dailysudoku.com

[Johan]

Two advanced steps for this one.

1. ER for digit <3> in Box 6, the ERI in R6C7 can see one of the strong links on <3> in C2, which eliminates <3> in R7C7.

2. XY-wing with [19] pivot in R6C9 eliminating <3> in R7C2, collapsing the puzzle.

The grid after basic steps :

[George Woods]

I found a solution based on the 13 in box 4 . Seeking a possible remote pair with the 13 in box9 it became evident that r6c2 if 1 brings a 39 pair to bear down on r8c9 and if 3 again denies 3 to this cell so r8c9 must be 1 .........

[Earl]

I have seldom used so many techniques in one puzzles - an x-wing, a kite, two xyz-wings and an xy wing. But they were all evident and the puzzle opened quickly. Perhaps someone found a single move that unlocked it, which is always neater.

Earl

[sdq_pete]

There's an X-wing on 6 in R25.
Thereafter, X-wing on 8 in R38. Then I saw a Finned X-wing on 3 in C29 (victim R7C7) and finally the XY-wing on 139 with pivot R6C9.

Peter

[Marty R.]

[Earl]

Marty,

Is that W-wing valid in Johan's grid?

Earl

[Marty R.]

[duffy]

Underlining Marty's observation about multiple solution paths, here is Johan's grid after utilizing the x-wing Peter noted:

[cgordon]

Like Earl - I threw the book at this one - starting with an X-wing on 4s (R38), which I felt clever spotting - then 2 more easier to spot x-wings - then the ER already mentioned - then an xyz (pivot R4C3) - then, after much staring, the 13,19,39 xy-wing with pivot R6C9. Though it appears I could have just thrown a couple of pages at it, instead of the whole book. Still -a challenge for sure!

[KSipher]

Would anyone be willing to explain the empty rectangle in box 6? I've searched the web for explanations of the empty rectangle but I still can't see it. Perhaps if it was explained specifically for this sudoku, I might be able to see it.

Thanks so much! I've learned so much from this group!
Kathy

[keith]

[Marty R.]

Maybe it's just me, but I couldn't get the hang of Empty Rectangles until I read this description. Now I use them regularly.

http://www.intosudoku.com/Doc/EmptyRectangles.html

[keith]

I took a look at the link I posted. With all due respect, I think it's confusing.

Here is the basic idea:

[KSipher]

Oh wow. I get it. I followed thru Keith's explanation and was still somewhat confused, then I followed Marty's link and then I finally got it. But I wondered if I would ever be able to actually identify a ER myself. But then I went back and saw Keith's second reply and it made it so much clearer! Thanks to both of you.

Kathy

[Asellus]

A couple of comments on the solutions used above...

(1) That ER elimination of <3> in Box 6: This can also be seen as a Sashimi Swordfish in Rows 3, 4 and 8. R8C9 is the fin and R8C7 is the "missing <3> part" of the Swordfish. Or, in this case, you could describe it as an ordinary Finned Swordfish with the fin in a "remote Box."

(2) The {13} W-Wing is activated by the ER in Box 7, speaking of ERs. ERs do provide a strong link. However, the link is between the two "arms" of the "hinge" rather than between two cells. (Some describe this as "group coloring.") There is always an external strong link involved in a W-Wing.

As an additional advanced comment: if the pivot cell in an ER "hinge" is occupied by an ER candidate digit, then the link created by the ER is what is called a "strongly inferential link" instead of the ordinary strong link. The difference is that, in such a link, both alternatives can be true. If the pivot cell is true, then both arms of the ER are true. It doesn't matter in either of the cases above. The ER target cell in "(1)" still must be false. For the W-Wing in "(2)", if the hinge pivot cell were present (it isn't in this case) and true, then both {13} cells would be <1>. But, that's okay: the W-Wing <1> eliminations are still valid.
_____

Edited to clarify that (1) is talking about the <3> elimination, not that the ER and Sashimi Fish are the same things.

[cgordon]

I'm a big fan of ERs because I find patterns easier to spot that numbers, e.g. xy-wings. So if I'd like to just add to Kieth's post that the hinges can be shaped like + (as in his example) or a T or an L as shown below. It's also worth mentioning that ALL the bits of the +, T and L DON'T have to be present. See the partial T example below.

T shape hinge

[storm_norm]

if you follow the "sudoku players forum", someone posted this puzzle there.

[storm_norm]

here is the link

http://www.sudoku.com/boards/viewtopic.php?t=5693[/url]

[Asellus]

Thanks, storm_norm! It's definitely worth taking a look at that other forum thread.

There is an interesting use of an otherwise useless XYZ-Wing extended by that B6 ER to make an elimination.

And, Ruud provides Eureka notation for the B6 ER elimination of that <3>, which I'll copy here:

(1=3)r6c2 - (3)r7c2 = (3)r8c13 - (3=1)r8c9 => r6c9<>1

Pursuant to my comment above, if the "pivot" cell R8C2 in the ER "hinge" also contained a <3> candidate, then the notation would be:

(1=3)r6c2 - (3)r78c2 = (3)r8c123 - (3=1)r8c9 => r6c9<>1

The pivot cell <3> occurs on both sides of the (inferential) strong link.

Ruud also points out that this elimination is also viewable as an ALS chain.

[keith]

These things are becoming pretty easy to spot!