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Hershey Bar game


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8 replies to this topic

#1 bonanova

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Posted 16 October 2012 - 08:14 AM

I unwrap a Hershey bar and notice it is 7 squares wide and 4 squares high. I propose a game. One of us will break a piece of the bar along a vertical line. The other will break a piece along a horizontal line. We alternate moves until one of us has no remaining moves. That player loses the game.

As an example, the first to move might break the bar along the third vertical line, leaving a 3x4 rectangle and a 4x4 square. The second player to move might break the square along the topmost horizontal line, changing it into 4x1and 4x3 rectangles. And so forth.

Someone will ask: can you rotate the pieces? The answer is No. Although it is permissible to eat the Hershey Bar and play the game with pencil and paper.

Here is the puzzle.

You may choose the orientation of your breaks or which of us moves first. Choose wisely and you can force a win.
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#2 phil1882

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Posted 16 October 2012 - 11:04 AM

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#3 bonanova

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Posted 17 October 2012 - 06:10 AM

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Yeah, true.

For instance, if my (first) move was to break on the third vertical line, as described in OP,
what (horizontal) second move would win for you?
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#4 Barcallica

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Posted 17 October 2012 - 06:31 AM

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#5 bonanova

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Posted 17 October 2012 - 07:44 AM

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OP says:
One of us will break a piece of the bar along a vertical line. The other will break a piece along a horizontal line.
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- Bertrand Russell

#6 phil1882

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Posted 17 October 2012 - 09:02 AM

For instance, if my (first) move was to break on the third vertical line, as described in OP,
what (horizontal) second move would win for you?

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#7 Barcallica

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Posted 17 October 2012 - 01:40 PM

OP says:
One of us will break a piece of the bar along a vertical line. The other will break a piece along a horizontal line.

Meaning one can slice 18 times at maximum?
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#8 bonanova

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Posted 17 October 2012 - 09:17 PM

Meaning one can slice 18 times at maximum?

Meaning that one player will eventually run out of his H or V moves and lose.

Edit: there is a fixed number of moves, but how they distribute between H and V moves depends on how the game progresses. At some point all the remaining moves will be H moves and the V player loses, or all the remaining moves will be V moves and the H layer loses.
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- Bertrand Russell

#9 platypust

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Posted 18 October 2012 - 04:59 AM

If I understood your game correctly...

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