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Set XY_03 Puzzle 047

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daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Thu Oct 29, 2009 3:09 am Post subject: Set XY_03 Puzzle 047

My solver didn't find a workaround for the XY-Chain.

Code:

XY puzzles can be solved using these techniques:

Basics: Naked/Hidden Single, Naked Pair/Triple, Locked Candidates 1/2
Basics+: Naked Quad, Hidden Pair/Triple/Quad
VH: BUG+1, UR Type 1, X-Wing, XY-Wing
VH+: 2-String Kite, Empty Rectangle, Remote Pair, Skyscraper,
XYZ-Wing, finned X-Wing, UR Type 2/4
XY: gM-Wing, W-Wing, XY-Chain, BUG+2, BUG+3, other URs

Code:

+-----------------------+
| 6 . 2 | . 1 . | 7 . . |
| . 8 . | . . . | . . . |
| 9 . 7 | 5 2 6 | . 3 . |
|-------+-------+-------|
| . . 9 | . 6 . | 2 . . |
| 1 . 5 | 7 3 . | . 6 . |
| . . 6 | . . 9 | . . 1 |
|-------+-------+-------|
| 5 . . | 6 . . | . . . |
| . . 3 | . 5 . | . . . |
| . . . | . . 2 | . . 5 |
+-----------------------+

Play this puzzle online at the Daily Sudoku site

arkietech

Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA

Posted: Thu Oct 29, 2009 7:53 am Post subject:

Code:

*-----------------------------------------------------------------------------*
| 6 5 2 | 38 1 38 | 7 49 49 |
| 3 8 1 | 49 479 47 |*56 25 2-6 |
| 9 4 7 | 5 2 6 | 1 3 8 |
|-------------------------+-------------------------+-------------------------|
| 48 37 9 | 1 6 5 | 2 48 a37 |
| 1 2 5 | 7 3 48 | 489 6 49 |
| 48 37 6 | 2 48 9 |b35 57 1 |
|-------------------------+-------------------------+-------------------------|
| 5 19 48 | 6 4789 13478 | 3489 124789 237 |
| 2 169 3 | 489 5 1478 | 489-6 14789 *67 |
| 7 169 48 | 3489 489 2 | 3489-6 1489 5 |
*-----------------------------------------------------------------------------*
(6=7)r8c9-(7=3)r4c9-(3=5)r6c7-(5=6)r2c7 => r2c9,r89c7<>6;
singles

Last edited by arkietech on Thu Oct 29, 2009 3:15 pm; edited 1 time in total

tlanglet

Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

Posted: Thu Oct 29, 2009 2:47 pm Post subject:

xy-wing 3-57 with vertex 37 in r4c9, pincer 35 in r6c7 and extended pincer 57: (7)r4c9 - (7=6)r8c9 - (6=2)r2c9 - (2=5)r2c8; r2c7<>5. Ted

Marty R.

Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

Posted: Fri Oct 30, 2009 3:51 am Post subject:

tlanglet wrote:

xy-wing 3-57 with vertex 37 in r4c9, pincer 35 in r6c7 and extended pincer 57: (7)r4c9 - (7=6)r8c9 - (6=2)r2c9 - (2=5)r2c8; r2c7<>5.

Ted

Ted,

You do have a good eye for spotting these things. I have a terminology question. Why is the 35 a pincer? Why wouldn't the extended pincer be something other than 57 since it's the 6s that do the pincing?

tlanglet

Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

Posted: Fri Oct 30, 2009 2:04 pm Post subject:

Marty R. wrote:

tlanglet wrote:

xy-wing 3-57 with vertex 37 in r4c9, pincer 35 in r6c7 and extended pincer 57: (7)r4c9 - (7=6)r8c9 - (6=2)r2c9 - (2=5)r2c8; r2c7<>5.

Ted

Marty,

I view the basic xy-wing as zx - xy - yz where the vertex is xy and z is the digit in the two pincers, zx & yz, that may provide eliminations. I know that the term "pivot" is sometimes used instead of "vertex" to describe the xy cell but understand that the term "pincer" is commern for the two outside cells, zx & yz.

In this code, I was looking for a xy-wing and found the two bivalue cells, 37 in r4c9 and 35 in r6c7, but did not see a third bivalue cell 57 visible to either of the other two. So I played WHAT IF and "assumed" that the 37 in r4c9 was the vertex (or pivot) cell xy, and that the 35 in r6c7 was one of the two pincers like zx. Now, if r4c9=3, then r6c7=5 but I needed to find another cell that would be forced to the value 5 when r4c9=7. In this case I found such a sequence: (7)r4c9 - (7=6)r8c9 - (6=2)r2c9 - (2=5)r2c8; r2c7<>5; or in words: if r4c9=7 then r8c9=6, then r2c9=2, then r2c8=5.

In summary, if the vertex 37 in r4c9=3, then r6c7=5 and if the vertex 37=7, then r2c8=5; digit 5 can be deleted from cell r2c7. For this example, the xy-wing relationship has x=3, y=7 and z=5; 5 is the common digit contained in the two pincers and is the value deleted in r2c7.

Of course, the entire pattern could be written as an AIC, just as the basic xy-wing is an AIC. However, I presented it as xy-wing with one pincer extended simply because that is how I found it; the process can be time consuming but simple to perform.

This is a long winded response to the question and I hope that it did not cause greater confusion. If further questions arise, please do not hesitate to bring them up.

Ted

Marty R.

Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

Posted: Fri Oct 30, 2009 3:52 pm Post subject:

Ted, Another senior moment. I saw your original XY-Wing statement, then looked at Dan's grid and saw the 6s eliminated. For some reason I linked the two, which led to my question about the pincers of 6 and how they could be possible in a 357 XY-Wing. But I still think you have a good eye for these things.

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Fri Oct 30, 2009 8:34 pm Post subject:

tlanglet wrote:

xy-wing 3-57 with vertex 37 in r4c9, pincer 35 in r6c7 and extended pincer 57: (7)r4c9 - (7=6)r8c9 - (6=2)r2c9 - (2=5)r2c8; r2c7<>5.

I don't see it Exclamation

You have a useless XY-Wing and ignore the pincer at r6c8 to, instead, create a chain from vertex r4c9 to another cell. That's not an extended XY-Wing IMO because it doesn't use all three cells in the XY-Wing. It's simply an XY-Chain:

Code:

(5=3)r6c7 - (3=7)r4c9 - (7=6)r8c9 - (6=2)r2c9 - (2=5)r2c8; r2c7,r6c8<>5

tlanglet

Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

Posted: Fri Oct 30, 2009 11:37 pm Post subject:

Danny,

As I noted in my comments to Marty,

Quote:

Of course, the entire pattern could be written as an AIC, just as the basic xy-wing is an AIC. However, I presented it as xy-wing with one pincer extended simply because that is how I found it; the process can be time consuming but simple to perform.

If you believe that it is more correct, I am happy to call these solutions xy-chains.

Ted

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sat Oct 31, 2009 12:03 am Post subject:

tlanglet wrote:

Danny,

As I noted in my comments to Marty,

Quote:

If you believe that it is more correct, I am happy to call these solutions xy-chains.

Ted,

An extended XY-Wing often turns out to be identical to an XY-Chain using the same cells. I accept the extended XY-Wing explanation because it relays information about how the person making the post derived the elimination. In fact, I respect what manual solvers have to do in order to derive some steps!!!

From what I recall, extended XY-Wings are extended through a pincer.

My problem is with this individual solution being called an extended XY-Wing. The extension is off of the vertex instead of a pincer. If you had said that you first spotted an XY-Wing and ignored one pincer in favor of a chain from the vertex, then I would have kept quiet.

Note: Since the cells of your "XY-Wing" are all in [b6], they're also a Naked Triple.

Regards, Danny

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