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Pile of cards

Source: Tournament of Towns, Fall 2002, Junior A Level, P6

May 17, 2014
combinatorics proposedcombinatorics

Problem Statement

There's a large pile of cards. On each card a number from 1,2,…n1,2,\ldots n is written. It is known that sum of all numbers on all of the cards is equal to k⋅n!k\cdot n! for some kk. Prove that it is possible to arrange cards into kk stacks so that sum of numbers written on the cards in each stack is equal to n!n!.
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