The game of eating chocolate

Two people play a game with a bar of chocolate made of $91$ pieces, in a $7$ x $13$ rectangle. The first person breaks off a part of the chocolate bar along the grooves dividing the pieces, and eats the part he broke off. Then the second player breaks off a part of the remaining part and eats it. The game continues until one piece is left. The winner is the one who leaves the other with the single piece (i.e. is the last to move). Which person has a perfect winning strategy?

If you have figured this out,

Can you generalize this to a $m$ x $k$ bar situation? In what condition player 1 has a perfect winning strategy? And in what condition player 2 has a perfect winning strategy?

Challenge: What about a three dimensional bar of $3$ x $6$ x $10$ ? And a bar of $m$ x $k$ x $j$ ?

#Logic

Easy Math Editor

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`\sum_{i=1}^3`	$\sum_{i=1}^3$
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Comments

No extra limitations? I mean, can you push one middlemost chocolate and break all 4 sides? Or the separation lines may only be one straight line each time?

Saya Suka - 2 months, 3 weeks ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$