MathDB

Initially there is a checker on every square of a

1\times n

board. The first move consists of moving a checker to an adjacent square thus creating a stack of two checkers. Then each time when making a move, one can choose a stack and move it in either direction as many squares on the board as there are checkers in the stack. If after the move the stack lands on a non-empty square, it is placed on top of the stack which is already there. Prove that it is possible to stack all the checkers on one square in

n - 1

moves.
(A Shapovalov)

Problem Statement