Troubleshooter #4: XYZ-Wing

This is part of a series on puzzle solving techniques. If you are stuck on a particular Krazydad puzzle, drop me a note, and I’ll use this space to help you out.

Michael wrote in an email:

Dad,
Good morning and an early happy thanksgiving. I really enjoy your puzzles and I have advanced to your tough ones now. I have been going through a bunch of them and I have a question for you. It seems like more recently you have been posting puzzles with no “logical” solution but that requires one to guess or work it out on the scratch pad. My question was is this a valid way of solving puzzles for you? As you will see I have gone through this puzzle attached and I can’t see a logical way to solve it. am I missing something here or do I just need to guess?

Here’s the puzzle that Michael got stuck on. This is a tough puzzle, book 85, puzzle #1. If you’d like to try it yourself, you’ll find it here:

In the next diagram, I’ve highlighed three cells which form an XYZ-Wing. XYZ-Wing is an advanced solving technique which is closely related to the more common XY-Wing, which I’ve covered in a previous column.

Take a look at cell D3, and the effect it has on cell F3.

If D3 is 4, then F3 can’t be 4.
If D3 is 5, then E1 must be 4, and F3 can’t be 4.
If D3 is 7, then A3 must be 4, and F3 can’t be 4.

Therefore, since this covers all the possible values for D3, F3 can’t ever be 4.

So we know that F3 must be 6. From here, the rest of the puzzle solves pretty easily.

As I said, this particular configuration, in which D3 contains XYZ, and E1 contains XZ, and A3 contains YZ, enabling us to eliminate Z from a 4th cell which is connected to all three cells, is called an XYZ-Wing.

It’s fairly rare, and only occurs in 8 of my tough puzzles, as compared to XY-Wing, which occurs 10 times more often. For the curious, the following puzzles contain an XYZ-Wing.

Book 25, puzzle 2
Book 42, puzzle 1
Book 55, puzzle 7
Book 56, puzzle 7
Book 62, puzzle 2
Book 71, puzzle 3
Book 85, puzzle 1
Book 93, puzzle 6

Happy solving!

This entry was posted on Thursday, November 24th, 2011 at 8:49 pm and is filed under Puzzles. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.