Key points are not available for this paper at this time.
This paper considers the following game on a hypercube, first suggested by Lagarias and Saks. Suppose 2ⁿ pebbles are distributed onto vertices of an n-cube (with 2ⁿ vertices). A pebbling step is to remove two pebbles from some vertex and then place one pebble at an adjacent vertex. The question of interest is to determine if it is possible to get one pebble to a specified vertex by repeatedly using the pebbling steps from any starting distribution of 2ⁿ pebbles. This question is answered affirmatively by proving several stronger and more general results.
Fan Chung (Wed,) studied this question.