The Rotten Egg Problem

Here is a deceptively complex logic problem that I solved in 2003:

1. You have a dozen eggs.

2. One of them is rotten, but they all look alike.

3. The rotten one is either heavier or lighter than the others, but you don't know which.  The others all weigh the same.

4. You have a balance scale, and you are permitted to use the scale only 3 times.  

Puzzle:  Which is the rotten egg?

I'm sure a lot of math heads out there have seen and maybe solved some version of this problem.  I confess that I probably put a good 3 hrs into it, usually sitting out in my front yard in the afternoon or evening, the shady side of the house...with a beer or wine or whatever...doodling and thinking about it for half an hour to at most one hour at a time.  That worked for me.

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