Two children take turns breaking chocolate bar that is 5*10 squares. They can only break the bar using the divisions between squares and can only do 1 break at a time.. The first player that when breaking the chocolate bar breaks off only a single square wins. Is there a winning strategy for any player?
Problem
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Tags: combinatorics unsolved, combinatorics
13.06.2012 05:03
If I am interpreting the problem correctly, it is equivalent to Chomp, a very well-known game. It is famous for having an ingenious proof (strategy-stealing) of the existence of a winning strategy for the first player, yet no general strategy has been constructed. Please let me know if I have misinterpreted the problem. In case my interpretation is correct, this belongs in the Combinatorics, as it deals with a mathematical game.
13.06.2012 17:37
As written the problem is incomprehensible: what does "to break into a single square" mean? What are the restrictions on the moves? As written, the first player could simply break along all edges between all squares, which presumably satisfies the condition of "breaking into a single square". Hopefully this was not the official wording . (It seems unlikely to me that, once everything is clarified, this will have anything to do with Chomp.) Edit: okay, revised version now makes sense (and, indeed, has nothing to do with Chomp).
15.06.2012 20:12
Sorry about the wording. I had to translate it from Spanish into English. I'll take a look into the original problem again and try to fix it. EDIT: Ok hopefully made it better.