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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.)

<hr> <h3> This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at http://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet. </h3> <hr>

Explanation

Copyright © 1996-2008 Alexander Bogomolny



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