Saturday, July 3, 2010

Vacation Post: Pentominoes

There are two other posts I'd like to write, but they'd take more effort, and I'm on vacation. My son is playing down at the beach with his second and third cousins, with another mom watching. I'm on the porch, with a cool breeze  at my back.

I've just been playing with Katamino, a lovely game I bought a few days ago at Mackinac Kite & Toy, in Grand Haven. It's a way to play with pentominoes in a two-person game. The X and I pieces are left out, each player gets three single squares and a two-square rectangle, and then players take turns picking the ten pentominoes. Then the players race to put their pieces into their side of the board. The whole game takes about two minutes, which is part of its charm.

When I had no one to play with, I started working the solitaire puzzles, which involve putting 3 of the pieces in a 3x5 area of the board, and then 4 pieces in a 4x5 area, and so on. (The board can change size from 3 to 12 rows.)

I've owned a set of pentominoes in a nice 8x8 case for quite a while, and I know there are many ways to put them in so the 4 extra spaces will be symmetrical. But I've never managed to come close to doing it. I just now realized that I should have long ago listened to George Polya's problem-solving advice: Try a simpler problem that has a similar structure. Katamino had me do that. The game includes a booklet with pictures of 7 different workable combinations of 3, and 19 different workable combinations of 4. (12C3 = 220 total combinations of 3, so it's good to know the ones that work.) I've done all the 3-piece puzzles, and I'm almost through the 4-piece puzzles. What fun!

I'm also enjoying some light summer reading. Blue Balliett has written three young adult novels in which Calder Pillay and his two friends solve mysteries surrounding works of art, and marvel at the coincidences in their lives. Calder plays with pentominoes, using them like an I Ching, for inspiration. The third book, The Calder Game, came out in paperback recently. And here's what made me write:
He'd decided on the Start Small, Move to Large approach that his Grandma Ranjana had taught him. It seemed to work with almost everything in life. After all, you couldn't leap to making twelve-piece pentomino rectangles when you'd never made a five-piece one.
Coincidence rules!


  1. This comment has been removed by the author.

  2. So the Grand Haven reference caught my eye! You are vacationing in my neighborhood. Welcome to the beautiful beaches in West Michigan.

  3. I love coming home to Michigan (where I grew up). I'm at a Math Circle Institute right now (at Notre Dame), but we might get in one more visit to Lake Michigan before we go back home to California.


Math Blog Directory