Though it irks be to be writing about sudoku once again (I think we can stop capitalising it now) it’s what I spent all weekend on, so it’s my own fault.

Previously I had devised a cunning rule to solve all sudoku puzzles, and I called this the Rule of N. Subsequently I got very bored of sudoku because the solving process became so mechanical. But on Friday my dad showed me a Daily Telegraph puzzle graded Diabolical (I think they have Easy, Medium and Hard, too, but I guess having a Very Hard would have left their marketing department wondering what to do with their time) and it appeared that this wasn’t solvable with the Rule of N — the only tool I had at my disposal other than “guess”.

Since it was possible we’d missed something, I spent all weekend writing a program to apply the Rule of N exhaustively to a sudoku puzzle. Once I was certain the program was correct (very rigorous unit tests) I gave it the Diabolical puzzle and… no joy. It got as far as we did and then gave up.

Since the Rule of N seems to have worked on every puzzle I’d encountered until this point, it’s still valuable, so I’m going to present it to you as a public service…

Suppose you have a cell group: a row, a column or a 3×3 box. Suppose you have a set of N cells in this group, and that you know what digits can go in each of these cells. Then if there are N such digits between the N cells you can eliminate all those digits from all of the other cells in the group.

Easy, eh? Okay, maybe it needs an example…

Here we know where to put the 4, 7, 6, and 1, but the other cells have several options. The 3rd, 7th and 9th cells between them share the digits 3, 8 and 9. These are three cells which must share three digits, so this is the Rule of N with N = 3. Therefore we can eliminate the digits 3, 8 and 9 from all the other cells in the row.

Using this rule I’ve managed to solve all previous puzzles, but on Sunday night that all came unstuck.

We did solve the Diabolical grid, by the way. We found a cell with just two options and picked one. And several steps later we found ourselves in an impossible position, so we had to backtrack and pick the other digit — which duly led to the solution.

But that’s not a good way to do things. I want certainty, not guesswork. So I’m now searching for another rule. I thought I came close this morning, but now I’m not so sure. Of course there are discussion boards dedicated to this kind of thing, and many others will have been here before, but I want to find this for myself.

I’ll let you know how I get on.

Tags: logic, deduction, sudoku