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Marty R. · Posted: Wed May 24, 2006 1:41 am Post subject: Rectangle question

The grid below just shows rows 6-7-8-9. Note the 39 rectangle in c7-8, with the 39s on a diagonal. I know for sure that r6c7 must be 6 or 7 or that r9c8 must be 2.

But can I do more? I was ready to do all sorts of candidate-zapping on the assumption that the 39 diagonals were conjugate. But thinking further, I can't see a reason why they couldn't be both 3s or both 9s.

At this point, I can't see anything to do with it other than starting a triple-implication chain (is that the right term?) on the possibilities at the end of the first paragraph above, if I were so inclined.

Myth Jellies · Guest

From just what you have here, the strong links between the 9's in row 6 and the 3's in row 9, along with the 29 cell in r7c8 allows you to eliminate the 3 in r6c7, and the 9 in r9c8.

Guest · Posted: Thu May 25, 2006 9:16 am Post subject:

Oops, there is no strong link in the 3's. But the reductions still hold since I did not use a strong link between 3's in the chain/loop.

Myth Jellies · Guest

The 3's are locked in r9b9, so you can eliminate the 3 in r9c5. The two aforementioned strong links with 3 and 9 are all you need to make the eliminations.

Marty R. · Posted: Thu May 25, 2006 5:05 pm Post subject:

Thank you, Mr. Jellies, for taking the time to help.

David Bryant · Joined: 29 Jul 2005 Posts: 559 Location: Denver, Colorado

Hi, Marty!

I wasn't going to reply to this one, because I'd rather look at the entire grid, and not just a (possibly unhelpful) piece of it. But since MJ pointed the way, I'll take a stab at it.

Here's the fragment you posted.

keith · Posted: Thu May 25, 2006 8:33 pm Post subject: Please post

Marty,

Can you please post the original starting point, and the complete grid? I'd like to examine it.

This is very much like a rectangle type that has been discussed in the Solver's Forum over the past few weeks. The pattern consists of the rectangle, plus a cell that contains one of the "deadly" values plus one of the "extra" values from the rectangle. Then, look for a short chain.

Keith

Marty R. · Posted: Thu May 25, 2006 8:43 pm Post subject:

Marty R. · Posted: Thu May 25, 2006 9:44 pm Post subject:

Keith, your post wasn't on here when I was making mine. I can't re-create the point where I was stuck, unless I start it over again, and I don't want to do that. It involved coloring, two X-Wings, a hidden pair, a rectangle and a DIC to get to where I was stuck, plus it was my second or third try at it, so I want it to be history.

Update: removing the "3" and "9" from the two cells was all it needed to easily solve the rest of it. Thank you again, MJ and DCB.

If anyone's interested, it was the May 12 "Tough" puzzle from www.sudoku.com.au . That site's puzzles give me trouble; I find them considerably harder than the "Nightmares."

keith · Posted: Thu May 25, 2006 11:26 pm Post subject: Thanks!

Marty,

Thank you. I took a look at the original puzzle and, yes, my solver did not recover the position you posted.

The pattern to look for is this: A UR plus a cell involving one deadly value (one of <39>) and one "extra" value (one of <267>). The "plus" cell here is <29>.

Tabulate the possible solutions of the five cells. Note which candidates are "missing" from the list of all solutions. These can be eliminated. Or, look for a chain.

Look at it this way: If R6C7 is <3>, it forces the non-unique rectangle.

If R9C8 is <9>, it forces the opposite non-unique rectangle, because of the strong link on <9> in R6.

Good stuff!

Keith

Marty R. · Posted: Fri May 26, 2006 12:29 am Post subject:

Thanks Keith, I'll add that to my burgeoning collection of solving techniques. Smile

Myth Jellies · Guest

Marty R. · Posted: Fri May 26, 2006 3:52 pm Post subject:

Thank you MJ, it has become much clearer now.