I visited Mr. Bredin, who taught math when i was in upper school, and dropped in on his class. He's thrilled with his new SmartBoard, which lets him save scribbles and (together with Geometer's Sketchpad) manipulate geometric diagrams just by pushing around lines and points with a finger. I always wanted to create something like Geometer's Sketchpad, so it's nice to see it in use in the classroom. It seems a bit trickier to use than it could be, though.
I got put on the spot to give the students something interesting to think about. So i told them about the peg solitaire problem from the 1993 IMO, in which you have an infinite grid of holes with pegs in some of them, and you can remove a peg by jumping over it (horizontally or vertically) with another peg. To win, you have to get down to one peg. I asked them to start with a 3-by-3 square of nine pegs and see whether they could win the game. As we neared the end of the period, i tried to describe the general solution, but i completely bungled the explanation, so i wrote it up later to clear things up.
Here's the first page, which gives the problem statement:
The second page looks at a few simple cases to start things off.
Spoilers: the solution is given on Page 3, Page 4, and Page 5.
The five pages together are also available as a single PDF document if you prefer. Hope you enjoy it.