"One Million Beans!"

This is an old question I was given by a Psychology student. I just changed it into a Math question, because I'm a Math student!

This is a very simple-to-solve problem, and requires no advanced Math. If you can do one of those "Billy has two apples" -type problems, then you will be able to do this one!

One Million Beans!

There are two jars: Jar A and Jar B.

To begin, Jar A contains P red beans, and Jar B contains P green beans.

From Jar A, Q red beans are removed and put into Jar B. Then, Jar B is shaken, and Q mixed beans are removed from Jar B and put into Jar A. There is no way to control or know how many of which colour beans were moved.

Now, there are n green beans in Jar A, and m red beans in Jar B.

1. Find | n - m | for all Natural P, n, m and Natural Q ≤ P.

2. Prove this is always the case.

This is one of my most favourite questions, mostly because it looks terribly harder than it actually is! The trick is to not over-complicate it, and to not rely on intuition. Rather, keep track of what you know, and you'll find the answer very easily.

I'll post the solution to this in a few weeks; because I'm submitting a more specific version of this problem to a workplace newsletter. Hehe!

--Charissa