The New Sudoku Players' Forum

[manofsteel520]

I feel I'm one observation away from cracking this, but not sure where to go from here. I'm only a little familiar with advanced techniques. I eliminated some candidates with X wing. I don't see any opportunities to apply XY wing. Could any of you help with the simplest technique to unlock this? Thank you!! - Nick

edit: couldn't attach even a small screenshot - figured it would help show how far I made it reducing candidates - but posting as text instead. (Also couldn't figure out a monospaced font to make a "pretty print" grid - happy to update post if someone can share how - thanks!)

..8.7.2...5.6.2.1.2...18..5..32574..5..146..24.298315.321.6...9.458.1.2.8.6.2.5.1

[Pat]

(use "code")

Code: Select all

..8.7.2...5.6.2.1.2...18..5..32574..5..146..24.298315.321.6...9.458.1.2.8.6.2.5.1

[Pat]

Code: Select all


 . . 8 | . 7 . | 2 . .
 . 5 . | 6 . 2 | . 1 .
 2 . . | . 1 8 | . . 5
-------+-------+------
 . . 3 | 2 5 7 | 4 . .
 5 . . | 1 4 6 | . . 2
 4 . 2 | 9 8 3 | 1 5 .
-------+-------+------
 3 2 1 | . 6 . | . . 9
 . 4 5 | 8 . 1 | . 2 .
 8 . 6 | . 2 . | 5 . 1


..8.7.2...5.6.2.1.2...18..5..32574..5..146..24.298315.321.6...9.458.1.2.8.6.2.5.1

[m_b_metcalf]

Could any of you help with the simplest technique to unlock this? Thank you!! - Nick

The simplest technique is, unfortunately, quite advanced: forcing chains.

Regards,

Mike

[jco]

After basics (NP(79) @ c1, NT(479) @ b1, LC(4) @ c8))

Code: Select all

.-----------------------------------------------------------.
| 16    136   8     | 345   7     459   | 2     369   346   |
| 79    5     479   | 6     39    2     | 3789  1     3478  |
| 2     36    479   | 34    1     8     | 3679  3679  5     |
|-------------------+-------------------+-------------------|
| 16    1689  3     | 2     5     7     | 4     689   68    |
| 5     789   79    | 1     4     6     | 3789  3789  2     |
| 4     67    2     | 9     8     3     | 1     5     67    |
|-------------------+-------------------+-------------------|
| 3     2     1     | 457   6     45    | 78    478   9     |
|b79    4     5     | 8    b39    1     | 367   2     367   |
| 8    a79    6     |c34-7  2     49    | 5     347   1     |
'-----------------------------------------------------------'


(7)r9c2 = (79-3)r8c15 = (3)r9c4 => -7 r9c4; ste
(or: (7=9)r8c2 - (9=457)b8p139 => -7 r9c4; ste)

[Leren]

After basic moves there are two X Wings, which I've shown on the diagram below.

Code: Select all

*------------------------------------------------*
| 16 136   8    | 345  7  459 | 2     369   346  |
|a79 5     47-9 | 6   a39 2   | 378-9 1     3478 |
| 2  36   b479  | 34   1  8   |b3679  367-9 5    |
|---------------+-------------+------------------|
| 16 1689  3    | 2    5  7   | 4     689   68   |
| 5  78-9 b79   | 1    4  6   |b3789  378-9 2    |
| 4  67    2    | 9    8  3   | 1     5     67   |
|---------------+-------------+------------------|
| 3  2     1    | 457  6  45  | 78    478   9    |
|a79 4     5    | 8   a39 1   | 367   2     367  |
| 8  79    6    | 347  2  49  | 5     347   1    |
*------------------------------------------------*

XWing in 9's c15 r28 => - 9 r2c37. XWing in 9's c37 r35=> - 9 r3c8, r5c28.

You can solve the puzzle with only one other technique - a Skyscraper (also known as a Sashimi Finned X Wing). I'll use the Skyscraper way of thinking here.

Code: Select all

*---------------------------------------------*
| 16  136  8   | 345 7  459 | 2     369  34-6 |
| 79  5    47  | 6   39 2   | 378   1    3478 |
| 2  c36   479 | 34  1  8   |d3679 d367  5    |
|--------------+------------+-----------------|
| 16  1689 3   | 2   5  7   | 4     689  68   |
| 5   78   79  | 1   4  6   | 3789  378  2    |
| 4  b67   2   | 9   8  3   | 1     5   a67   |
|--------------+------------+-----------------|
| 3   2    1   | 457 6  45  | 78    478  9    |
| 79  4    5   | 8   39 1   | 367   2    367  |
| 8   79   6   | 347 2  49  | 5     347  1    |
*---------------------------------------------*

Grouped Skyscraper (6) r6c9 + 6c2 / r3c2 + r3c78 => - 6 r1c9

Code: Select all

*--------------------------------------------*
| 16 136  8   | 345  7  459 | 2    369 d34   |
| 79 5    47  | 6   a39 2   | 78-3 1   d3478 |
| 2  36   479 | 34   1  8   | 3679 367  5    |
|-------------+-------------+----------------|
| 16 1689 3   | 2    5  7   | 4    689  68   |
| 5  78   79  | 1    4  6   | 3789 378  2    |
| 4  67   2   | 9    8  3   | 1    5    67   |
|-------------+-------------+----------------|
| 3  2    1   | 457  6  45  | 78   478  9    |
| 79 4    5   | 8   b39 1   | 367  2   c367  |
| 8  79   6   | 347  2  49  | 5    347  1    |
*--------------------------------------------*

Grouped Skyscraper (3) r2c5 + 8c5 / r8c9 + r12c9 => - 3 r2c7

Code: Select all

*-------------------------------------------*
| 16  136  8   | 345 7  459 | 2   369  34   |
| 79  5    47  | 6   39 2   | 78  1    3478 |
| 2   36   479 | 34  1  8   | 369 367  5    |
|--------------+------------+---------------|
| 16  1689 3   | 2   5  7   | 4   689  68   |
| 5   78   79  | 1   4  6   | 39  378  2    |
| 4  a67   2   | 9   8  3   | 1   5   b67   |
|--------------+------------+---------------|
| 3   2    1   | 457 6  45  | 78  478  9    |
|d79  4    5   | 8   39 1   | 36  2   c367  |
| 8   9-7  6   | 347 2  49  | 5   347  1    |
*-------------------------------------------*

Skyscraper in cells a-b-c-d => - 7 r9c2. The puzzle should solve with singles from there.

In each of these Skyscraper moves, one of cells marked a or the 1 or 2 cells marked d must be true, so you can eliminate the Skyscraper digit from cells that can see both the a and d cells.

You can read about Skyscrapers here or Sashimi Finned XWings here.

Leren

[Leren]

Removed and transferred to the post above. Leren

[denis_berthier]

.
Only very elementary techniques are needed.

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whip[1]: c9n4{r2 .} ==> r3c8≠4, r1c8≠4
Resolution state after Singles and whips[1]:
   +----------------+----------------+----------------+
   ! 169  1369 8    ! 345  7    459  ! 2    369  346  !
   ! 79   5    479  ! 6    39   2    ! 3789 1    3478 !
   ! 2    3679 479  ! 34   1    8    ! 3679 3679 5    !
   +----------------+----------------+----------------+
   ! 169  1689 3    ! 2    5    7    ! 4    689  68   !
   ! 5    789  79   ! 1    4    6    ! 3789 3789 2    !
   ! 4    67   2    ! 9    8    3    ! 1    5    67   !
   +----------------+----------------+----------------+
   ! 3    2    1    ! 457  6    45   ! 78   478  9    !
   ! 79   4    5    ! 8    39   1    ! 367  2    367  !
   ! 8    79   6    ! 347  2    49   ! 5    347  1    !
   +----------------+----------------+----------------+
110 candidates.

Code: Select all

naked-pairs-in-a-column: c1{r2 r8}{n7 n9} ==> r4c1≠9, r1c1≠9
x-wing-in-columns: n9{c1 c5}{r2 r8} ==> r2c7≠9, r2c3≠9
x-wing-in-columns: n9{c3 c7}{r3 r5} ==> r5c8≠9, r5c2≠9, r3c8≠9, r3c2≠9
finned-x-wing-in-columns: n3{c5 c9}{r8 r2} ==> r2c7≠3
naked-pairs-in-a-column: c7{r2 r7}{n7 n8} ==> r8c7≠7, r5c7≠8, r5c7≠7, r3c7≠7
finned-x-wing-in-columns: n7{c1 c7}{r2 r8} ==> r8c9≠7
stte

This is how you can post a puzzle in grid form:

Code: Select all

     +-------+-------+-------+
     ! . . 8 ! . 7 . ! 2 . . !
     ! . 5 . ! 6 . 2 ! . 1 . !
     ! 2 . . ! . 1 8 ! . . 5 !
     +-------+-------+-------+
     ! . . 3 ! 2 5 7 ! 4 . . !
     ! 5 . . ! 1 4 6 ! . . 2 !
     ! 4 . 2 ! 9 8 3 ! 1 5 . !
     +-------+-------+-------+
     ! 3 2 1 ! . 6 . ! . . 9 !
     ! . 4 5 ! 8 . 1 ! . 2 . !
     ! 8 . 6 ! . 2 . ! 5 . 1 !
     +-------+-------+-------+

[RSW]

Another solution using a short chain as follows:
After basics:

Code: Select all

 +-------------+-------------+----------------+
 | 16 136  8   |  345 7  459 | 2    369  346  |
 | 79 5    479 |  6   39 2   | 3789 1    3478 |
 | 2  36   479 |  34  1  8   | 3679 3679 5    |
 +-------------+-------------+----------------+
 | 16 1689 3   |  2   5  7   | 4    689  68   |
 | 5  789  79  |  1   4  6   | 3789 3789 2    |
 | 4  67   2   |  9   8  3   | 1    5    67   |
 +-------------+-------------+----------------+
 | 3  2    1   |  457 6  45  | 78   478  9    |
 | 79 4    5   |  8  a39 1   | 367  2    367  |
 | 8  79   6   |ab347 2 a49  | 5   c37-4 1    |
 +-------------+-------------+----------------+


A chain involving an almost locked set in box 8
(4=397)b8p579 - (3)r9c4 = (3)r9c8 => -4r9c8
Then singles to the end.

[manofsteel520]

Thanks all for the helpful replies! Apologies for newbie formatting question - first post - appreciate your patience

I'm proud to say I had found the X-wings before posting! First time trying this technique and I was able to eliminate the 9s.

For those that pointed out the Finned X-wings (Leren, denis_berthier), I read up and I do understand the logic and conclusions. My main question is: how would I ever see this on my own? Say I chose 6s to review - if there are only two candidates in a row, I could keep an eye out for another row with two, and if they form a rectangle it's X-wing and if a "right trapezoid" it's Skyscraper. But for Grouped Skyscraper it sounds like I need to look out for two-candidate and three-candidate rows and see when they almost overlap? Any suggestions on a process I could use to look for this? (Do you typically use software? I tend to work from print - perhaps that's limiting my ability to see candidate patterns... maybe I should starting using software and input any printed puzzles I'm struggling with? If so, any suggestions on which software?)

Thanks again!

[manofsteel520]

Thanks all for the helpful replies! Apologies for newbie formatting question - first post - appreciate your patience

I'm proud to say I had found the X-wings before posting! First time trying this technique and I was able to eliminate the 9s.

For those that pointed out the Finned X-wings (Leren, denis_berthier), I read up and I do understand the logic and conclusions. My main question is: how would I ever see this on my own? Say I chose 6s to review - if there are only two candidates in a row, I could keep an eye out for another row with two, and if they form a rectangle it's X-wing and if a "right trapezoid" it's Skyscraper. But for Grouped Skyscraper it sounds like I need to look out for two-candidate and three-candidate rows and see when they almost overlap? Any suggestions on a process I could use to look for this? (Do you typically use software? I tend to work from print - perhaps that's limiting my ability to see candidate patterns... maybe I should starting using software and input any printed puzzles I'm struggling with? If so, any suggestions on which software?)

Thanks again!

[elisatems]

Thanks all for the helpful replies! Apologies for newbie formatting question - first post - appreciate your patience

I'm proud to say I had found the X-wings before posting! First time trying this technique and I was able to eliminate the 9s.

For those that pointed out the Finned X-wings (Leren, denis_berthier), I read up and I do understand the logic and conclusions. My main question is: how would I ever see this on my own? Say I chose 6s to review - if there are only two candidates in a row, I could keep an eye out for another row with two, and if they form a rectangle it's X-wing and if a "right trapezoid" it's Skyscraper. But for Grouped Skyscraper it sounds like I need to look out for two-candidate and three-candidate rows and see when they almost overlap? Any suggestions on a process I could use to look for this? (Do you typically use software? I tend to work from print - perhaps that's limiting my ability to see candidate patterns... maybe I should starting using software and input any printed puzzles I'm struggling with? If so, any suggestions on which software?)

Thanks again!

"Two candidates in a row" (or a column) is indeed something to watch out for to apply several of the solving strategies you mention - they're also called "conjugate pairs". X-Wings will always be a parallel pair of CPs. Even Swordfish will rarely have three parallel groups of three in a row or column - most often one or more of the base sets will lack one member, so CPs are again the thing to look out for when looking for any kind of "fish" (an X-Wing is the simplest kind of fish). Finned fish, like finned X-Wings are harder, but again, there will always be one CP involved, so the presence of a CP should alert you to the possibility of a straight or finned X-Wing.

BTW I solved your puzzle with only one X-Wing and a Finned X-Wing, the straight X-Wing in columns on 9 that I noticed after doing eliminations from the naked pair in c1 and the finned one on 3 (I think), also in columns. The only other "advanced" technique I needed was two 3-link X-Chains, one on 6 and the other on 7. (I don't use the terms skyscraper, 2-string kite, turbot fish since there are usually equivalent chains that you can construct out of the same two endpoints, and they might well be of different shapes.) Again, for those, conjugate pairs are your friend.