# Pile of cards(Tournament of Towns)

I have been trying this problem for a while.But somehow, my proof(I tried an inductive approach) appears to be break down at some point.Here it is:

There is a large pile of cards.On each card one of the numbers 1,2,..,n is written.It is known that the sum of all the numbers of all the cards is equal to $kn!$ for some integer $k$.Prove that it is possible to arrange the cards into $k$ stacks so that the sum of the numbers written on the cards in each stack is equal to $n!$.(Tournament of Towns,2002)

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Can you show us the steps you've taken to try and prove this statement so far? –  Chris Taylor Sep 12 '11 at 14:23
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## 1 Answer

You may want to refer to the file of Tournament of the Towns Problems and Solutions. The problem is Problem 4, Fall 2002, Senior A-Level. If you prefer not to look, the proof given is by induction.

There are many very nice "Russian-flavoured" problems on this site, at various levels. A great resource!

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Thank you very much! –  Eisen Sep 12 '11 at 15:09
You are welcome. It was easy to find: I already had the site bookmarked, many nice questions. –  André Nicolas Sep 12 '11 at 15:11
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