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I came across an interesting question in a competition (it is long over by now, but I haven't found a solution yet):

In a chess tournament $2^n$ ($n \in \mathbb{N}$) players play each other round-robin (everybody against everybody). If a game draws it is repeated until one of the player wins. Show that it is possible to pick a sequence of $n+1$ players in which each player won over his predecessors.

Obviously this is true for $n = 1$. But I'm stuck even to show this for any higher number.

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    You should get an award for the most non-descriptive question title ever. And it's not like others hadn't tried...2011-11-12
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    Took it upon myself to provide a more informative title.2011-11-12

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