MathDB

Consider the following one-person game played on the real line. During the game disks are piled at some of the integer points on the line. To perform a move in the game, the player chooses a point

j

at which at least two disks are piled and then takes two disks from the point

j

and places one of them at j\minus{}1 and one at j\plus{}1. Initially, 2n\plus{}1 disks are placed at point

0

. The player proceeds to perform moves as long as possible. Prove that after \frac{1}{6} n(n\plus{}1)(2n\plus{}1) moves no further moves will be possible and that at this stage, one disks remains at each of the positions \minus{}n,\minus{}n\plus{}1,...,0,...n.

Problem Statement