# 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