A sort of... Y-Thing...?

Advanced methods and approaches for solving Sudoku puzzles

A sort of... Y-Thing...?

Postby 999_Springs » Mon Sep 01, 2008 3:13 pm

I haven't posted in this forum for ages.

I was doing #8 of the top95 and found this thing...

Basic techniques get here:

Code: Select all

    69 |     5 |     2 ||     4 |     8 |     1 ||    79 |   3679 |   367
-------+-------+-------||-------+-------+-------||-------+--------+-------
  4689 |   346 |   348 ||    69 |     7 |   569 ||     1 |  24569 | 24568
-------+-------+-------||-------+-------+-------||-------+--------+-------
  4689 |    17 |    17 ||     3 |     2 |   569 ||  4589 |   4569 |  4568
=======================||=======================||========================
   456 |  1467 |  1457 ||     8 |  1469 |     2 ||  4579 | 134579 | 13457
-------+-------+-------||-------+-------+-------||-------+--------+-------
     3 |   124 |  1458 ||   179 |   149 |   479 ||     6 |  12459 | 12458
-------+-------+-------||-------+-------+-------||-------+--------+-------
  2468 |     9 |  1478 ||     5 |   146 |     3 ||  2478 |   1247 | 12478
=======================||=======================||========================
     1 |   248 |     6 ||    79 |     3 |  4789 ||  2457 |   2457 |  2457
-------+-------+-------||-------+-------+-------||-------+--------+-------
   245 |   234 |   345 ||   167 |    14 |   467 ||  2347 |      8 |     9
-------+-------+-------||-------+-------+-------||-------+--------+-------
     7 |   348 |     9 ||     2 |     5 |    48 ||    34 |     16 |    16

Then I found an ALS xz
ALS A=r7c46r8c5r9c6
ALS B=r456c5r5c6
x=1 z=7 r8c6<>7
(It's not that necessary but I hardly ever find these things, so I might as well use it...)

Here is the Thing.
Strong link of 7s in r8c47
r7c4 and r1c7=79
r1c1 and r2c4=69
Therefore r2c12<>6
(Puzzle completes with singles.)

The Thing is a sort of two Y-wings on top of each other.

Does this "Y-Thing" have its own name? Does it ought to have one?
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Postby 999_Springs » Tue Sep 02, 2008 2:59 pm

Here's the example for #10 of the top95.

Code: Select all
   

    67 |     9 |     2 ||     3 |     5 |     1 ||    68 |   478 |  4678
-------+-------+-------||-------+-------+-------||-------+-------+-------
  3567 |   347 |   345 ||    67 |     8 |   679 ||     1 | 23579 | 23679
-------+-------+-------||-------+-------+-------||-------+-------+-------
  3567 |    18 |    18 ||     4 |     2 |   679 ||  3569 |  3579 |  3679
=======================||=======================||=======================
     1 |   235 |     7 ||    68 |     4 |  3568 ||  2389 |  2389 |  2389
-------+-------+-------||-------+-------+-------||-------+-------+-------
   239 |   234 |   349 ||   178 |    13 |   378 ||  2348 |     6 |     5
-------+-------+-------||-------+-------+-------||-------+-------+-------
     8 |   345 |     6 ||     2 |     9 |    35 ||    34 |    17 |    17
=======================||=======================||=======================
   379 |     6 |  1389 ||     5 |   137 |     2 ||   389 | 13489 | 13489
-------+-------+-------||-------+-------+-------||-------+-------+-------
     4 |   123 |  1359 ||   168 |   136 |   368 ||     7 | 12359 | 12369
-------+-------+-------||-------+-------+-------||-------+-------+-------
  2357 | 12378 |  1358 ||     9 |  1367 |     4 || 23568 | 12358 | 12368


(als xz: r5c6<>8)

Y-Thing: strong link of 8s in r5
bivalue cells: r4c4, r1c7; r2c4, r1c1
r2c12<>7
(puzzle completes with singles)
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Postby ronk » Tue Sep 02, 2008 3:54 pm

Rather than y-wing, the more common term on this board is w-wing ... and I see your chains as extended w-wings.
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Postby DonM » Tue Sep 02, 2008 10:29 pm

ronk wrote:Rather than y-wing, the more common term on this board is w-wing ... and I see your chains as extended w-wings.


Seems to be a lot of confusion out there when it comes to the term: Y-Wing. Andrew Stuart, using the term Y-Wing, describes what we know to be an XY-Wing and more than one site gives Y-Wing as another name for XY-Wing; that's always been my understanding of the term.

A W-Wing, of course, is quite different from an XY-Wing/Y-Wing. I agree that the above is in the W-Wing camp.
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Postby ronk » Wed Sep 03, 2008 4:27 am

DonM wrote:... more than one site gives Y-Wing as another name for XY-Wing ...

Another possible origin for this confusion are posts that used the y-wing term for any of several possible chains that have three strong inferences -- bivalue and bilocation inferences including grouped, I suppose.

By this "definition" (which I don't use), an xy-wing would be a y-wing ... and a w-wing would also be a y-wing.
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