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# Hershey Bar game

## Question

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.

## 8 answers to this question

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I'd like to be the person that goes second.

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I'd like to be the person that goes second.

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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After every slice, number of pieces increases by 1. 4*7=28 means total 27 slices can be made. Person who slices first will also do 27th slice so I would choose to be the person who goes first. Horizontal or vertical doesn't matter.

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After every slice, number of pieces increases by 1. 4*7=28 means total 27 slices can be made. Person who slices first will also do 27th slice so I would choose to be the person who goes first. Horizontal or vertical doesn't matter.

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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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?

breaking on the second horizontal line on the 3x4 rectangle.

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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.

Meaning one can slice 18 times at maximum?

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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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If I understood your game correctly...

I would go second and choose to break along the vertical line.

If OP chooses:

(a) to cut the first or third horizontal line,

>I would cut any of the 6 vertical lines in either the top 1x7 bar, or the bottom 1x7 bar, which was formed by him.

>Then he has to cut another horizontal line which could be the 2nd line or the other line.

>In whichever case, I would still continue cutting the 1x7 bar.

>Then he has to cut the last horizontal line.

>Still, I would continue breaking any available vertical line.

>He has no move left and I'd win!

(b) to cut the second horizontal line,

>I'd cut the fourth vertical line on top. Now there would be a 2x4 bar on the top left, 2x3 bar on the top right, and still a 2x7 bar below.

>He could cut any of the three bars horizontally forming two 1xn bars. (e.g. if he cuts the 2x3 bar, then it would form two 1x3 bars.)

>I would cut vertically any of the 1xn bars.

>Just like his previous move, he has to again cut horizontally any of the 2xn bars which he didn't cut. The same thing would happen which is two 1xn bars would form.

>Again, I would cut vertically any of the 1xn bars.

>Finally, he has to cut the last 2xn bar.

>I still have plenty more vertical lines to cut.

>He has no more horizontal lines left, so I'd win!

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