dailysudoku.com

[keith]

I came up with a weird way to solve this one. I now see there is an easier way. A little more than "Very Hard".

[tlanglet]

[keith]

Ted,

You have found the simpler solution: Your chain is a W-Wing:

[tlanglet]

[nataraj]

edit 1804 GMT+2: What I wrote is complete nonsense. There is NO strong link on 9 in row 4, therefore no elimination can be made. Sorry for the confusion. I leave my original post below so references to it will make sense.

I found the other UR elimination (the one that keith describes) but somehow when I looked at the pattern again my brain started cheating on me and made me believe there was this nice and easy way and then I was done. Another one of these "lucky" strikes
________________________

I don't think the 39 UR (r49c46) is "complicated" or weird. I would not have seen it but I like it a lot. It is a one step solution:

using the strong link on 9 in row 4, we can remove 9 from r9c6 (if r9c6=9 then r4c6=3 then r4c4=9 then r9c4=3 which is the deadly pattern) and the puzzle is solved.

Fast, clean, elegant.

[keith]

[cgordon]

For the life of me I cannot see a UR here. I realise these are the only two 3’s in R4 and the only two 9’s in R9. If the 39’s weren’t diagonal, I could see the makings of a Type 4 UR. And I realise you cannot remove both the 6 and 7 cos this would leave a Deadly Pattern. But I can’t follow Nataraj’s logic behind the removal of R9C6.

And as for “Forcing Chains” isn’t that just a fancy word for guessing.

Hey – I became “officially old” today so I am allowed to be a miserable curmudgeon

[nataraj]

Craig,
you cannot follow my logic because that logic was flawed. I edited my original post.

There is valid UR logic though like keith pointed out:

[nataraj]

[cgordon]

Nataraj: I missed your retraction – but I would have still demanded an explanation. Fortunately your next post provided this. Thank you. I followed everything OK - but I still need to get some things straight (Sudoku that is – I’m too old for anything else).

I have never gotten into the strong links/weak link definitions - but I know you are referring to the fact that the UR coincides with a row or column that contains only two of that number. Just like a Type 4 UR. Here we have two such cases with both 3’s and 9’s.

Question 1: Is it correct to assume that eliminations would still be possible if only one of these strong links had been available - i.e EITHER 3 or 9. Not both.

Q2: Is this solution unique to this Sudoku – or can I establish a typical rule. I gotta have rote-rules.

Q3: How do I describe this when I am the first to post my elegant solutions? Is this still a Type 4 UR with a diagonal variant?

And thanks for the Birthday Greetings.

Craig

[nataraj]

Craig,

here's my attempt at answering your questions:

Q1: yes. The two eliminations are independent of each other. If there had been only a strong link on 3 in row 4, we'd still have been able to eliminate 3 from r9c6.

Q2: no, it is not specific to this sudoku, it is a general principle ("typical rule") applicable to this situation:

[Marty R.]

I don't know what the technique is called, I just call it breaking up a deadly pattern. This is an almost Type 6. A Type 6 exists when one of the deadly candidates is an X-Wing, in which case the bivalue cells are solved with that number.

When it's not a Type 6 but there is a strong link in a row or column, that candidate can be eliminated from the polyvalue cell in the other row or column.

[cgordon]

[keith]