Sunday, November 17, 2013

Zone defense

I don't usually spend a lot of time looking for patterns when I'm solving sudokus.  Bifurcation works much faster and easier than x-wings or y-wings or any of the fishy patterns.  But there's one kind of pattern that's worth looking for -- in order to avoid it!

You see, if the puzzlemaker did it right, a puzzle will have a single solution.  That means that a pattern where four squares in the same zone that are the corners of a rectangle can have only two symbols between them if at least one of them is a given.

1|4
4|1  for example, would be easy to reverse and become

4|1
1|4 unless at least one corner can't be changed.

Of course, the corners aren't generally next to each other, since the symbols have to fall into different squares.   But it's fairly easy to see that you can go from single symbols to twoshares and apply the same principle.

So, if you have two spaces such that  1/4 |   | 1/4  in some triad, then there cannot be an identical parallel anywhere within the zone.  You can either use this to decide you are going to use the 2 in a configuration where you've got a parallel that looks like 1/2/4 |    | 1/4, or you can find a pair of 1s that parallel and know that there can't be a 4 in either space joining them.

That's short enough and easy enough that even I'll take a minute to check to see if I can use the pattern.