Pennies in Boxes

Here is a problem:

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 = 2n, pennies can be moved into a single box.

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

If you are reading this, your browser is not set to run Java applets. Try IE11 or Safari and declare the site as trusted in the Java setup.

Pennies in Boxes

What if applet does not run?



  1. G. Chang and T. W. Sederberg, Over And Over Again, MAA, 1997, pp. 27-28

|Contact| |Front page| |Contents| |Algebra| |Eye opener|

Copyright © 1996-2018 Alexander Bogomolny
[an error occurred while processing this directive]
[an error occurred while processing this directive]