MathDB

Let

n

be a positive integer. Marc has

2n

boxes, and in particular, he has one box filled with

k

apples for each

k=1,2,3,\ldots,2n

. Every day, Marc opens a box and eats all the apples in it. However, if he eats strictly more than

2n+1

apples in two consecutive days, he gets stomach ache. Prove that Marc has exactly

2^n

distinct ways of choosing the boxes so that he eats all the apples but doesn't get stomach ache.

Problem Statement