Erich Prisner
Fall 2003 

Chip Firing on the Cube 

Random starting distributions

Set number of chips:  

Period 1: Period 2: Period 3: Period 4: Period 5: Period 6: Period 7: Period 8:

Find period

Why don't we just try all possible start configurations, instead of chosing random ones? The reason becomes clear when we compute the number of possible configurations of N chips on the cube graph. It is (N+7 choose 7).
For N= 24, for instance, this is (31*30*29*28*27*26*25)/(7*6*5*4*3*2*1), which is 2,629,575. On my old PentiumII, one round until the period is found takes about 1/5 seconds. Therefore, to test all these 2,629,575 possible start configurations would take about 525915 seconds, which is 6 days and 2 hours.