The New Sudoku Players' Forum

[urhegyi]

A member on a sudoku group asked for harder sudokus. So I genererated one myself. Advice on solving appreciated.

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007020090080010000000004628039070004800000000050900000200007060000040300000500019

nr1.png (15.34 KiB) Viewed 980 times

[denis_berthier]

SER 7.8

***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = W+SFin
*** Using CLIPS 6.32-r779
***********************************************************************************************
9 singles
163 candidates, 778 csp-links and 778 links. Density = 5.89%
whip[1]: c8n3{r6 .} ==> r6c9 ≠ 3, r5c9 ≠ 3
whip[1]: c8n5{r5 .} ==> r4c7 ≠ 5
whip[1]: r3n1{c3 .} ==> r1c2 ≠ 1, r1c1 ≠ 1
finned-x-wing-in-rows: n2{r9 r4}{c7 c6} ==> r6c6 ≠ 2
whip[1]: r6n2{c9 .} ==> r4c7 ≠ 2
finned-swordfish-in-rows: n6{r2 r4 r8}{c4 c6 c1} ==> r9c1 ≠ 6

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RESOLUTION STATE AT THIS POINT:
   3456      46        7         368       2         3568      15        9         13       
   3569      8         2         36        1         3569      57        4         37       
   1359      19        135       7         359       4         6         2         8         
   16        3         9         1268      7         12568     18        58        4         
   8         2         16        4         356       1356      9         357       167       
   7         5         4         9         368       1368      128       38        126       
   2         149       138       138       389       7         48        6         5         
   1569      1679      1568      1268      4         12689     3         78        27       
   34        467       368       5         368       2368      2478      1         9         

Nothing noticeable after that, except that it doesn't use whips even though they were active:

Hidden Text: Show

z-chain[3]: c4n2{r4 r8} - c9n2{r8 r6} - r6n6{c9 .} ==> r4c4 ≠ 6
finned-x-wing-in-rows: n6{r4 r2}{c1 c6} ==> r1c6 ≠ 6
t-whip-cn[3]: c3n6{r9 r5} - c9n6{r5 r6} - c5n6{r6 .} ==> r9c2 ≠ 6
t-whip[3]: r6c8{n3 n8} - r4c7{n8 n1} - r6n1{c9 .} ==> r6c6 ≠ 3
biv-chain[4]: r9c1{n3 n4} - r9c2{n4 n7} - c7n7{r9 r2} - r2c9{n7 n3} ==> r2c1 ≠ 3
biv-chain[4]: r1n4{c1 c2} - r9c2{n4 n7} - c7n7{r9 r2} - b3n5{r2c7 r1c7} ==> r1c1 ≠ 5
z-chain[4]: r1c2{n6 n4} - r1c1{n4 n3} - c9n3{r1 r2} - r2c4{n3 .} ==> r2c1 ≠ 6
whip[1]: r2n6{c6 .} ==> r1c4 ≠ 6
hidden-pairs-in-a-row: r1{n4 n6}{c1 c2} ==> r1c1 ≠ 3
whip[1]: b1n3{r3c3 .} ==> r3c5 ≠ 3
t-whip[4]: r5c3{n1 n6} - c9n6{r5 r6} - r6n2{c9 c7} - r6n1{c7 .} ==> r5c6 ≠ 1
t-whip[4]: r9c1{n3 n4} - r1c1{n4 n6} - r4n6{c1 c6} - c5n6{r6 .} ==> r9c5 ≠ 3
biv-chain[5]: c3n5{r8 r3} - b1n3{r3c3 r3c1} - r9c1{n3 n4} - r1c1{n4 n6} - b4n6{r4c1 r5c3} ==> r8c3 ≠ 6
finned-x-wing-in-columns: n6{c3 c5}{r9 r5} ==> r5c6 ≠ 6
biv-chain[2]: c3n6{r9 r5} - r4n6{c1 c6} ==> r9c6 ≠ 6
swordfish-in-columns: n6{c3 c5 c9}{r5 r9 r6} ==> r6c6 ≠ 6
biv-chain[3]: r5c6{n3 n5} - c5n5{r5 r3} - b2n9{r3c5 r2c6} ==> r2c6 ≠ 3
biv-chain[4]: r4c7{n8 n1} - r5n1{c9 c3} - c3n6{r5 r9} - r9c5{n6 n8} ==> r9c7 ≠ 8
biv-chain[4]: r9n2{c6 c7} - r6n2{c7 c9} - r6n6{c9 c5} - r9c5{n6 n8} ==> r9c6 ≠ 8
hidden-pairs-in-a-row: r9{n6 n8}{c3 c5} ==> r9c3 ≠ 3
biv-chain[4]: c5n5{r3 r5} - r5c6{n5 n3} - r9n3{c6 c1} - b1n3{r3c1 r3c3} ==> r3c3 ≠ 5
hidden-single-in-a-column ==> r8c3 = 5
finned-swordfish-in-columns: n8{c3 c5 c7}{r7 r9 r6} ==> r6c8 ≠ 8
naked-single ==> r6c8 = 3
naked-pairs-in-a-column: c5{r6 r9}{n6 n8} ==> r7c5 ≠ 8, r5c5 ≠ 6
naked-pairs-in-a-block: b5{r5c5 r5c6}{n3 n5} ==> r4c6 ≠ 5
singles ==> r4c8 = 5, r5c8 = 7, r8c8 = 8, r7c7 = 4
naked-pairs-in-a-column: c2{r3 r7}{n1 n9} ==> r8c2 ≠ 9, r8c2 ≠ 1
x-wing-in-columns: n9{c2 c5}{r3 r7} ==> r3c1 ≠ 9
biv-chain-rc[4]: r5c6{n5 n3} - r9c6{n3 n2} - r9c7{n2 n7} - r2c7{n7 n5} ==> r2c6 ≠ 5
biv-chain[3]: c4n6{r8 r2} - r2c6{n6 n9} - c1n9{r2 r8} ==> r8c1 ≠ 6
naked-pairs-in-a-block: b7{r7c2 r8c1}{n1 n9} ==> r7c3 ≠ 1
biv-chain[4]: c9n2{r6 r8} - r8n7{c9 c2} - b7n6{r8c2 r9c3} - c5n6{r9 r6} ==> r6c9 ≠ 6
stte

.

[AnotherLife]

A member on a sudoku group asked for harder sudokus. So I genererated one myself. Advice on solving appreciated.

I have no doubt that this puzzle can be solved by a programme but is it possible to solve this one by human means? I made use of this solver https://www.sudokuwiki.org/sudoku.htm and tried to read about Grouped X-Cycles and Alternating Inference Chains but I think it's very hard to apply these methods in practice.

[denis_berthier]

A member on a sudoku group asked for harder sudokus. So I genererated one myself. Advice on solving appreciated.

I have no doubt that this puzzle can be solved by a programme but is it possible to solve this one by human means? I made use of this solver https://www.sudokuwiki.org/sudoku.htm and tried to read about Grouped X-Cycles and Alternating Inference Chains but I think it's very hard to apply these methods in practice.

My solution is doable by a human solver. It involves only short chains, probably much shorter than any AIC based solution.
If you don't want to use chains of any kind, you'd better play with simpler puzzles.

[AnotherLife]

SER 7.8
z-chain[3]: c4n2{r4 r8} - c9n2{r8 r6} - r6n6{c9 .} ==> r4c4 ≠ 6
.

Could you explain what you mean by Z-Chains? Where can I read about the terms you use?

[denis_berthier]

A z-chain is a generalisation of a bivalue-chain with additional candidates linked to the target (z).

For all the formal definitions, you can start here: http://forum.enjoysudoku.com/pattern-based-constraint-satisfaction-2nd-edition-t32567.html
All the references mentioned there are available on researchgate: https://www.researchgate.net/profile/Denis_Berthier

However, for understanding the main chains, it may be easier to start by reading the part of the User Manual for CSP-Rules that provide graphical representations for them: https://www.researchgate.net/publication/343737968_Basic_User_Manual_for_CSP-Rules-V21

The software that implements all this is available here: https://github.com/denis-berthier/CSP-Rules-V2.1. By experimenting with it, you can see the various chains in action.

[eleven]

Where is SpAce ???

No good manual solver i know of uses Denis' chains. Don't waste your time, AnotherLife.

The puzzle is solvable manually, preferable with methods often used here. But you would need time to practice them up to AIC chains, and you would need a lot of patience for each puzzle of that difficulty.
If you want to see how to solve this one, e.g. check out Hodoku.

[ghfick]

I am now appreciating the videos of Sudoku Swami [SS]. At the SS website [ sudokuswami.com ] there are several videos on AICs both Type I and Type II. Many hours of material. Good to start with his introductory videos first. Worth it though.
As eleven says, there are AICs in this puzzle. So much fun!

[denis_berthier]

Eleven waking up for his usual rantings about my chains. No much surprise.
About AICs, how long has it been since anyone posted an AIC solution of any hard puzzle? I'm curious to see a full one for this puzzle.

[yzfwsf]

This is the complete solution path of my solver for your reference.

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Hidden Single: 9 in b6 => r5c7=9
Hidden Single: 4 in b5 => r5c4=4
Hidden Single: 2 in b1 => r2c3=2
Hidden Single: 2 in b4 => r5c2=2
Hidden Single: 7 in b4 => r6c1=7
Hidden Single: 4 in b4 => r6c3=4
Hidden Single: 4 in c8 => r2c8=4
Hidden Single: 7 in r3 => r3c4=7
Naked Single: r7c9=5
Locked Candidates 1 (Pointing): 1 in b3 => r1c1<>1,r1c2<>1
Locked Candidates 1 (Pointing): 5 in b3 => r4c7<>5
Locked Candidates 2 (Claiming): 3 in c8 => r5c9<>3,r6c9<>3
Skyscraper : 2 in r4c4,r6c9 connected by r8c49 => r4c7,r6c6 <> 2
Grouped 2-String Kite: 6 in r4c1,r9c5 connected by r4c46,r56c5 => r9c1 <> 6
Finned Swordfish:6c359\r569 fr8c3 => r9c2<>6
AIC Type2:4r1c1 = r1c2 - (4=7)r9c2 - r9c7 = (7-5)r2c7 = 5r1c7 => r1c1<>5
AIC Type1:6r1c2 = (6-7)r8c2 = r9c2 - r9c7 = r2c7 - (7=3)r2c9 - (3=6)r2c4 => r1c4<>6 r1c6<>6 r2c1<>6
Hidden Pair: 46 in r1c1,r1c2 => r1c1<>3
AIC Type2:(6=3)r2c4 - (3=7)r2c9 - (7=2)r8c9 - r8c4 = 2r4c4 => r4c4<>6
AIC Type1:(3=7)r2c9 - r2c7 = r9c7 - (7=4)r9c2 - (4=3)r9c1 => r2c1<>3
Locked Candidates 1 (Pointing): 3 in b1 => r3c5<>3
AIC Type2:6r5c3 = r4c1 - (6=4)r1c1 - (4=3)r9c1 - r3c1 = (3-5)r3c3 = 5r8c3 => r8c3<>6
Swordfish:6c359\r569  => r569c6<>6
AIC Type2:(3=4)r9c1 - (4=6)r1c1 - r4c1 = r5c3 - r9c3 = 6r9c5 => r9c5<>3
AIC Type1:(8=1)r4c7 - (1=6)r4c1 - r5c3 = r9c3 - (6=8)r9c5 => r9c7<>8
AIC Type2:5r8c3 = (5-3)r3c3 = r3c1 - (3=4)r9c1 - r9c7 = (4-8)r7c7 = 8r8c8 => r8c3<>8
Grouped 2-String Kite: 8 in r6c5,r8c8 connected by r8c46,r79c5 => r6c8 <> 8
Naked Single: r6c8=3
Naked Pair: in r6c5,r9c5 => r5c5<>6,r7c5<>8,
AIC Type2:9r2c6 = r8c6 - (9=3)r7c5 - r5c5 = 3r5c6 => r2c6<>3
AIC Type2:(1=3)r1c9 - r2c9 = (3-6)r2c4 = r8c4 - r9c5 = r6c5 - r6c9 = 6r5c9 => r5c9<>1
XY-Chain:(5=9)r3c5 - (9=3)r7c5 - (3=5)r5c5 - (5=7)r5c8 - (7=6)r5c9 - (6=1)r5c3 - (1=5)r8c3 => r3c3<>5
Hidden Single: 5 in c3 => r8c3=5
XY-Chain:(3=1)r3c3 - (1=6)r5c3 - (6=7)r5c9 - (7=5)r5c8 - (5=8)r4c8 - (8=1)r4c7 - (1=6)r4c1 - (6=4)r1c1 - (4=3)r9c1 => r3c1<>3 r7c3<>3 r9c3<>3
Hidden Single: 3 in b7 => r9c1=3
Hidden Single: 3 in b1 => r3c3=3
Hidden Single: 4 in c1 => r1c1=4
Hidden Single: 6 in b1 => r1c2=6
Naked Pair: in r9c3,r9c5 => r9c6<>8,
Naked Single: r9c6=2
Hidden Single: 2 in b9 => r8c9=2
Hidden Single: 2 in b6 => r6c7=2
Hidden Single: 2 in b5 => r4c4=2
Locked Candidates 1 (Pointing): 8 in b6 => r4c6<>8
Locked Candidates 2 (Claiming): 1 in c4 => r8c6<>1
W-Wing: 16 in r4c1,r6c9 connected by 6r5 => r4c7<>1
Hidden Single: 1 in b6 => r6c9=1
Hidden Single: 6 in b6 => r5c9=6
Hidden Single: 7 in b6 => r5c8=7
Hidden Single: 7 in b9 => r9c7=7
Hidden Single: 4 in b9 => r7c7=4
Full House: r8c8=8
Full House: r4c8=5
Full House: r4c7=8
Hidden Single: 4 in b7 => r9c2=4
Hidden Single: 7 in b7 => r8c2=7
Hidden Single: 6 in b4 => r4c1=6
Full House: r4c6=1
Full House: r5c3=1
Hidden Single: 6 in b7 => r9c3=6
Full House: r9c5=8
Full House: r7c3=8
Hidden Single: 6 in b5 => r6c5=6
Full House: r6c6=8
Hidden Single: 1 in b3 => r1c7=1
Full House: r2c7=5
Hidden Single: 7 in b3 => r2c9=7
Full House: r1c9=3
Hidden Single: 3 in b2 => r2c4=3
Hidden Single: 3 in b8 => r7c5=3
Hidden Single: 9 in b8 => r8c6=9
Hidden Single: 6 in b8 => r8c4=6
Full House: r8c1=1
Full House: r7c2=9
Full House: r7c4=1
Full House: r3c2=1
Full House: r1c4=8
Full House: r1c6=5
Hidden Single: 3 in b5 => r5c6=3
Full House: r5c5=5
Full House: r3c5=9
Full House: r3c1=5
Full House: r2c1=9
Full House: r2c6=6


[denis_berthier]

This is the complete solution path of my solver for your reference.

As far as I can see, your longest chain, an xy-chain has length 9. My solution uses chains of length ≤ 5.

[yzfwsf]

As far as I can see, your longest chain, an xy-chain has length 9. My solution uses chains of length ≤ 5.

Because your chain only lists strong links, and my solver lists strong links + weak links. If you want to compare the length, then my chain length needs to be divided by 2 and then compared with you. And when I code Did not deliberately limit the chain length, because I use breadth first algorithm.

[denis_berthier]

As far as I can see, your longest chain, an xy-chain has length 9. My solution uses chains of length ≤ 5.

Because your chain only lists strong links, and my solver lists strong links + weak links. If you want to compare the length, then my chain length needs to be divided by 2 and then compared with you. And when I code Did not deliberately limit the chain length, because I use breadth first algorithm.

You can check: I counted only the "strong links" in your xy-chain; it's easy to count, it's the number of = signs. I get 9.

[yzfwsf]

You are right.As I said in the previous post, I have no control over the chain length. At the PM when the length of the XY-Chain is 9 that you mentioned, if you use Find all possible steps, my solver can find the XY-Chain with a shorter chain length.

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XY-Chain:(6=1)r4c1 - (1=8)r4c7 - (8=5)r4c8 - (5=7)r5c8 - (7=6)r5c9 => r5c3<>6

[denis_berthier]

You are right.As I said in the previous post, I have no control over the chain length. At the PM when the length of the XY-Chain is 9 that you mentioned, if you use Find all possible steps, my solver can find the XY-Chain with a shorter chain length.

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XY-Chain:(6=1)r4c1 - (1=8)r4c7 - (8=5)r4c8 - (5=7)r5c8 - (7=6)r5c9 => r5c3<>6

OK. I believe you. As you know, as I'm on a Mac, I can't use your software.

What about the previous xy-chain, of length 7?

XY-Chain:(5=9)r3c5 - (9=3)r7c5 - (3=5)r5c5 - (5=7)r5c8 - (7=6)r5c9 - (6=1)r5c3 - (1=5)r8c3 => r3c3<>5