Solution to Weights Problem (Finally!)

A while back I posted an interesting problem:

A genie walks up to you and says, "Hey you, can you help me figure out which of my magic lamps is fake? I have 12 here, and know 11 of them are genuine. The one fake lamp doesn't weigh the same as the other 11 lamps, but I don't know whether it's heavier or lighter. I also have this pair of scales, but they're weird. They can lean either to one side or the other, or stay even, but that's it. And they can only weigh stuff 3 times. Can you devise a method to figure out which lamp is the odd one out using just three measurements? Hurry, Survivor's on, and I only have a few minutes to spare.

I finally put up the solution. You can view it here.

It's quite a long solution, and I put a lot of effort into it, so you should check it out.