October 4th, 2005

Visiting SJR.

While in Winnipeg, i stopped by SJR, where i spent most of my waking hours from Grade 2 to Grade 12. The place has changed and grown and gotten fancier; the lower school play structure is gone, replaced by the new primary school building, and there's a new structure on the main field. When i went there, it was all boys up to Grade 8. But girls have been admitted into Kindergarten for a couple of years now, so the boys-only grades in the middle are slowly being squeezed out, and in a few years the entire school will be co-ed.

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.