The New Sudoku Players' Forum

[Draco]

Here's a puzzle that I generated. SE rates it at 7.3, but needs a Turbot + 12 chains to crack it). Looks like there are a lot of potential paths thru this one after SSTS. I found one way using a contradiction chain, some singles and a forcing chain that cracks it to singles.

Looking forward to learning from your solutions; happy to share mine on request (PMs shown after SSTS):

Code: Select all

3..7.....26.....8...8.9..5.62...75....75.16....34...79.1..5.4...3.....25.....4..6

3    459  1459 | 7    1248 258  | 129  6   124
2    6    1459 | 13   14   35   | 1379 8   1347
147  47   8    | 1236 9    236  | 123  5   1234
---------------+----------------+--------------
6    2    14   | 9    38   7    | 5    134 138
489  489  7    | 5    238  1    | 6    34  238
158  58   3    | 4    268  268  | 128  7   9   
---------------+----------------+--------------
789  1    269  | 2368 5    2369 | 4    39  378
4789 3    469  | 168  167  69   | 178  2   5   
5789 5789 259  | 1238 127  4    | 1378 139 6 

Cheers...

- drac

(my ref: fc>=2, 28 spots, # 51848340)

[daj95376]

Seven chains + XY-Wing

Code: Select all

 (2)A = (2-3)B = (3-8)C = D => A<>8
 (1)E = F - (1=4)G - H = I => E<>4
 +--------------------------------------------------------------+
 |  3     459   1459  |  7     1248  258   |  129   6     124   |
 |  2     6     1459  |  13    14    35    |  1379  8     1347  |
 | E147   47    8     |  1236  9     236   |  123   5     1234  |
 |--------------------+--------------------+--------------------|
 |  6     2    G14    |  9    C38    7     |  5     134  D138   |
 |  489   489   7     |  5    B238   1     |  6     34   A238   |
 | F158   58    3     |  4     268   268   |  128   7     9     |
 |--------------------+--------------------+--------------------|
 |  789   1     269   |  2368  5     2369  |  4     39    378   |
 | I4789  3    H469   |  168   167   69    |  178   2     5     |
 |  5789  5789  259   |  1238  127   4     |  1378  139   6     |
 +--------------------------------------------------------------+


Code: Select all

 (1)A = B - (1=7)C - D = (7-8)E = F => A<>8
 +--------------------------------------------------------------+
 |  3     459   1459  |  7     1248  258   |  129   6     124   |
 |  2     6     1459  |  13    14    35    |  1379  8     1347  |
 | C17    47    8     |  1236  9     236   |  123   5     1234  |
 |--------------------+--------------------+--------------------|
 |  6     2     14    |  9     38    7     |  5     134  F138   |
 |  489   489   7     |  5     238   1     |  6     34    23    |
 | B158   58    3     |  4     268   268   | A128   7     9     |
 |--------------------+--------------------+--------------------|
 | D789   1     269   |  2368  5     2369  |  4     39   E378   |
 |  4789  3     469   |  168   167   69    |  178   2     5     |
 |  5789  5789  259   |  1238  127   4     |  1378  139   6     |
 +--------------------------------------------------------------+


Code: Select all

 (1)A = B - (1=2)C - (2=9)D - E = F => F<>1
 (4=1)G - (1=3)H - II = J - (3=7)K - L = (7-9)E = F => F<>4
 (5)M = (5-8)N = P - (8=2)Q - R = C - (2=9)D - E = F => F<>5
 +--------------------------------------------------------------+
 |  3     459   1459  |  7    P1248 N258   | D29    6     124   |
 |  2     6    F1459  | H13   G14   M35    | E379   8    L1347  |
 | A17    47    8     |  1236  9     236   |  23    5     1234  |
 |--------------------+--------------------+--------------------|
 |  6     2     14    |  9     3     7     |  5     14    8     |
 |  489   489   7     |  5    Q28    1     |  6     34   R23    |
 | B158   58    3     |  4     268   268   | C12    7     9     |
 |--------------------+--------------------+--------------------|
 |  789   1     269   | I2368  5    J2369  |  4     39   K37    |
 |  4789  3     469   |  168   167   69    |  178   2     5     |
 |  5789  5789  259   | I1238  127   4     |  1378  139   6     |
 +--------------------------------------------------------------+


Code: Select all

 (1)A = (1-5)B = C - D = E => E<>1
 +--------------------------------------------------------------+
 |  3    C45   B145   |  7     1248  28    |  9     6     124   |
 |  2     6     9     |  13    14    5     |  37    8     1347  |
 | A17    47    8     |  1236  9     236   |  23    5     1234  |
 |--------------------+--------------------+--------------------|
 |  6     2     14    |  9     3     7     |  5     14    8     |
 |  489   489   7     |  5     28    1     |  6     34    23    |
 | E158  D58    3     |  4     268   268   |  12    7     9     |
 |--------------------+--------------------+--------------------|
 |  789   1     26    |  2368  5     2369  |  4     39    37    |
 |  4789  3     46    |  168   167   69    |  178   2     5     |
 |  5789  5789  25    |  1238  127   4     |  1378  139   6     |
 +--------------------------------------------------------------+


Code: Select all

 XY-Wing  [r7c9]/[r7c1]+[r9c7]  =>  [r9c12]<>8


[ronk]

Code: Select all

 (2)A = (2-3)B = (3-8)C = D => A<>8
 (1)E = F - (1=4)G - H = I => E<>4
 +--------------------------------------------------------------+
 |  3     459   1459  |  7     1248  258   |  129   6     124   |
 |  2     6     1459  |  13    14    35    |  1379  8     1347  |
 | E147   47    8     |  1236  9     236   |  123   5     1234  |
 |--------------------+--------------------+--------------------|
 |  6     2    G14    |  9    C38    7     |  5     134  D138   |
 |  489   489   7     |  5    B238   1     |  6     34   A238   |
 | F158   58    3     |  4     268   268   |  128   7     9     |
 |--------------------+--------------------+--------------------|
 |  789   1     269   |  2368  5     2369  |  4     39    378   |
 | I4789  3    H469   |  168   167   69    |  178   2     5     |
 |  5789  5789  259   |  1238  127   4     |  1378  139   6     |
 +--------------------------------------------------------------+


daj95376, that A ... B ... C ... notation style probably doubles the amount of time it takes to follow a chain through the pencilmarks.

[daj95376]

daj95376, that A ... B ... C ... notation style probably doubles the amount of time it takes to follow a chain through the pencilmarks.

Hmmmm! Myth Jellies uses this approach and I actually find it easy to follow his chains. We use it in another forum. It reduces the possibility of my having a typo (from a modest case of dyslexia).

I encountered long and/or multiple chains per PM on this puzzle, so I decided to use the A..Z labeling. If I'd posted anything fancier than plain vanilla chains, then I would have used rncn cell notation and not cared if lines wrapped across the screen. As is, I expect most people will just look at the chain's conclusion to see if its elimination matches one they found.

I'll return to rncn notation for cells in the future.

[aran]

Code: Select all

3    459  1459 | 7    1248 258  | 129  6   124
2    6    1459 | 13   14   35   | 1379 8   1347
147  47   8    | 1236 9    236  | 123  5   1234
---------------+----------------+--------------
6    2    14   | 9    38   7    | 5    134 138
489  489  7    | 5    238  1    | 6    34  238
158  58   3    | 4    268  268  | 128  7   9   
---------------+----------------+--------------
789  1    269  | 2368 5    2369 | 4    39  378
4789 3    469  | 168  167  69   | 178  2   5   
5789 5789 259  | 1238 127  4    | 1378 139 6 

1.4r8c1=4r8c3-(4=1)r4c3-(14=59)r12c3-(59=4)r1c2 : =><4>r3c1
2.134r2c459=7r2c9-7r7c9=7r7c1-(7=1)r3c1 : =><1>r2c3
3.134r2c459=7r2c9-7r7c9=7r7c1-(7=1)r3c1-(1=58r6c12)-(8=26)r6c56-(28=1)r6c7-(1=34)r45c8-(3=9)r7c8-9r7c7=236r367c6 : =><3>=5r2c6 =><5>r2c3
4.459b1=1r1c3-(1=4)r4c3-(4=89)r5c12-(8=5)r6c2-(5=49)(r1c2+r2c3) : =><4>=7r3c2
multiple singles reducing to a simple finale

[Draco]

Code: Select all

3    459  1459 | 7    1248 258  | 129  6   124
2    6    1459 | 13   14   35   | 1379 8   1347
147  47   8    | 1236 9    236  | 123  5   1234
---------------+----------------+--------------
6    2    14   | 9    38   7    | 5    134 138
489  489  7    | 5    238  1    | 6    34  238
158  58   3    | 4    268  268  | 128  7   9   
---------------+----------------+--------------
789  1    269  | 2368 5    2369 | 4    39  378
4789 3    469  | 168  167  69   | 178  2   5   
5789 5789 259  | 1238 127  4    | 1378 139 6 

1.4r8c1=4r8c3-(4=1)r4c3-(14=59)r12c3-(59=4)r1c2 : =><4>r3c1
2.134r2c459=7r2c9-7r7c9=7r7c1-(7=1)r3c1 : =><1>r2c3
3.134r2c459=7r2c9-7r7c9=7r7c1-(7=1)r3c1-(1=58r6c12)-(8=26)r6c56-(28=1)r6c7-(1=34)r45c8-(3=9)r7c8-9r7c7=236r367c6 : =><3>=5r2c6 =><5>r2c3
4.459b1=1r1c3-(1=4)r4c3-(4=89)r5c12-(8=5)r6c2-(5=49)(r1c2+r2c3) : =><4>=7r3c2
multiple singles reducing to a simple finale

I thought I posted tis; apparently I didn't.

Aran you lost me on the first chain; I must be misreading the notation. I think your conclusion for #1 is r3c1<>4, is that right? If not, the what? if so, then why isn't it r3c12<>4??

Cheers...

- drac

[aran]

Code: Select all

3    459  1459 | 7    1248 258  | 129  6   124
2    6    1459 | 13   14   35   | 1379 8   1347
147  47   8    | 1236 9    236  | 123  5   1234
---------------+----------------+--------------
6    2    14   | 9    38   7    | 5    134 138
489  489  7    | 5    238  1    | 6    34  238
158  58   3    | 4    268  268  | 128  7   9   
---------------+----------------+--------------
789  1    269  | 2368 5    2369 | 4    39  378
4789 3    469  | 168  167  69   | 178  2   5   
5789 5789 259  | 1238 127  4    | 1378 139 6 

1.4r8c1=4r8c3-(4=1)r4c3-(14=59)r12c3-(59=4)r1c2 : =><4>r3c1
2.134r2c459=7r2c9-7r7c9=7r7c1-(7=1)r3c1 : =><1>r2c3
3.134r2c459=7r2c9-7r7c9=7r7c1-(7=1)r3c1-(1=58r6c12)-(8=26)r6c56-(28=1)r6c7-(1=34)r45c8-(3=9)r7c8-9r7c7=236r367c6 : =><3>=5r2c6 =><5>r2c3
4.459b1=1r1c3-(1=4)r4c3-(4=89)r5c12-(8=5)r6c2-(5=49)(r1c2+r2c3) : =><4>=7r3c2
multiple singles reducing to a simple finale

I thought I posted tis; apparently I didn't.

Draco : not sure what you mean. I didn't see any posting by you other than the initial post with this :

Here's a puzzle that I generated. SE rates it at 7.3, but needs a Turbot + 12 chains to crack it). Looks like there are a lot of potential paths thru this one after SSTS. I found one way using a contradiction chain, some singles and a forcing chain that cracks it to singles

Aran you lost me on the first chain; I must be misreading the notation. I think your conclusion for #1 is r3c1<>4, is that right? If not, the what? if so, then why isn't it r3c12<>4??

Endpoints of the first chain are 4r8c1 and 4r1c2, so they eliminate what they both see : 4r3c1 (but not 4r3c2 which is not seen by both).
Just to present in words that first chain : 4r8c1=4r8c3-(4=1)r4c3-(14=59)r12c3-(59=4)r1c2
r8c1 not 4=>r8c3 is 4=>r4c3 not 4, is 1=>neither 1 nor 4 in r12c3=>hence r12c3 is pair 59=>59 removed from r1c2 which becomes 4.

[Draco]

I thought I posted tis; apparently I didn't.

Draco : not sure what you mean. I didn't see any posting by you other than the initial post with this :

Here's a puzzle that I generated. SE rates it at 7.3, but needs a Turbot + 12 chains to crack it). Looks like there are a lot of potential paths thru this one after SSTS. I found one way using a contradiction chain, some singles and a forcing chain that cracks it to singles

Quite right... sorry for the confusion. It was a bit of venting because I wrote this second post earlier in the day and apparently lost it, so had to recreate it.

Aran you lost me on the first chain; I must be misreading the notation. I think your conclusion for #1 is r3c1<>4, is that right? If not, the what? if so, then why isn't it r3c12<>4??

Endpoints of the first chain are 4r8c1 and 4r1c2, so they eliminate what they both see : 4r3c1 (but not 4r3c2 which is not seen by both).
Just to present in words that first chain : 4r8c1=4r8c3-(4=1)r4c3-(14=59)r12c3-(59=4)r1c2
r8c1 not 4=>r8c3 is 4=>r4c3 not 4, is 1=>neither 1 nor 4 in r12c3=>hence r12c3 is pair 59=>59 removed from r1c2 which becomes 4.

Thank you for the detailed explaination. I often find myself thrown off by the initial digit included in this sort of notation (i.e. 4r8c1=4r8c3...). Said confusion led me to a cascading set of erroronous assumptions. What is the purpose of the initial 4? What info does that add that is missing from: r8c1=4r8c3-(4=1)r4c3-(14=59)r12c3-(59=4)r1c2?

Cheers...

- drac

[aran]

Thank you for the detailed explaination. I often find myself thrown off by the initial digit included in this sort of notation (i.e. 4r8c1=4r8c3...). Said confusion led me to a cascading set of erroronous assumptions. What is the purpose of the initial 4? What info does that add that is missing from: r8c1=4r8c3-(4=1)r4c3-(14=59)r12c3-(59=4)r1c2

Draco : you're right : the initial candidate could be excluded insofar as what else could it be.

If it is excluded though, then anyone examining the chain has to look to the second node and then back to the first (just to make sure there really was a 4 there in the first place ) so perhaps it is better to keep it.

I don't quite see why including it would cause confusion - do explain if you wish.

[Draco]

Thank you for the detailed explaination. I often find myself thrown off by the initial digit included in this sort of notation (i.e. 4r8c1=4r8c3...). Said confusion led me to a cascading set of erroronous assumptions. What is the purpose of the initial 4? What info does that add that is missing from: r8c1=4r8c3-(4=1)r4c3-(14=59)r12c3-(59=4)r1c2

Draco : you're right : the initial candidate could be excluded insofar as what else could it be.

If it is excluded though, then anyone examining the chain has to look to the second node and then back to the first (just to make sure there really was a 4 there in the first place ) so perhaps it is better to keep it.

I don't quite see why including it would cause confusion - do explain if you wish.

Inferring additional meaning to the initial 4, I wrongly assumed it was some sort of continuous loop (which I could not quite connect), proving the initinal assumption to be true (which lead me to think that r3c2<>4 was also "proved").

Cheers...

- drac