MathDB

Let there be three cups

A, B

and

C

, which start with

a, b

and

c

(all of them are natural numbers) units of gallium filled. It is also believed that all cups are large enough to contain the total amount of gallium available. It is now allowed to move gallium from one cup to another cup, provided that the contents of the latter cup are exactly double. (a) For which starting positions is it possible to empty one of the cups? (b) For which starting positions is it possible to put all of the gallium in one cup?

Problem Statement