MathDB

A pile of cards, numbered with

1

2

, ...,

n

, is being shuffled. Afterwards, the following operation is repeatedly performed: If the uppermost card of the pile has the number

k

, then we reverse the order of the

k

uppermost cards. Prove that, after finitely many executions of this operation, the card with the number

1

will become the uppermost card of the pile.

Problem Statement