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And the 91-13-35-59 chain takes out the same 9 as the xy-wing.

And the 91-13-35-59 chain takes out the same 9 as the xy-wing.

And from a chain-ganger: 18-85-51-19-91

And from a chain-ganger:

18-85-51-19-91

Or: 58-89-98-85

Or: 58-89-98-85

Or the 1s chain that I saw before the 9s chain: [91-(17-79]-98-84-41)

Or the 1s chain that I saw before the 9s chain:

[91-(17-79]-98-84-41)

And another solution is the 379 xy-wing followed by a 359 xyz-wing.

A 79s w-wing in columns 1 and 2 did it for me.

Or to put it another way that I can understand, the center column in box 7 must contain the 3 in that box since the rest of that column in the boxes above it doesn't contain a 3. Therefore, the 3 can ...

I saw the long path extended xy-chain from the 28 to the 23 before I saw the short wing: <28-83-36-62>-23=23

And the 68-87-74-46 chain also solves the puzzle.

And the 68-87-74-46 chain also solves the puzzle.

And from there the xy-chain 65-51-13-38-84-45-56 also solves it.

And from there the xy-chain 65-51-13-38-84-45-56 also solves it.

I didn't check which of these XYs turned out to be unnecessary:

59-97-75
72-29-94-49-97
73-34-42-27
48-82-29-94
95-57-79

My solution was the xy chain 34-46-69-91-13.

Since I look for xy chains instead of xy-wings, I'm as likely to find a long chain as a 3-member chain (wing). Flitting around from one linked pair to t ...

Thanks, daj, for addressing my questions.

I didn't realize that you have to make a guess to solve any sudoku with multiple solutions, but perhaps that's obvious. I don't really want to do puzzles t ...

It's interesting that the responders to my last post completely ignored my questions Exclamation

Since the FAQs state that "In our view, a Sudoku with more than one solution i ...

I don't know anything about how sudokus are created, and how it's verified that they have only one solution. Could you solve a puzzle with mutliple solutions without noticing that there are more than ...

I'm sure this has been asked before but I haven't heard the answer:

I don't like the thought of using a technique that requires that I know that a sudoku has a unique solution. How do I know that a ...

The same grid depicts the 9s skyscraper.

Denny

I print out the sudokus and do them on paper. That's probably very old-fashioned of me.

X-wings are first to try on my official list of advanced techniques, probably because that was the first advanced technique I learned, but also because they're pretty useful. In practice I usually loo ...

The 38-84-47-78-83 xy-chain solved it for me, eliminating the 3 in r5c8.

The 38-84-47-78-83 xy-chain solved it for me, eliminating the 3 in r5c8.