Tuesday, October 20, 2009

Make Your Own Sudoku

When I fly home for the holidays, I usually take a book of sudoku puzzles with me. They keep me occupied to prevent both boredom and anxiety about flying that I've never completely shaken.

Sometimes I bring along a very challenging sudoku book, one where I might not finish a puzzle before landing. While I'm usually up for a challenge, I've often found myself more frustrated with these puzzles than the stresses of travel. It's the only book where I've finished multiple puzzles only to realize I had done so incorrectly (How did I get two 9's in the first row? Arggh!). Nevertheless, I keep bringing it along every so often, vowing to conquer the mighty challenges within. You can guess how most of these struggles end.

It was in one of these moments that, instead of paying airport prices to buy an easier book, I thought it would be an interesting challenge to make my own sudoku. I would start with a blank 9 x 9 grid and fill in the numbers from scratch. All I needed was blank paper, a pencil and time.

I started as I sometimes do with traditional puzzles: fitting the same number in each of the nine 3 x 3 boxes. In this case, it didn't matter the starting number, or the order after that. You still have to use the same skills and logic that you do when solving a regular puzzle. Mathmatically speaking, at some point early on, you lock yourself into that one solution that all sudoku puzzles have, so it's not long before you're basically doing a regular puzzle.

I wondered if I could start with specific patterns and still create a working puzzle. Could I fill a row with 1 through 9 in order from left to right? What about crossing through that with a vertical line of 1 through 9 in order? Could I make patterns in one 3 by 3 box and simply repeat them in the other boxes with very few changes? Could I fill a 3 by 3 box like a telephone keypad? If I could create a pattern one way, could I simply rotate the nine 3 by 3 boxes around? Finally, and perhaps most importantly, when I set these starting parameters, how much am limiting the possible solutions?

There are a lot of possibilities, and it's a good, challenging puzzle exercise for curious young minds. First, sudoku by nature teaches critical thinking skills like logic and problem solving. There's one solution, but many ways to get there. When students start creating their own strategies, they're thinking on a higher level. Spatial relationships are so important throughout higher level mathematics, and the basic ideas of ordering, positioning and arrangement are always needed to solve (and create) these puzzles. "How does this fit together?" and "How can I take this apart?" are key for success in geometry (among many other things).

So I would give this to students as a challenge, first giving them blank grids and perhaps starting one together. Have them complete some on their own, then either show them or give them the "starter" sudoku to explore some of the questions I raised earlier. I think you could do this with upper elementary students and up--and it would be great for homeschoolers as well!

Blank printable sudoku grids (six)
"Starter" printable sudoku grids (six)

Tried something similar? Share your experiences and resources in the comments.