The New Sudoku Players' Forum

[ghfick]

[yzfwsf]How did you use your solver to display the solution path? I cannot copy and paste from the solution path window. Is there a set of keystrokes to save the path? May I suggest a Copy Path button be added to the Edit pull down ?

[yzfwsf and Denis] For me, the length of the chain is not an issue when 'human' solving. Often, I will take a piece of an existing chain [like a 2 string kite] and then look for links to extend the chain. Sometimes, two pieces can be joined. It is very helpful with YZF_Sudoku to be able to manually build chains.

[Denis] I am here referring to [naked] chains and not the hidden chains developed through the 4 grids [rc, rn, cn, bn]. I am still a beginner with hidden chains but it does appear that chain length might more relevant with hidden chains.

[Denis] One can use wine with older Mac OSs. Wine enables one to run YZF_Sudoku on a Mac. For this reason alone, I have not 'upgraded' my Mac to the most recent OS. OS 10.11 continues to be very stable and flexible [for me]

[yzfwsf]

[yzfwsf]How did you use your solver to display the solution path? I cannot copy and paste from the solution path window. Is there a set of keystrokes to save the path? May I suggest a Copy Path button be added to the Edit pull down ?

The solution path window has a Right click menu named "Copy Solution Path".

[denis_berthier]

For me, the length of the chain is not an issue when 'human' solving.

But we were not talking of human solving. yzfwsf posted the path proposed by his solver. I find it highly wrong that a solver would propose a chain[9] when a chain[5] is available.
What I think is, like many of the available "solvers", yzfwsf is interface-based. It's not designed as a full-fledged real solver but as a user helping system.

One can use wine with older Mac OSs. Wine enables one to run YZF_Sudoku on a Mac. For this reason alone, I have not 'upgraded' my Mac to the most recent OS. OS 10.11 continues to be very stable and flexible [for me]

The incompatibility with Wine dates back to the end of support for 32-bit, i.e. now almost 3 years ago (but announced almost 6 years ago). No serious developer can now invoke Wine for compatibility (yzfwsf no longer does it).
Not updating your Mac is your choice; you miss all the safety updates. My choice is different. I always update as soon as reasonably possible, i.e. as soon as a few fanboys, or guinea pigs if you prefer, have tested the new version.

[ghfick]

YZF_Sudoku displays a 'default' solution path. Using this solver, at any step, you can display all of the steps available. This 'All Possible Steps' option is like HoDoKu. With the puzzle being considered in this thread, after the exclusion based on the Finned Swordfish, there are five AICs available : 2 Type Is and 3 Type IIs. Lengths all 7+ links. There are also numerous ALS steps, Death Blossoms and Krakens listed. After the next listed step, there are six AICs available. I am unsure how the default path is determined by YZF. As I said, chain length is one issue but not the only one. For example, if a particular chain gives three exclusions, should it be listed before a chain that gives only one exclusion?
I continue to follow the advances with Wine. I see that Wine 6.0 has just been released. I would surmise that it is only a matter of time before Wine works with newer Mac OSs. Currently Wine runs on Mac OSs up to 10.14. My aging Mac might not like the 'newest' OS anyhow. I do know that the Wine developers are more focussed on Linux. I am not savvy about 32 bit versus 64 bit. This may be a matter for yzfwsf moving forward.

[AnotherLife]

I have not seen an understandable solution of this puzzle so far, and it was just a competition between computer programmes. I have made an attempt to work out my own solution to this sudoku with similar methods that can be easily described graphically. The solution is split into some logical steps, and every method except for Singles is accompanied by an image.

Among the methods of 'extreme' category I have applied only Finned Swordfish and Death Blossom with two petals, which is an easy variant of Almost Locked Set XY-Wing with a bivalue cell as a linking set. That is, there are no AIC's, Z-Chains, T-Whips, etc, in my solution.

Code: Select all

007020090080010000000004628039070004800000000050900000200007060000040300000500019

1. Easy Steps
After spotting 9 singles we can take some easy steps. Locked Candidates Type 1 (Pointing): 1 in b3 => r1c12<>1, Locked Candidates Type 1 (Pointing): 3 in b3 => r56c9<>3, Locked Candidates Type 1 (Pointing): 5 in b3 => r4c7<>5, Skyscraper: 2 in r4c4,r6c9 (connected by r8c49) => r4c7,r6c6<>2. All these steps can be illustrated by one image:https://disk.yandex.ru/i/Mw_5TQAkpHcdfQ

2. Eliminating the 6's
Finned Swordfish: 6 c359 r569 fr8c3 => r9c12<>6 https://disk.yandex.ru/i/Qoysi_gk1MiIDA
Death Blossom: [r9c1], -3- r579c3 {1368}, -4- r3789c2 {14679} => r8c3<>6 https://disk.yandex.ru/i/TATUfSiW2MO8ng
Swordfish: 6 c359 r569 => r569c6<>6 https://disk.yandex.ru/i/C1EVILOvqAp_vw
The following method is a preliminary step. Death Blossom: [r9c2], -4- r23489c1 {134569}, -7- r14679c7 {124578} => r1c1<>5 https://disk.yandex.ru/i/92woTLoUSlN1_A
Now we can eliminate three 6's with a single stroke. https://disk.yandex.ru/i/RGTV8aTi_8gOqg
It is easy to spot the hidden pair 46 in row 1, so r1c1<>3.

3. Eliminating the 8's
Death Blossom: [r1c1], -4- r9c135 {3468}, -6- r4c17 {168} => r9c7<>8 https://disk.yandex.ru/i/g_SZamKZCwrSYQ
Death Blossom: [r9c1], -3- r579c3 {1368}, -4- r8c89,r9c7 {2478} => r8c3<>8 https://disk.yandex.ru/i/Iq9dCj-ZsEL8eg
Finned Swordfish: 8 r148 c468 fr4c7 => r6c8<>8 https://disk.yandex.ru/i/TQj1cbU-4-dTJg
It is easy to spot the naked single r6c8=3.
Death Blossom: [r4c1], -1- r4c7 {18}, -6- r3578c3 {13568} => r7c7<>8 https://disk.yandex.ru/i/FBq_OvF_Piov2Q

4. Easy Steps
After finding 4 singles we can take the following steps illustrated by one image. Naked Pair: 1,6 in r5c39 => r5c5<>6, r5c6<>1, Naked Pair: 1,9 in r37c2 => r8c2<>1, r8c2<>9, X-Wing: 9 r28 c16 => r3c1<>9 https://disk.yandex.ru/i/Hsm-Nf4lR58EaA

5. Eliminating the candidates from column 6
Firstly, we must take a preliminary step. Death Blossom: [r8c9], -2- r9c127 {2347}, -7- r2c9 {37} => r2c1<>3, Locked Candidates Type 1 (Pointing): 3 in b1 => r3c5<>3 https://disk.yandex.ru/i/mpywp-0YBcC9kw
Now we are ready to start removing the digits from column 6 by typical methods.
XYZ-Wing: 3/5/8 in r1c46,r5c6 => r2c6<>3 https://disk.yandex.ru/i/JvnlJ7ciUSfNyA
Death Blossom: [r9c7], -2- r1569c6 {12358}, -7- r124c7 {1578} => r6c7<>1, r4c6<>8 https://disk.yandex.ru/i/7nixS8QZUOkwbg
Death Blossom: [r9c7], -2- r159c6 {2358}, -7- r2c7 {57} => r2c6<>5 https://disk.yandex.ru/i/NDp_JSQWf_mYfA
Death Blossom: [r9c7], -2- r6c57 {268}, -7- r2c167 {5679} => r4c6<>6 https://disk.yandex.ru/i/tFxYqTZLFSnTsw
Hidden Pair: 6,9 in r28c6 => r8c6<>1, r8c6<>2, Locked Candidates Type 1 (Pointing): 1 in b8 => r4c4<>1 https://disk.yandex.ru/i/BUQPNLQQ337cPg
Death Blossom: [r9c7], -2- r8c29 {267}, -7- r2c167 {5679} => r8c6<>6 https://disk.yandex.ru/i/RDJ-0Yqn1DblOw

Finally we have a long sequence of singles. That is all.

[denis_berthier]

.
As this puzzle is brought to light again, I thought of trying the new SudoRules anti-backdoors and try-to-eliminate-candidates functionalities.

After trivial Singles and whips[1] (intersections), the PM is:

Code: Select all

   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     128       58        4         
   8         2         16        4         356       1356      9         357       167       
   7         5         4         9         368       12368     128       38        126       
   2         149       138       138       389       7         48        6         5         
   1569      1679      1568      1268      4         12689     3         78        27       
   346       467       368       5         368       2368      2478      1         9         


Then the following whip gives a single step solution (stte):

Code: Select all

whip[15]: c9n6{r5 r6} - c9n2{r6 r8} - b8n2{r8c4 r9c6} - r6n2{c6 c7} - r6n1{c7 c6} - r5n1{c6 c9} - r1n1{c9 c7} - r4c7{n1 n8} - b9n8{r7c7 r8c8} - c6n8{r8 r1} - r1n5{c6 c1} - c1n4{r1 r9} - r9c7{n4 n7} - r9c2{n7 n6} - c5n6{r9 .} ==> r5c3 ≠ 6
stte


Of course, this is a long chain, but for single-step solution lovers, that's the best one I could find.

[jco]

Hello,

I found a solution in 4 main steps. It all started from noticing the configuration of 6. There is a
nice "road" in column 2 that called my attention due to the strong link (6)r1c2=(6)r89c2,
followed by the weak link to (6)r89c3 and the strong link with (6)r5c3, that can be weakly linked to
the (6)r5c9 and then strongly to (6)r6c9. Noticing this, I started to see if some progress
could be made in the other side of the chain. We can go to digit 4 using the BVC at r1c2 and make a
strong link of 4 at r1c1, that is (4)r1c2=(4)r1c1, and then go down to (4)r9c1. At this point
I got stuck for a while, trying to see how to advance. Then, noticed an ALS asking to be used,
so I tried using the ALS with cells r9c1356 with digits 23684 (5 digits in 4 cells). At this point,
it was clear how to proceed, link weakly to (2)r9c7 and finally strongly to (2)r8c9. The two extremes
of the chain "meet" and 2 is eliminated from r6c9. Next, I checked the logic, just to make sure
there is no mistake: if 2 is false at r8c9, then it must be true at r9c7 making the digits (3684) locked
in the cells r9c1356, so that in column 1, 4 cannot be at r1c1. So, in row 1, 4 must be in r1c2,
which makes 6 false in that cell. This implies that in column 2, one of the 6s in r89 must the true,
so both 6s in r89c3 must be false, which implies that 6 would be the correct digit in r5c3, and this
implies that the 6 in r5c9 is false, so 6 must be true in r9c6 which finally implies that 2 is false
there. Since the other possibility implies that 2 is false in that cell (r6c9), this reasoning confirms
the elimination. The corresponding AIC is

Hidden Text: Show

Code: Select all

   1      2      3      4      5     6        7     8     9
.---------------------+--------------------+-------------------.
| d3456  e46     7    | 368    2     3568  |  15    9     13   | 1
|  3569   8      2    | 36     1     3569  |  57    4     37   | 2
|  1359   19     135  | 7      359   4     |  6     2     8    | 3
|---------------------+--------------------+-------------------|
|  16     3      9    | 1268   7     12568 |  128   58    4    | 4
|  8      2     h16   | 4      356   1356  |  9     357  i167  | 5
|  7      5      4    | 9      368   12368 |  128   38   j1-26 | 6
|---------------------+--------------------+-------------------|
|  2      149    138  | 138    389   7     |  48    6     5    | 7
|  1569  f1679  g1568 | 1268   4     12689 |  3     78   a27   | 8
| c346   f467  gc368  | 5     c368  c2368  | b2478  1     9    | 9
'---------------------+--------------------+-------------------'

Code: Select all

(2)r8c9=(2)r9c7-(2=3684)r9c1356-(4)r1c1=(4-6)r1c2=(6)r89c2-(6)r89c3=(6)r5c3-(6)r5c9=(6)r6c9 => -2 r6c9

After this, I used a finned swordfish on (6) [too many 6s in the puzzle], and an AIC to eliminate more 6s

Hidden Text: Show

Code: Select all

(6=4)r1c2-(4=7)r9c2-(7)r9c7=(7-5)r2c7=(5-1)r1c7=(1)r4c7-(1=6)r4c1 => -6 r12c1

Next, after some basics, I found the XY-chain

Hidden Text: Show

Code: Select all

(8=1)r4c7-(1=6)r4c1-(6=1)r5c3-(1=8)r7c3-(8=4)r7c7-(4=7)r9c7-(7=8)r8c8 => -8 r46c8, -8 r7c7

After this we have only singles. I really liked the first move, found as described (I was searching
for something else that I did not find). I was lucky this time. The puzzle gets seriously weakened
to colouring after this move.
Regards,
jco
Edit: correction on the number of main steps (thanks Cenoman!)

[AnotherLife]

Code: Select all

(2)r8c9=(2)r9c7-(2=3684)r9c1356-(4)r1c1=(4-6)r1c2=(6)r89c2-(6)r89c3=(6)r5c3-(6)r5c9=(6)r6c9 => -2 r6c9

jco

This is human but very complex. You were really lucky to find this one because it makes the rest of the work much simpler. Actually, it is a combination of Grouped AIC and ALS Chain, and such methods are not supported by HoDoKu (as far as I see).

.
Then the following whip gives a single step solution (stte):
[code]whip[15]: c9n6{r5 r6} - c9n2{r6 r8} - b8n2{r8c4 r9c6} - r6n2{c6 c7} - r6n1{c7 c6} - r5n1{c6 c9} - r1n1{c9 c7} - r4c7{n1 n8} - b9n8{r7c7 r8c8} - c6n8{r8 r1} - r1n5{c6 c1} - c1n4{r1 r9} - r9c7{n4 n7} - r9c2{n7 n6} - c5n6{r9 .} ==> r5c3 ≠ 6

As to this one, even Mikhail Tal with his extraordinary combinatorial abilities could not have calculated these steps! I have worked quite a lot with chess programmes, and I got to know that their solutions are often useless for a human player.

[Cenoman]

I found a solution in 5 main steps...
...The corresponding AIC is
(2)r8c9=(2)r9c7-(2=3684)r9c1356-(4)r1c1=(4-6)r1c2=(6)r89c2-(6)r89c3=(6)r5c3-(6)r5c9=(6)r6c9 => -2 r6c9
I really liked the first move, found as described.

Hi jco,

Welcome, as a solver player, on the puzzle forum. You already posted on this forum and others, but unless I'am wrong, it's the first time you post a solution. And what a solution ! You liked your first move and you are right, it is great. Applause !
You count 5 steps, but I count only 4.

I have a similar solution to yours (with the same 1st step):

Hidden Text: Show

Code: Select all

 +-----------------------+-----------------------+---------------------+
 |  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   |  128    58    4     |
 |  8      2      16     |  4      356   1356    |  9      357   167   |
 |  7      5      4      |  9      368   12368   |  128    38    126   |
 +-----------------------+-----------------------+---------------------+
 |  2      149    138    |  138    389   7       |  48     6     5     |
 |  1569   1679   1568   |  1268   4     12689   |  3      78    27    |
 |  346    467    368    |  5      368   2368    |  2478   1     9     |
 +-----------------------+-----------------------+---------------------+

1. (6)r6c9=r6c56-r4c46=r4c1-r5c3=r89c3-r89c2=(6-4)r1c2=r1c1-r9c1=(4-72)r9c27=(2)r8c9 =>-2r6c9;

Code: Select all

 +-----------------------+---------------------+--------------------+
 |  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     |
 +-----------------------+---------------------+--------------------+
 | d16     3      9      |  2     7     1568   | c18    58    4     |
 |  8      2     e16*    |  4     356*  1356   |  9     357   167*  |
 |  7      5      4      |  9     368*  1368   |  2     38    16*   |
 +-----------------------+---------------------+--------------------+
 |  2      149    138    |  138   389   7      | c48    6     5     |
 |  1569  a1679  f1568#  |  168   4     689    |  3    b78    2     |
 |  346    467   f368*   |  5     368*  2      | c478   1     9     |
 +-----------------------+---------------------+--------------------+

2. Finned swordfish (*,#) (6)c359\r569 fr8c3 =>-6r9c12
3. (7)r8c2=r8c8-(7=481)r479c7-(1=6)r4c1-r5c3=(6)r89c3 =>-6r8c2

Code: Select all

 +-------------------+---------------------+-------------------+
 |  4     6     7    |  38    2     358    |  15   9     13    |
 |  59    8     2    |  36    1     3569   |  57   4     37    |
 |  159   19    3    |  7     59    4      |  6    2     8     |
 +-------------------+---------------------+-------------------+
 | a16    3     9    |  2     7     1568   | e18   58    4     |
 |  8     2    b16   |  4     356   1356   |  9    357   167   |
 |  7     5     4    |  9     368   1368   |  2    38    16    |
 +-------------------+---------------------+-------------------+
 |  2     149  c18   |  138   389   7      | d48   6     5     |
 |  169   179   5    |  168   4     689    |  3    78    2     |
 |  3     47    68   |  5     68    2      |  47   1     9     |
 +-------------------+---------------------+-------------------+

4. S-Wing (1)r4c1=r5c3-(1=8)r7c3-r7c7=(8)r4c7 =>-1r4c7; ste

[AnotherLife]

(2)r8c9=(2)r9c7-(2=3684)r9c1356-(4)r1c1=(4-6)r1c2=(6)r89c2-(6)r89c3=(6)r5c3-(6)r5c9=(6)r6c9 => -2 r6c9

I would like to add to my previous post that Hodoku can find your solution if the option 'Allow ALS in chains' is switched on in Edit/Preferences/Steps (the default option is 'off'):
Grouped Discontinuous Nice Loop: 2 r6c9 -2- r8c9 =2= r9c7 -2- ALS:r9c1356 -4- r1c1 =4= r1c2 =6= r89c2 -6- r89c3 =6= r5c3 -6- r5c9 =6= r6c9 => r6c9<>2 https://disk.yandex.ru/i/3Bzaw_XJ5y4aCA
I also like your solution.

[jco]

Hello Cenoman,

You are right: that was my first time posting a solution in this amazing puzzle section.
Many thanks for your kind words!
Regards,
jco

[champagne]

Here is the path suggested by SKFR cloning Sudoku Explainer

singles and locked candidates to

Code: Select all


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 |128  58  4   
8    2    16   |4    356 1356  |9    357 167
7    5    4    |9    368 12368 |128  38  126
--------------------------------------------
2    149  138  |138  389 7     |48   6   5   
1569 1679 1568 |1268 4   12689 |3    78  27 
346  467  368  |5    368 2368  |2478 1   9   


2r4c7 - 2r4c4 = 2r8c4 - 2r8c9 = 2r6c9 - 2r4c7
2r6c6 - 2r4c4 = 2r8c4 - 2r8c9 = 2r6c9 - 2r6c6
6r4c4 - 6r2c4 = 3r2c4 - 3r2c9 = 7r2c9 - 7r8c9 = 2r8c9 - 2r8c4 = 2r4c4 - 6r4c4

Code: Select all

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    |128  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 
346  467  368  |5    368 2368  |2478 1   9   


6r1c6 - 6r4c6 = 6r4c1 -6r2c1
6r1c6 - 6r1c1,6r1c2 = 6r2c1
<6r1c6>

6r4c1 - 6r9c1
6r4c6 - 6r5c5,6r6c5 = 6r9c5 -6r9c1
<6r9c1>

6r4c1 - 6r1c1,6r2c1 = 6r1c2 - 6r9c2
6r4c6 - 6r5c5,6r6c5 = 6r9c5 - 6r9c2
<6r9c2>

Code: Select all

3456 46   7    |368  2   358   |15   9   13 
3569 8    2    |36   1   3569  |57   4   37 
1359 19   135  |7    359 4     |6    2   8   
--------------------------------------------
16   3    9    |128  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   47   368  |5    368 2368  |2478 1   9   


from here, not more than bi-value chains

6r2c1 - 6r1c2 = 4r1c2 - 4r9c2 = 7r9c2 - 7r9c7 = 7r2c7 - 7r2c9 = 3r2c9 - 3r2c4 = 6r2c4 - 6r2c1
Hidden pair 46 r1c12 in box 1 Naked pair 46 in row 1

3r2c1 - 3r2c9 = 7r2c9 - 7r2c7 = 7r9c7 - 7r9c2 = 4r9c2 - 4r9c1 = 3r9c1 - 3r2c1
digit 3 locked in box 1

Code: Select all

46   46   7    |38   2   358   |15   9   13 
59   8    2    |36   1   3569  |57   4   37 
1359 19   135  |7    59  4     |6    2   8   
--------------------------------------------
16   3    9    |128  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   47   368  |5    368 2368  |2478 1   9   



6r8c3 - 6r5c3 = 6r4c1 - 6r1c1 = 4r1c1 - 4r9c1 = 3r9c1 - 3r3c1 = 3r3c3 - 5r3c3 = 5r8c3 - 6r8c3
SwordFish digit 6 rows 569 columns 359

Code: Select all

46   46   7   |38   2   358   |15   9   13 
59   8    2   |36   1   3569  |57   4   37 
1359 19   135 |7    59  4     |6    2   8   
-------------------------------------------
16   3    9   |128  7   12568 |18   58  4   
8    2    16  |4    356 135   |9    357 167
7    5    4   |9    368 138   |128  38  126
-------------------------------------------
2    149  138 |138  389 7     |48   6   5   
1569 1679 158 |1268 4   12689 |3    78  27 
34   47   368 |5    368 238   |2478 1   9   


3r9c6 - 3r9c1 = 4r9c1 - 4r1c1 = 6r1c1 - 6r4c1 = 6r5c3 - 6r5c9 = 6r6c9 - 2r6c9 = 2r6c7 - 2r9c7 = 2r9c6 - 3r9c6
3r9c5 - 3r9c1 = 4r9c1 - 4r1c1 = 6r1c1 - 6r1c2 = 6r8c2 - 6r9c3 = 6r9c5 - 3r9c5
digit 3 locked in box 7

Code: Select all

46   46   7   |38   2   358   |15   9   13 
59   8    2   |36   1   3569  |57   4   37 
1359 19   135 |7    59  4     |6    2   8   
-------------------------------------------
16   3    9   |128  7   12568 |18   58  4   
8    2    16  |4    356 135   |9    357 167
7    5    4   |9    368 138   |128  38  126
-------------------------------------------
2    149  18  |138  389 7     |48   6   5   
1569 1679 158 |1268 4   12689 |3    78  27 
34   47   368 |5    68  28    |2478 1   9   


8r7c7 - 8r4c7 = 1r4c7 - 1r4c1 = 1r5c3 - 1r7c3 = 8r7c3 - 8r7c7
r7c7=4
2r4c6 - 6r4c6 = 6r4c1 - 6r5c3 = 6r9c3 - 6r9c5 = 8r9c5 - 8r9c6 = 2r9c6 - 2r4c6
r4c4=2
2r6c9 - 2r6c7 = 2r9c7 - 2r9c6 = 8r9c6 - 8r9c5 = 6r9c5 - 6r6c5 = 6r6c9 - 2r6c9
r6c7=2
8r9c6 -8r9c5 = 6r9c5 - 6r6c5 = 6r6c9 - 2r6c9 = 2r6c7 - 2r9c7 = 2r9c6 - 8r9c6
r9c6=2
8r9c7 - 8r4c7 = 1r4c7 - 1r4c1 = 6r4c1 - 6r5c3 = 6r9c3 - 6r9c5 = 8r9c5 - 8r9c7

stte

[AnotherLife]

Here is the path suggested by SKFR cloning Sudoku Explainer

This is almost the same as HoDoKu's default path but HoDoKu interprets some AIC's as geometrical structures, so they can be better understood. For example, this is Skyscraper
2r4c7 - 2r4c4 = 2r8c4 - 2r8c9 = 2r6c9 - 2r4c7
2r6c6 - 2r4c4 = 2r8c4 - 2r8c9 = 2r6c9 - 2r6c6,

this is Empty Rectangle
6r1c6 - 6r4c6 = 6r4c1 -6r2c1
6r1c6 - 6r1c1,6r1c2 = 6r2c1
<6r1c6>,

these two candidates can be eliminated by Finned Swordfish
6r4c1 - 6r9c1
6r4c6 - 6r5c5,6r6c5 = 6r9c5 -6r9c1
<6r9c1>

6r4c1 - 6r1c1,6r2c1 = 6r1c2 - 6r9c2
6r4c6 - 6r5c5,6r6c5 = 6r9c5 - 6r9c2
<6r9c2>,

this is W-Wing
8r7c7 - 8r4c7 = 1r4c7 - 1r4c1 = 1r5c3 - 1r7c3 = 8r7c3 - 8r7c7 and so on.
I think that every computer solution will have some drawbacks from a human point of view, so I prefer HoDoKu because it offers many possibilities and allows any human solver to choose between them.

[champagne]

Here is the path suggested by SKFR cloning Sudoku Explainer

This is almost the same as HoDoKu's default path but HoDoKu interprets some AIC's as geometrical structures, so they can be better understood. For example, this is Skyscraper ...

Sudoku Explainer is a very old process, When the program was released, many of the common patterns had not been identified. This program remains a kind of reference just because it has been the first solving any sudoku without "brute force" and giving a rating still used as reference in the interactive game.

I did not try to solve the puzzle with my last code.

[creint]

Then the following whip gives a single step solution (stte):

Code: Select all

whip[15]: c9n6{r5 r6} - c9n2{r6 r8} - b8n2{r8c4 r9c6} - r6n2{c6 c7} - r6n1{c7 c6} - r5n1{c6 c9} - r1n1{c9 c7} - r4c7{n1 n8} - b9n8{r7c7 r8c8} - c6n8{r8 r1} - r1n5{c6 c1} - c1n4{r1 r9} - r9c7{n4 n7} - r9c2{n7 n6} - c5n6{r9 .} ==> r5c3 ≠ 6
stte


Of course, this is a long chain, but for single-step solution lovers, that's the best one I could find.

How long did it take to find this, how fast is CLIPS?
Do you have a method to find the first/best rank 0 for a give sudoku state?