## Sudoku Troubleshooter #3 – X-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.

This is a tough puzzle, book 7, puzzle 7. It was submitted by Stephen, who got stuck after solving 4 numbers, like so:

If you’d like to try the puzzle yourself, before reading the rest of this, you’ll find the original here.

When I get stuck, I often look at one number at a time, looking for patterns. Let’s take a look at all the cells that appear to have 1 as a possibility. Am I missing any 1s?

Okay, looks like I got them all. That’s a lot of 1s! Now take a closer look at rows 1 and 4.

You’ll notice that in those rows, the 1s form the corners of a square. No other cells, but those 4 corner squares can take on the value of 1. This formation is called an X-Wing. It means that if C1 is 1, than F4 must be 1. If F1 is 1, then C4 must be 1. Thus, in both the rows and columns that are occupied by these squares, these are the only 4 cells that can take on the value of 1.

The X-pattern formed by the relationships between these 4 squares is where the ‘X’ in X-Wing comes from (and the columns and rows that shoot out are the “wings”). It means that in the columns, we can also eliminate 1 as a possibility from C2, F2, C5, F5 and C8. Having eliminated C8 as a possibility, we can now fill in the 1 for A8.

Can you see where to put a 4 now?

September 3rd, 2011 at 8:54 am

I get it so far except the 8 in E8. How is the 8 being eliminated from E2 or E5, or D8 or F8? Appreciate the tips!

September 3rd, 2011 at 1:43 pm

Here’s an illustration:

http://i.imgur.com/RTgZW.png

In column E, E2 or E5 must be 1.

In row 9, B9 can’t be 3. So D9 or F9 must be 3, which means E8 can’t be 3. This means E2 or E5 must be 3.

So (E2,E5) make a naked pair that use up the 1 and 3, leaving the 8 for E8.

September 3rd, 2011 at 3:35 pm

Makes me feel dense not to have seen that before. Guess that’s why these are considered “tough.” I better go back and review tips #1 and #2. I’ve now become addicted to Ken-Ken puzzles (in the NYT) also, assume some of the “tips” might apply to them as well. Thanks for the response.

September 3rd, 2011 at 9:02 pm

The Inkie puzzles on this site are very similar to Ken-Ken. If you get stuck on one of those, I’d be happy to explain on the blog.

September 8th, 2011 at 9:14 am

You do a great job explaining difficult concepts, and I really appreciate that! Thank you. However, I ended up a bit confused about why C2 and F2 were not eliminated in the Sudoku Troubleshooter #3 – X-Wing explanation. Can you help me understand? Shouldn’t all 1’s be eliminated from the C and F columns given that the X-Wing numbers will ultimately cover those columns once solved?

Thanks in advance for your help.

September 8th, 2011 at 9:42 am

Kimberly, those squares should also be eliminated. Thanks for catching that! I’ve corrected the tutorial.