Friday 27 March 2009

Jigsaw Falling Into Place


Tom Collyer does the Times Super Fiendish sudoku

(yes yes, I’m still keeping with my Radiohead song title for my titles.)

Ok lots of people at some point or another have been interested into how I do sudoku. In particular I am able to give a vague idea of what I do, but i seems to go over most people’s head. Possibly the most baffling thing about my solving technique is that (most of the time) I solve quickly without guessing – even on the harder puzzles.

Now I believe guessing on easier puzzles is stupid, and always slower, but on hard puzzles things get more interesting. At this point I’m going to assume those still reading know a little bit about sudoku and have come across advanced solving techniques – in particular the x-wing and the swordfish. There was a helpful page on The Times website but it seems to have gone. Oh well. Anyhow, most people think that these techniques are slow, clunky, require too much notation and are generally more bother than the time spent looking for them are worth. On the other hand the constructive logic (as opposed to contradictory associated with guessing) makes for a much more satisfying solve. And isn’t necessarily slow either!

Ok so the best way to illustrate this is through a quick walk-through. That means I’ll show some of my steps along the way but ideally you should go through it too. The puzzle in question is the Super-Fiendish published in The Times today (Friday 27th March 2009). It looks like this:

With most sudoku puzzles, there are always a few “gimme numbers” you can place without too much bother. Like this:

But then I come to a sticking point. Time to start looking for some weak subsets. What I mean by these are rows or columns or 3×3 boxes that are nearly filled out (i.e. have <5 numbers left to be filled in). There aren't very many boxes here, but the rows and columns look promoising. As it happens, I seem to naturally check columns before rows - and the ones that catch my eye here are 3, 4, 6 and 7. In particular, the gaps in 4 and 7 seem to line up very nicely. Sure enough, we spot the first x-wing with the 9's. Let's mark that in:

That doesn’t seem to give anything. So I continue on, scanning the rows in a similar fashion. Lo and behold I find another with the 8’s:

Well that’s all well and good, but they don’t obviously seem to be giving me any information. Clearly I’ve missed something…I’m very good at over looking obvious things, so I bet you can already see where! Ok a little bit further down the line things are looking more promising – in particular the x-wing with 8 wasn’t actually needed:

Now the x-wing with the 9’s comes into play. Observe it gives us the 9 in the bottom left box:

This essentially breaks the puzzle. I’m a little slow to finish it off from that point – but if you can complete a difficult level sudoku then there shouldn’t really be any problems finishing it off:

EDIT: Just noticed I’ve made a trademark transposition error (again!!!) in this image. The 6/7 in the middle box should be reversed!

The time I recorded there was just over 5 minutes. Actually I reckon with a bit more sharpness on my part (slow day obviously – the point at which the puzzle was effectively broken was just before 3 minutes and even then there was a bit of faffing around) I could knock a minute off that time. Swordfish are sometimes a little trickier to spot but the principles remain the same.

Anyhow, I captured the whole thing as a video if the pictures don’t tell you everything. You can find it here:

David M: I hope this highlights things a little better. Please let me know what you think!

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