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Problem : Two players have in front of them a single pile of objects, say a stack of 7 pennies. The first player divides the original stack into two stacks that must be unequal. Each player alternatively thereafter does the same to some single stack when it is his turn to play. The game proceeds until each stack has either just one penny or two—at which point continuation becomes impossible. The player who first cannot play is the loser. Show, by drawing a game tree, whether any of the players can always win.

My question is why does 4-2-1 not go to 2-2-2-1 ?

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  • $\begingroup$ The title you have chosen is not well suited to representing your question. Please take some time to improve it; we have collected some advice here. Thank you! $\endgroup$ – Raphael Nov 21 '18 at 23:53
  • $\begingroup$ Note that 4-3 doesn't go to 3-2-2 either. $\endgroup$ – Raphael Nov 21 '18 at 23:55
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    $\begingroup$ Possible duplicate of Nim game tree + minimax $\endgroup$ – ThePopa611 Dec 8 '18 at 15:35
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According to the rules:

player divides the original stack into two stacks that must be unequal.

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