dailysudoku.com

[Earl]

A long wait for a glass-jaw VH, which goes down with a single xy-wing (179).

Early Earl

[Marty R.]

I used a Type 6 UR on 18.

Edited 4-4: Thanks to a PM I received I tried again and realized that I must've erred since I couldn't solve it with just the UR.

[cgordon]

A 157 xyz wing is another one punch KO.

[Kdelle]

I was looking forward to a VH, but this one practically solved itself!

[Ema Nymton]

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Perhaps it is easy to some.

I come to a point where logic cannot take me further unless I am overlooking the obvious.

Using the 'Draw/Play,' the hint is to place a 9 in column 7 row 4. My question is why? I am able to figure the possible choices as either 9 or 1. But either choice is as valid as the other.

So why the 9?

~@:o?
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[Marty R.]

Hi Ema, welcome to the forum.

[Ema Nymton]

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Thank you for the welcome; and quick response.

I recognize we are talking about the same square. But I do not understand you when you say, "an XY-Wing 79-19-17 pivoted in r2c8".

FYI- I have been doing Sudoku for a long while and think I am fair at it. But I am not sure I follow your terminology "an XY-Wing 79-19-17 pivoted in r2c8".

I have worked this particular puzzle for at least a week. I can see I am at a critical point, but cannot determine why I should pick a 9.

Thanks,

~@:o?
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[keith]

[Ema Nymton]

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Sorry for being so dense.

Column 7 has possibilities:
row 1 = 17
row 2 = 679
row 4 = 19
Column 8 has possibilities:
row 1 = 157
row 2 = 79
row 6 = 19

I cannot find a way to eliminate the 1 at r4c7.

Please be patient with me. I am slow.

~@:o?
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[keith]

[nataraj]

(edit April 18, 0858 GMT+2: added "click-clack" and link to the : "click-clack" aria)


Ema,

you are not dense at all. Obviously you are not familiar with the xy-wing technique, so no wonder you cannot crack the puzzle. I will not give an in-depth explanation, but rather an illustration. Read up on the xy-wing, it is a most powerful tool, especially for the puzzles on this site, where it cracks some 80% of all very hards !

Here - in Marty's grid - I've circled the xy-wing in red:


3 cells with 2 candidates each, but there are only 3 candidates present in any of the 3 cells: 1,7 and 9

The "wing" has a center (or "pivot") cell (r2c8: "79") and two wingtip (or "pincer") cells (r1c7: "17" and r6c8 "19")

Observe that both pincer cells contain "1". We will show that a cell that sees both pincers cannot contain "1". Like, the cell r4c7.

Here goes.


Let's look at r1c7. One of the pincers. If it is 1, then ... of course r4c7 cannot be 1 (no two "1"s in the same column, right?)

But if it is NOT "1", then it is 7.
Which means r2c8 (the "pivot") is "9" and .... (ta daaaa!)
.... r6c8 is "1" and r4c7 cannot be "1" (no two "1"s in the same box, right?). For this "click-clack" effect, it is essential that each cell in the wings "sees" the next one.

So.... no matter what the solution for r1c7 is, we know that r4c7 cannot be 1.

That is the magic of the xy-wing. click-clack.

It works from the other side, too.

If r6c8=1 then r4c7 cannot be "1".
If r6c8 is NOT "1", then r2c8=7 (click) and then r1c7=1 (clack). Again r4c7 cannot be "1".

The magic works every time you find such a wing.

___

edit: Keith was quicker ....
[url][/url]

[Ema Nymton]

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Thank you.

It makes sense. For longer than a week, I have looked and not seen. I have faced this issue many time when playing this 'blankety-blank- blank' game. I have been beaten by this formation time and again.

Your solutions are understandable. Now that I know what to look for, watch out.

Again thank you for the answers and your patience.

~@:o?
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[nataraj]

happy winging!