The New Sudoku Players' Forum

[shawntown]

Here’s the puzzle: https://imgur.com/a/55U8zVV

I keep getting stuck around here, puzzle after puzzle. Here’s my process (need advice on how to improve it and what I should do next):

1) Fill in obvious singles
2) pencil mark all pairs within the boxes
3) use basic logic to fill in as many cells as possible
4) pencil mark everything else
5) use the basic techniques, like claiming, pointing, hidden doubles, hidden triples, hidden quadruples to eliminate candidates
6) start looking for X-Wings, finned X-Wings, Swordfish, Skyscrapers, and XY Chains
7) if at this point, the puzzle hasn’t solved itself, I go back and double check all my pencil marks
8) get stuck (if I haven’t solved it by now)…what’s next?

[Leren]

9..238.7....6....8.3.1........829.....2761.9..69354..7...5167..6..4825...5.973..4

It's a tough finish for a commercial site puzzle and you have done pretty well to get where you are. You will have to use some AIC's at least and some Unique Rectangles might also help. Try the Hodoku site here.

Leren

[denis_berthier]

.
I can't see any problem with your process. The only thing is, when you try to solve harder puzzles, you need more powerful techniques - i.e. in general some kind of chains
(Also: when you post a puzzle, instead of putting an external link, could you use one of the standard forms below (puzzle or PM)?

Starting from the original puzzle:

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     +-------+-------+-------+
     ! 9 . . ! 2 3 8 ! . 7 . !
     ! . . . ! 6 . . ! . . 8 !
     ! . 3 . ! 1 . . ! . . . !
     +-------+-------+-------+
     ! . . . ! 8 2 9 ! . . . !
     ! . . 2 ! 7 6 1 ! . 9 . !
     ! . 6 9 ! 3 5 4 ! . . 7 !
     +-------+-------+-------+
     ! . . . ! 5 1 6 ! 7 . . !
     ! 6 . . ! 4 8 2 ! 5 . . !
     ! . 5 . ! 9 7 3 ! . . 4 !
     +-------+-------+-------+
9..238.7....6....8.3.1........829.....2761.9..69354..7...5167..6..4825...5.973..4
SER = 8.4, W = 5, tW = 5, Z = 8

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whip[1]: c7n9{r3 .} ==> r3c9≠9
Resolution state after Singles and whips[1]:
   +-------------------+-------------------+-------------------+
   ! 9     14    1456  ! 2     3     8     ! 146   7     156   !
   ! 12457 1247  1457  ! 6     49    57    ! 12349 12345 8     !
   ! 24578 3     45678 ! 1     49    57    ! 2469  2456  256   !
   +-------------------+-------------------+-------------------+
   ! 13457 147   13457 ! 8     2     9     ! 1346  13456 1356  !
   ! 3458  48    2     ! 7     6     1     ! 348   9     35    !
   ! 18    6     9     ! 3     5     4     ! 128   128   7     !
   +-------------------+-------------------+-------------------+
   ! 2348  2489  348   ! 5     1     6     ! 7     238   239   !
   ! 6     179   137   ! 4     8     2     ! 5     13    139   !
   ! 128   5     18    ! 9     7     3     ! 1268  1268  4     !
   +-------------------+-------------------+-------------------+
150 candidates.

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finned-x-wing-in-columns: n2{c9 c2}{r7 r3} ==> r3c1≠2
whip[1]: r3n2{c9 .} ==> r2c7≠2, r2c8≠2
finned-x-wing-in-rows: n5{r5 r1}{c9 c1} ==> r3c1≠5, r2c1≠5
whip[1]: c1n5{r5 .} ==> r4c3≠5
   +-------------------+-------------------+-------------------+
   ! 9     14    1456  ! 2     3     8     ! 146   7     156   !
   ! 1247  1247  1457  ! 6     49    57    ! 1349  1345  8     !
   ! 478   3     45678 ! 1     49    57    ! 2469  2456  256   !
   +-------------------+-------------------+-------------------+
   ! 13457 147   1347  ! 8     2     9     ! 1346  13456 1356  !
   ! 3458  48    2     ! 7     6     1     ! 348   9     35    !
   ! 18    6     9     ! 3     5     4     ! 128   128   7     !
   +-------------------+-------------------+-------------------+
   ! 2348  2489  348   ! 5     1     6     ! 7     238   239   !
   ! 6     179   137   ! 4     8     2     ! 5     13    139   !
   ! 128   5     18    ! 9     7     3     ! 1268  1268  4     !
   +-------------------+-------------------+-------------------+

At this point, the only difference with your PM is candidate n1r2c1. It can be eliminated by a bivalue-chain[3] that also eliminates n1r4c2.

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biv-chain[3]: r1c2{n1 n4} - r5c2{n4 n8} - r6c1{n8 n1} ==> r2c1≠1, r4c2≠1

You can now apply two more bivalue-chains:

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biv-chain[3]: r6c1{n1 n8} - b1n8{r3c1 r3c3} - r9c3{n8 n1} ==> r4c3≠1, r9c1≠1
biv-chain[4]: r3n8{c1 c3} - b1n6{r3c3 r1c3} - r1n5{c3 c9} - r5n5{c9 c1} ==> r5c1≠8
Resolution state RS2

But you need more than bivalue-chains if you want to go farther than RS2.
Here is an idea of what you can get if you use the full power of whips (and the simplest-first strategy):

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t-whip[4]: r9c1{n2 n8} - r7n8{c3 c8} - r6n8{c8 c7} - r6n2{c7 .} ==> r9c8≠2
z-chain[5]: c3n6{r3 r1} - c3n5{r1 r2} - c6n5{r2 r3} - r3n7{c6 c1} - r3n8{c1 .} ==> r3c3≠4
t-whip[5]: r3n8{c1 c3} - c3n6{r3 r1} - r1n5{c3 c9} - r3n5{c9 c6} - r3n7{c6 .} ==> r3c1≠4
biv-chain[3]: r3c1{n7 n8} - r9c1{n8 n2} - b1n2{r2c1 r2c2} ==> r2c2≠7
t-whip[5]: c3n6{r1 r3} - r3n8{c3 c1} - r3n7{c1 c6} - r2c6{n7 n5} - c3n5{r2 .} ==> r1c3≠1, r1c3≠4
finned-x-wing-in-rows: n4{r1 r5}{c7 c2} ==> r4c2≠4
singles ==> r4c2=7, r8c3=7
whip[1]: r8n3{c9 .} ==> r7c8≠3, r7c9≠3
biv-chain[4]: r6c1{n1 n8} - c2n8{r5 r7} - r7c8{n8 n2} - b6n2{r6c8 r6c7} ==> r6c7≠1
t-whip[4]: r7c8{n2 n8} - c2n8{r7 r5} - r6c1{n8 n1} - r6c8{n1 .} ==> r3c8≠2
t-whip[4]: r5c9{n5 n3} - c7n3{r5 r2} - c7n9{r2 r3} - r3n2{c7 .} ==> r3c9≠5
biv-chain[5]: r8n3{c9 c8} - b3n3{r2c8 r2c7} - c7n9{r2 r3} - r3n2{c7 c9} - r7c9{n2 n9} ==> r8c9≠9
singles ==> r7c9=9, r8c2=9, r9c3=1, r3c9=2
biv-chain[3]: r1n4{c7 c2} - r2c3{n4 n5} - r1c3{n5 n6} ==> r1c7≠6
naked-pairs-in-a-row: r1{c2 c7}{n1 n4} ==> r1c9≠1
biv-chain[4]: r5c9{n3 n5} - r1n5{c9 c3} - r2c3{n5 n4} - r4c3{n4 n3} ==> r4c7≠3, r4c8≠3, r4c9≠3, r5c1≠3
biv-chain[4]: r1c9{n6 n5} - r5c9{n5 n3} - c7n3{r5 r2} - b3n9{r2c7 r3c7} ==> r3c7≠6
naked-pairs-in-a-row: r3{c5 c7}{n4 n9} ==> r3c8≠4
naked-pairs-in-a-block: b3{r1c9 r3c8}{n5 n6} ==> r2c8≠5
biv-chain[3]: c3n8{r7 r3} - r3n6{c3 c8} - r9c8{n6 n8} ==> r9c1≠8, r7c8≠8
stte

The solution shows only z-chains and t-whips are needed.
If you prefer to use only reversible chains with no embedded Subsets, you'll find a solution in Z8 (simpler but longer chains):

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z-chain[5]: r9c1{n2 n8} - r6c1{n8 n1} - r6c8{n1 n8} - b9n8{r7c8 r9c7} - r9n6{c7 .} ==> r9c8≠2
z-chain[5]: c3n6{r3 r1} - c3n5{r1 r2} - c6n5{r2 r3} - r3n7{c6 c1} - r3n8{c1 .} ==> r3c3≠4
z-chain[7]: r9c3{n1 n8} - c2n8{r7 r5} - c7n8{r5 r6} - c7n2{r6 r3} - c7n9{r3 r2} - r2n3{c7 c8} - r8c8{n3 .} ==> r9c7≠1
z-chain[4]: r9n1{c3 c8} - r9n6{c8 c7} - r1n6{c7 c9} - r1n5{c9 .} ==> r1c3≠1
z-chain[6]: r8c8{n1 n3} - r2n3{c8 c7} - c7n1{r2 r1} - r1c2{n1 n4} - r5c2{n4 n8} - r6c1{n8 .} ==> r6c8≠1
z-chain[8]: c2n2{r2 r7} - r9c1{n2 n8} - r3n8{c1 c3} - c3n6{r3 r1} - r1n5{c3 c9} - r5n5{c9 c1} - r5n4{c1 c7} - r1n4{c7 .} ==> r2c2≠4
z-chain[8]: r6n2{c7 c8} - b6n8{r6c8 r5c7} - c2n8{r5 r7} - r7n9{c2 c9} - c9n2{r7 r3} - c7n2{r3 r9} - r9c1{n2 n8} - r6c1{n8 .} ==> r6c7≠1
singles ==> r6c1=1, r5c2=8
finned-x-wing-in-rows: n4{r5 r1}{c7 c1} ==> r3c1≠4, r2c1≠4
naked-triplets-in-a-column: c1{r2 r3 r9}{n2 n7 n8} ==> r7c1≠8, r7c1≠2, r4c1≠7
whip[1]: c1n7{r3 .} ==> r2c2≠7, r2c3≠7, r3c3≠7
biv-chain[5]: r1n5{c9 c3} - b1n6{r1c3 r3c3} - b1n8{r3c3 r3c1} - r3n7{c1 c6} - b2n5{r3c6 r2c6} ==> r2c8≠5
z-chain[6]: c3n6{r1 r3} - c3n5{r3 r2} - r2c6{n5 n7} - r2c1{n7 n2} - r2c2{n2 n1} - r1c2{n1 .} ==> r1c3≠4
finned-x-wing-in-rows: n4{r1 r5}{c7 c2} ==> r4c2≠4
singles ==> r4c2=7, r8c3=7
whip[1]: r8n3{c9 .} ==> r7c8≠3, r7c9≠3
naked-pairs-in-a-column: c8{r6 r7}{n2 n8} ==> r9c8≠8, r3c8≠2
z-chain[4]: r2n3{c8 c7} - r5c7{n3 n4} - r1n4{c7 c2} - r1n1{c2 .} ==> r2c8≠1
biv-chain[4]: r2c8{n4 n3} - r8n3{c8 c9} - r5c9{n3 n5} - c8n5{r4 r3} ==> r3c8≠4
hidden-pairs-in-a-row: r3{n4 n9}{c5 c7} ==> r3c7≠6, r3c7≠2
stte

However, you can also cdecide you don't want to use chains with z-candidates.
Then you'll get a solution in tW5:

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t-whip[4]: r9c1{n2 n8} - r7n8{c3 c8} - r6n8{c8 c7} - r6n2{c7 .} ==> r9c8≠2
t-whip[5]: r3n8{c1 c3} - c3n6{r3 r1} - r1n5{c3 c9} - r3n5{c9 c6} - r3n7{c6 .} ==> r3c1≠4
biv-chain[3]: r3c1{n7 n8} - r9c1{n8 n2} - b1n2{r2c1 r2c2} ==> r2c2≠7
t-whip[5]: c3n6{r1 r3} - r3n8{c3 c1} - r3n7{c1 c6} - r2c6{n7 n5} - c3n5{r2 .} ==> r1c3≠1, r1c3≠4
finned-x-wing-in-rows: n4{r1 r5}{c7 c2} ==> r4c2≠4
singles ==> r4c2=7, r8c3=7
whip[1]: r8n3{c9 .} ==> r7c8≠3, r7c9≠3
biv-chain[4]: r6c1{n1 n8} - c2n8{r5 r7} - r7c8{n8 n2} - b6n2{r6c8 r6c7} ==> r6c7≠1
t-whip[4]: r7c8{n2 n8} - c2n8{r7 r5} - r6c1{n8 n1} - r6c8{n1 .} ==> r3c8≠2
t-whip[4]: r5c9{n5 n3} - c7n3{r5 r2} - c7n9{r2 r3} - r3n2{c7 .} ==> r3c9≠5
biv-chain[5]: r8n3{c9 c8} - b3n3{r2c8 r2c7} - c7n9{r2 r3} - r3n2{c7 c9} - r7c9{n2 n9} ==> r8c9≠9
singles ==> r7c9=9, r8c2=9, r9c3=1, r3c9=2
biv-chain[3]: r1n4{c7 c2} - r2c3{n4 n5} - r1c3{n5 n6} ==> r1c7≠6
naked-pairs-in-a-row: r1{c2 c7}{n1 n4} ==> r1c9≠1
biv-chain[4]: r5c9{n3 n5} - r1n5{c9 c3} - r2c3{n5 n4} - r4c3{n4 n3} ==> r4c7≠3, r4c8≠3, r4c9≠3, r5c1≠3
biv-chain[4]: r1c9{n6 n5} - r5c9{n5 n3} - c7n3{r5 r2} - b3n9{r2c7 r3c7} ==> r3c7≠6
naked-pairs-in-a-row: r3{c5 c7}{n4 n9} ==> r3c8≠4, r3c3≠4
naked-pairs-in-a-block: b3{r1c9 r3c8}{n5 n6} ==> r2c8≠5
biv-chain[3]: c3n8{r7 r3} - r3n6{c3 c8} - r9c8{n6 n8} ==> r9c1≠8, r7c8≠8
stte

[shawntown]

Thanks. I’ll look up the techniques you both named to try and learn them. I don’t know how to read Sudoku notation (that’s why I post a picture of it using IMGUR). So like, the long string of numbers and dots you guys typed is gibberish to me. Guess I’ve still got a long way to go! I thought I was getting good at Sudoku because I can do Easy difficulty without any pencil marks, and I can do Expert difficulty on the Sudoku.com site (keep getting stuck on Evil, their highest difficulty level, though). But since most everything you both typed in your replies is total Greek to me, I’m thinking I’m still a beginner. But I appreciate your help!

[denis_berthier]

I don’t know how to read Sudoku notation (that’s why I post a picture of it using IMGUR). So like, the long string of numbers and dots you guys typed is gibberish to me.

Quite easy: start with an empty string; take each cell one by one (from top to bottom and from left to right); add a dot to the string if there is no given in that cell; otherwise add the given.
As for the other 2D representations, they speak for themselves.

Guess I’ve still got a long way to go! I thought I was getting good at Sudoku because I can do Easy difficulty without any pencil marks, and I can do Expert difficulty on the Sudoku.com site (keep getting stuck on Evil, their highest difficulty level, though). But since most everything you both typed in your replies is total Greek to me, I’m thinking I’m still a beginner. But I appreciate your help!

Solving without pencilmarks is a very good exercise, but it doesn't allow to solve puzzles as hard as if use you them.

[Steerpike58]

Quite easy: start with an empty string; take each cell one by one (from top to bottom and from left to right); add a dot to the string if there is no given in that cell; otherwise add the given.

I'm a beginner, just learning, but the bolded part above seems wrong - 'top to bottom and from left to right' sounds like you start with R1 C1, then R1 C2, R1 C3, R1 C4, etc and then move on to R2 C1, R2 C2, R2 C3, etc. Whereas in fact, you go 'left to right' first, then 'top to bottom'. To put it another (less ambiguous, perhaps) way, you lay down the entire first row (columns 1-9), then go to 2nd row, and lay down columns 1-9, then row 3 ... etc.

[denis_berthier]

Quite easy: start with an empty string; take each cell one by one (from top to bottom and from left to right); add a dot to the string if there is no given in that cell; otherwise add the given.

I'm a beginner, just learning, but the bolded part above seems wrong - 'top to bottom and from left to right' sounds like you start with R1 C1, then R1 C2, R1 C3, R1 C4, etc and then move on to R2 C1, R2 C2, R2 C3, etc. Whereas in fact, you go 'left to right' first, then 'top to bottom'. To put it another (less ambiguous, perhaps) way, you lay down the entire first row (columns 1-9), then go to 2nd row, and lay down columns 1-9, then row 3 ... etc.

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for r = 1 to 9
    for c = 1 to 9
        ...