Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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)

share|improve this question
    
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

1 Answer 1

up vote 3 down vote accepted

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!

share|improve this answer
    
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

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.