The New Sudoku Players' Forum

[Gee]

I got this far with puzzle. Where do I go from here? Seems like a difficult puzzle to me.

Code: Select all


 
 
 *-----------------------------------------------------------*
 | 9     1     2     | 4     67    3     | 8     567   57    |
 | 467   8     47    | 2     5     1     | 9     67    3     |
 | 5     67    3     | 67    9     8     | 1     2     4     |
 |-------------------+-------------------+-------------------|
 | 1     4     57    | 3568  268   25    | 35    9     578   |
 | 78    2     9     | 35    48    45    | 357   1     6     |
 | 68    3     56    | 9     1     7     | 2     4     58    |
 |-------------------+-------------------+-------------------|
 | 46    567   467   | 1     3     9     | 567   8     2     |
 | 2     9     8     | 57    47    6     | 457   3     1     |
 | 3     567   1     | 578   2478  245   | 4567  57    9     |
 *-----------------------------------------------------------*




Original Puzzle

Code: Select all


 
 *-----------------------------------------------------------------------------*
 | 12679   1679    2679    | 4       67      13      | 8       23567   357     |
 | 146789  16789   4679    | 2       5       138     | 134679  3467    347     |
 | 5       1678    3       | 1678    9       18      | 12467   2467    47      |
 |-------------------------+-------------------------+-------------------------|
 | 1678    4       567     | 3568    268     2358    | 2357    9       3578    |
 | 789     2       579     | 358     48      3458    | 3457    1       6       |
 | 68      3568    56      | 9       1       7       | 2345    23458   3458    |
 |-------------------------+-------------------------+-------------------------|
 | 4679    5679    45679   | 1578    3       14589   | 4567    45678   2       |
 | 2479    579     8       | 57      247     6       | 3457    3457    1       |
 | 3       567     1       | 578     2478    2458    | 4567    45678   9       |
 *-----------------------------------------------------------------------------*



[999_Springs]

I got this far with puzzle. Where do I go from here? Seems like a difficult puzzle to me.

Code: Select all


 
 
 *-----------------------------------------------------------*
 | 9     1     2     | 4     67    3     | 8     567   57    |
 | 467   8     47    | 2     5     1     | 9     67    3     |
 | 5     67    3     | 67    9     8     | 1     2     4     |
 |-------------------+-------------------+-------------------|
 | 1     4     57    | 3568  268   25    | 35    9     578   |
 | 78    2     9     | 35    48    45    | 357   1     6     |
 | 68    3     56    | 9     1     7     | 2     4     58    |
 |-------------------+-------------------+-------------------|
 | 46    567   467   | 1     3     9     | 567   8     2     |
 | 2     9     8     | 57    47    6     | 457   3     1     |
 | 3     567   1     | 578   2478  245   | 4567  57    9     |
 *-----------------------------------------------------------*




W-wing/Y-wing:
strong link 5 in r6
bivalue cells r4c3 and r1c9
=> r4c9<>7
Puzzle completes with singles.

Code: Select all

 *-----------------------------------------------------------*
 | 9     1     2     | 4     67    3     | 8     567   *57   |
 | 467   8     47    | 2     5     1     | 9     67    3     |
 | 5     67    3     | 67    9     8     | 1     2     4     |
 |-------------------+-------------------+-------------------|
 | 1     4     *57   | 3568  268   25    | 35    9     5-78  |
 | 78    2     9     | 35    48    45    | 357   1     6     |
 | 68    3     *56   | 9     1     7     | 2     4     *58   |
 |-------------------+-------------------+-------------------|
 | 46    567   467   | 1     3     9     | 567   8     2     |
 | 2     9     8     | 57    47    6     | 457   3     1     |
 | 3     567   1     | 578   2478  245   | 4567  57    9     |
 *-----------------------------------------------------------*

[Draco]

Or a very short forcing chain to break the puzzle to singles (touches the same squares as 999_Springs solution, but with a different elimination):

r1c9=5 r4c9=7 r6c9=8 r6c3=5 + r1c9=7 r4c3=7 ==> r4c3<>5

Cheers...

- drac

[udosuk]

r1c9=5 r4c9=7 r6c9=8 r6c3=5 + r1c9=7 r4c3=7 ==> r4c3<>5

I think you can make it even shorter:

r4c3=5 r4c9=7 r6c9=8 r6c3=5 ==> r4c3<>5

But I can see some people don't like chains presented like this.

On the other hand, I think r46c39 forms a classical strong wing situation:

7 @ r4 locked @ r4c39
8 @ c9 locked @ r46c9
5 @ r6 locked @ r6c39
5 @ c3 locked @ r46c3

r4c9 can't be 7 & 8 simultaneously
=> either r4c3=7, or r6c9=8, or both
=> r6c3 must be 5

[Gee]

Thanks for the replies. Seems so easy when once you are shown.

I do have one question. I know what a Y-wing is but not a W-wing and as written by 999_springs, a W-wing/Y-wing really leaves me baffled. I wonder if that can be explained or at least I could be pointed to a reference source. Thanks.

[daj95376]

Thanks for the replies. Seems so easy when once you are shown.

I do have one question. I know what a Y-wing is but not a W-wing and as written by 999_springs, a W-wing/Y-wing really leaves me baffled. I wonder if that can be explained or at least I could be pointed to a reference source. Thanks.

http://www.dailysudoku.com/sudoku/forums/viewtopic.php?p=8277&sid=1d601fda1f8caa3447bd4590ea547dfc#8277

Code: Select all

 after basics: XY-Chain a-b-c-d-e-f-g-h => [r1c5]<>7; BUG+1
 +--------------------------------------------------------------+
 |  9     1     2     |  4     6-7   3     |  8     567  h57    |
 |  467   8     467   |  2     5     1     |  9     367   37    |
 |  5     67    3     |  67    9     8     |  1     2     4     |
 |--------------------+--------------------+--------------------|
 |  1     4    d57    |  3568  268   25    |  357   9     3578  |
 | c78    2     9     |  358  b48    45    |  357   1     6     |
 | f68    3    e56    |  9     1     7     |  2     4    g58    |
 |--------------------+--------------------+--------------------|
 |  467   567   467   |  1     3     9     |  567   8     2     |
 |  2     9     8     |  57   a47    6     |  3457  357   1     |
 |  3     567   1     |  578   2478  245   |  4567  57    9     |
 +--------------------------------------------------------------+
 # 63 eliminations remain


[999_Springs]

I do have one question. I know what a Y-wing is but not a W-wing and as written by 999_springs, a W-wing/Y-wing really leaves me baffled. I wonder if that can be explained or at least I could be pointed to a reference source. Thanks.

W-wing and Y-wing and semi-remote pair are three different names for the same technique. I don't know why.

[Draco]

I think you can make it even shorter:

r4c3=5 r4c9=7 r6c9=8 r6c3=5 ==> r4c3<>5

But I can see some people don't like chains presented like this

I think contradiction loops/chains like this are just fine

I am no expert on NL's but this looks like it could be one.

Cheers & Merry Xmas,

- drac

[daj95376]

I do have one question. I know what a Y-wing is but not a W-wing and as written by 999_springs, a W-wing/Y-wing really leaves me baffled. I wonder if that can be explained or at least I could be pointed to a reference source. Thanks.

W-wing and Y-wing and semi-remote pair are three different names for the same technique. I don't know why.

You might want to research these three techniques again. They are not the same!

[999_Springs]

Code: Select all

+-------------------+-------------------+-------------------+
| 189   6     3     | 2     189   19    | 57    57    4     |
|-1589  58    4     | 7     189   6     | 3     2    *18    |
|*18    7     2     | 3     5     4     | 9    -18    6     |
+-------------------+-------------------+-------------------+
| 78    38    6     | 5     379   2     | 4     18    189   |
|*578   2     1     | 4     36    79    | 57    36   *89    |
| 4     35    9     | 1     67    8     | 2     67    35    |
+-------------------+-------------------+-------------------+
| 2     1     5     | 8     4     3     | 6     9     7     |
| 6     4     7     | 9     12    15    | 8     35    235   |
| 3     9     8     | 6     27    57    | 1     4     25    |
+-------------------+-------------------+-------------------+

W-wing/Y-wing/semi-remote-pair:
8 @ r5 locked @ r5c19
=> r2c9+r3c1 can't be both 8
=> r2c1+r3c8, seeing r2c9+r3c1, can't be 1
=> r3c18=[18], r2c9=r4c8=1

Code: Select all

+----------------+----------------+----------------+
|*89   6    3    | 2    189 *19   | 57   57   4    |
| 589  58   4    | 7    89   6    | 3    2    1    |
| 1    7    2    | 3    5    4    | 9    8    6    |
+----------------+----------------+----------------+
| 78   38   6    | 5    379  2    | 4    1    89   |
| 57-8 2    1    | 4    36  *79   | 57   36  *89   |
| 4    35   9    | 1    67   8    | 2    67   35   |
+----------------+----------------+----------------+
| 2    1    5    | 8    4    3    | 6    9    7    |
| 6    4    7    | 9    12   15   | 8    35   235  |
| 3    9    8    | 6    27   57   | 1    4    25   |
+----------------+----------------+----------------+

W-wing/Y-wing/semi-remote-pair:
9 @ c6 locked @ r15c6
=> r1c1+r5c9 can't be both 9
=> r5c1, seeing r1c1+r5c9, can't be 8

It certainly seems like you can apply all three names to a bilocation with two bivalue cells sticking out of it.

[daj95376]

Code: Select all

+-------------------+-------------------+-------------------+
| 189   6     3     | 2     189   19    | 57    57    4     |
|-1589  58    4     | 7     189   6     | 3     2    *18    |
|*18    7     2     | 3     5     4     | 9    -18    6     |
+-------------------+-------------------+-------------------+
| 78    38    6     | 5     379   2     | 4     18    189   |
|*578   2     1     | 4     36    79    | 57    36   *89    |
| 4     35    9     | 1     67    8     | 2     67    35    |
+-------------------+-------------------+-------------------+
| 2     1     5     | 8     4     3     | 6     9     7     |
| 6     4     7     | 9     12    15    | 8     35    235   |
| 3     9     8     | 6     27    57    | 1     4     25    |
+-------------------+-------------------+-------------------+

W-wing/Y-wing/semi-remote-pair:
8 @ r5 locked @ r5c19
=> r2c9+r3c1 can't be both 8
=> r2c1+r3c8, seeing r2c9+r3c1, can't be 1
=> r3c18=[18], r2c9=r4c8=1

Code: Select all

+----------------+----------------+----------------+
|*89   6    3    | 2    189 *19   | 57   57   4    |
| 589  58   4    | 7    89   6    | 3    2    1    |
| 1    7    2    | 3    5    4    | 9    8    6    |
+----------------+----------------+----------------+
| 78   38   6    | 5    379  2    | 4    1    89   |
| 57-8 2    1    | 4    36  *79   | 57   36  *89   |
| 4    35   9    | 1    67   8    | 2    67   35   |
+----------------+----------------+----------------+
| 2    1    5    | 8    4    3    | 6    9    7    |
| 6    4    7    | 9    12   15   | 8    35   235  |
| 3    9    8    | 6    27   57   | 1    4    25   |
+----------------+----------------+----------------+

W-wing/Y-wing/semi-remote-pair:
9 @ c6 locked @ r15c6
=> r1c1+r5c9 can't be both 9
=> r5c1, seeing r1c1+r5c9, can't be 8

It certainly seems like you can apply all three names to a bilocation with two bivalue cells sticking out of it.

First off, a Y-Wing is the same thing as an XY-Wing, but that isn't what Udosuk is demonstrating above. You and he seem to be under the misconception that a Y-Wing Styles is the same as a Y-Wing, which it's not.

Now, I'll agree that a Y-Wing Styles is the same as a W-Wing, but I will only concede that they are a subset of Semi-Remote Naked Pair, which Keith calls a General Remote Pair. The SRNP/GNP pattern can extend beyond four cells. The Y-Wing Styles and W-Wing pattern can not!

[ronk]

I'll agree that a Y-Wing Styles is the same as a W-Wing, but I will only concede that they are a subset of Semi-Remote Naked Pair ...

Let's see ...

An xy-wing is one of the y-wing styles,
a w-wing is one of the y-wing styles,
and an xy-wing is sometimes called a y-wing.

No wonder newcomers and even oldtimers are confused. As I've stated before, I think the y-wing term, and hence the y-wing styles term, should be deep-sixed.

[daj95376]

As I've stated before, I think the y-wing term, and hence the y-wing styles term, should be deep-sixed.

I agree!!!