4$ grid and play the following game. Taking turns starting with Charlie, they break the chocolate along a straight grid line through the remaining chocolate, eating the smaller piece and leaving the larger piece for the opponent. The game continues until a player is unable to make a move, and this player has lost the game.

If they play optimally, who will win?

Alex Charlie It is impossible to know

1 solution

Jakub Bober
Jun 8, 2016

Charlie breaks the initial grid into the $3 \times 3$ grid.
Alex has to brake it into the $2 \times 3$ grid
Charlie breaks it into the $2 \times 2$ grid
Alex has to brake it into the $1 \times 2$ grid
Charlie breaks it into the $1 \times 1$ grid
Alex loses, Charlie wins

I don't believe Charlie wins this game. Based on your solution Charlie loses. When a 2x1 grid is left, Charlie breaks off a 1x1 piece, therefore he should lose.

Other scenarios:

C 3x3 >A 3x2 > C 3x1 > A 2x1 Charlie loses both 3x3 scenarios

C 4x2 > A 2x2 > C2x1 Alex loses so instead they would break it into 3x2 and Charlie is forced to lose as shown above in the other scenarios.

I think the wording of the question is incorrect. For Charlie to be the winner it should say the loser of the game is the one taking the last 1x1 piece, not breaking off a 1x1 piece.

Keith Dodgshon - 5 years ago

You're right. I've filed a report for you.

Pi Han Goh - 5 years ago

The best way to present your solution is to state the winning positions for Charlie. Charlie can win by always moving to a square, and we have to verify that this is indeed possible.

Calvin Lin Staff - 4 years, 12 months ago

Peculiar Eating Competition

1 solution

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