MathDB

divisibility the number of ways

Source: Tuymaada 2013, Day 2, Problem 8 Seniors

July 26, 2013

linear algebramatrixinductioncombinatorics proposedcombinatorics

Problem Statement

Cards numbered from 1 to

2^n

are distributed among

k

children,

1\leq k\leq 2^n

, so that each child gets at least one card. Prove that the number of ways to do that is divisible by

2^{k-1}

but not by

2^k

.
M. Ivanov