Suppose N pennies are randomly distributed into several boxes. Take any two boxes A and B with p and q pennies, respectively. If p ≥ q you are allowed to remove q pennies from box A and put them into box B, and this action is called an operation. Show that regardless of the original distribution of pennies, a finite number of such operations can move all the pennies into one or two boxes. If N = 2^{n}, pennies can be moved into a single box.

(To perform an operation in the applet below click on two boxes - circles - in succession.)