MathDB

There is a large pile of cards. On each card one of the numbers

1

2

\cdots

n

is written. It is known that the sum of all numbers of all the cards is equal to

k \cdot n!

for some integer

k

. Prove that it is possible to arrange cards into

k

stacks so that the sum of numbers written on the cards in each stack is equal to

n!

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