Analysis of zz-www.sudokuoftheday.co.uk-20060315-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006

level: medium

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006

position: .7..........926....2.7...3.8..16.52.....4.....36....8.2.4....78.1.87........1.25. initial

Autosolve

position: .7......2...926....2.7...3.8..16.52...2.48....362...8.2.4...178.1.872.......1.25. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C3: 5,8 => CTR => C3: 1,9
* DIS # I3: 1,4 => CTR => I3: 5,6,9
* DIS # A6: 4,9 => CTR => A6: 1,5,7
* DIS # I4: 4,9 => CTR => I4: 3,7
* DIS # A5: 7,9 => CTR => A5: 1,5
* DIS # A6: 7,9 => CTR => A6: 1,4,5
* PRF # F4: 7,9 => SOL
* DIS # F4: 3 => CTR => F4: 7,9
* DIS # I4: 7,9 => CTR => I4: 3,4
* DIS # C9: 7,9 => CTR => C9: 3,8
* PRF # A5: 5,9 => SOL
* DIS # D1: 3,5 => CTR => D1: 4
* DIS # F6: 5,9 => CTR => F6: 7
* PRF # A6: 1,4,7 => SOL
* DIS # B9: 6,9 => CTR => B9: 8
* DIS # I8: 3,9 => CTR => I8: 4,6
* DIS # A9: 3,9 => CTR => A9: 7
* DIS # I5: 3,9 => CTR => I5: 1,6,7
* CNT  18 HDP CHAINS /  45 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* DIS # C3: 5,8 => CTR => C3: 1,9
* DIS C3: 1,9 # I3: 1,4 => CTR => I3: 5,6,9
* DIS C3: 1,9 + I3: 5,6,9 # A6: 4,9 => CTR => A6: 1,5,7
* DIS C3: 1,9 + I3: 5,6,9 + A6: 1,5,7 # A5: 7,9 => CTR => A5: 1,5
* PRF C3: 1,9 + I3: 5,6,9 + A6: 1,5,7 + A5: 1,5 # F4: 7,9 => SOL
* STA C3: 1,9 + I3: 5,6,9 + A6: 1,5,7 + A5: 1,5 + F4: 7,9
* CNT   5 HDP CHAINS /  13 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Details

Positions

.7..........926....2.7...3.8..16.52.....4.....36....8.2.4....78.1.87........1.25. initial
.7......2...926....2.7...3.8..16.52...2.48....362...8.2.4...178.1.872.......1.25. autosolve
671435892358926417429781635847169523592348761136257984264593178915872346783614259 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (11)
E3: 5,8
H2: 1,4
B4: 4,9
C4: 7,9
B5: 5,9
D5: 3,5
E6: 5,9
B7: 6,9
D9: 4,6
F9: 4,9
I9: 3,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F1,F3: 1.. / F1 = 1  => 12 pairs (_) / F3 = 1  => 11 pairs (_)
A5,A6: 1.. / A5 = 1  => 13 pairs (_) / A6 = 1  =>  0 pairs (*)
A6,I6: 1.. / A6 = 1  =>  0 pairs (*) / I6 = 1  =>  0 pairs (X)
A2,C2: 3.. / A2 = 3  => 13 pairs (_) / C2 = 3  => 13 pairs (_)
F4,D5: 3.. / F4 = 3  =>  0 pairs (X) / D5 = 3  =>  0 pairs (_)
F4,I4: 3.. / F4 = 3  =>  0 pairs (X) / I4 = 3  =>  0 pairs (_)
E1,E7: 3.. / E1 = 3  => 12 pairs (_) / E7 = 3  => 18 pairs (_)
G5,G8: 3.. / G5 = 3  =>  0 pairs (X) / G8 = 3  => 18 pairs (_)
B4,A6: 4.. / B4 = 4  => 11 pairs (_) / A6 = 4  =>  0 pairs (X)
D9,F9: 4.. / D9 = 4  =>  0 pairs (X) / F9 = 4  => 11 pairs (_)
B4,I4: 4.. / B4 = 4  => 11 pairs (_) / I4 = 4  =>  0 pairs (X)
B2,B4: 4.. / B2 = 4  =>  0 pairs (X) / B4 = 4  => 11 pairs (_)
D1,D9: 4.. / D1 = 4  => 11 pairs (_) / D9 = 4  =>  0 pairs (X)
I2,I3: 5.. / I2 = 5  =>  0 pairs (X) / I3 = 5  => 13 pairs (_)
A8,C8: 5.. / A8 = 5  =>  0 pairs (X) / C8 = 5  => 12 pairs (_)
B2,B5: 5.. / B2 = 5  =>  0 pairs (*) / B5 = 5  =>  0 pairs (X)
A1,A3: 6.. / A1 = 6  => 11 pairs (_) / A3 = 6  => 11 pairs (_)
B7,B9: 6.. / B7 = 6  => 11 pairs (_) / B9 = 6  =>  0 pairs (X)
D7,D9: 6.. / D7 = 6  =>  0 pairs (X) / D9 = 6  => 11 pairs (_)
B7,D7: 6.. / B7 = 6  => 11 pairs (_) / D7 = 6  =>  0 pairs (X)
B9,D9: 6.. / B9 = 6  =>  0 pairs (X) / D9 = 6  => 11 pairs (_)
G2,I2: 7.. / G2 = 7  => 12 pairs (_) / I2 = 7  => 15 pairs (_)
F4,F6: 7.. / F4 = 7  =>  0 pairs (X) / F6 = 7  => 13 pairs (_)
A9,C9: 7.. / A9 = 7  => 12 pairs (_) / C9 = 7  =>  0 pairs (X)
C4,C9: 7.. / C4 = 7  => 12 pairs (_) / C9 = 7  =>  0 pairs (X)
E1,E3: 8.. / E1 = 8  =>  0 pairs (X) / E3 = 8  => 11 pairs (_)
B9,C9: 8.. / B9 = 8  => 14 pairs (_) / C9 = 8  =>  0 pairs (X)
B2,B9: 8.. / B2 = 8  =>  0 pairs (X) / B9 = 8  => 14 pairs (_)
E6,E7: 9.. / E6 = 9  => 14 pairs (_) / E7 = 9  =>  0 pairs (*)
* DURATION: 0:00:29.563514  START: 19:49:10.087354  END: 19:49:39.650868 2019-04-30
* CP COUNT: (29)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B5,B7,C4,D5,D9,E3,E6,F9,H2,I9)
* .7......2...926....2.7...3.8..16.52...2.48....362...8.2.4...178.1.872.......1.25.
* PAIR E3: 5,8 BLK 2
E1: 5,8,3                                # reduction candidate for 5,8
E1: 5,8                                  # 18 pairs
E1: 3                                    # 12 pairs
* PAIR E3: 5,8 ROW 3
C3: 5,8,1,9                              # reduction candidate for 5,8
C3: 5,8 => CTR
* .7.4..8.2...9267.5.2.781.3.84.16.523.52348....362...8.294...178.1.8723......14259
C3: 1,9                                  # 12 pairs
* PAIR H2: 1,4 BLK 3
H1: 1,4,6,9                              # reduction candidate for 1,4
H1: 1,4                                  # 16 pairs
I2: 1,4,5,7                              # reduction candidate for 1,4
I2: 1,4                                  # 26 pairs
I3: 1,4,5,6,9                            # reduction candidate for 1,4
I3: 1,4 => CTR
* .7.4....2...9267.5.2.7...3.84.16.523.52348....362...8.294...178.1.8723......14259
I3: 5,6,9                                # 11 pairs
* PAIR B4: 4,9 BLK 4
A6: 4,9,1,5,7                            # reduction candidate for 4,9
A6: 4,9 => CTR
* .7......23..926....2.7...3.8.7169523152348...93625748129463517851.8723..7.3.1.259
A6: 1,5,7                                # 11 pairs
* PAIR B4: 4,9 ROW 4
I4: 4,9,3,7                              # reduction candidate for 4,9
I4: 4,9 => CTR
* .7.435..2.5392681..2.7...35847163529192548.6.536297481264359178.15872..6789614253
I4: 3,7                                  # 12 pairs
* PAIR C4: 7,9 BLK 4
A5: 7,9,1,5                              # reduction candidate for 7,9
A5: 7,9 => CTR
* .7......2.8.926....2.7...3.84.16.523.52348...1362...8.2946..17851.8723......1.259
A5: 1,5                                  # 13 pairs
A6: 7,9,1,4,5                            # reduction candidate for 7,9
A6: 7,9 => CTR
* .7......2.8.926....2.7...3.84.16.523152348....362..4812946..17851.8723......1.259
A6: 1,4,5                                # 11 pairs
* PAIR C4: 7,9 ROW 4
F4: 7,9,3                                # reduction candidate for 7,9
F4: 7,9 => SOLVED
* 671435892358926417429781635847169523592348761136257984264593178915872346783614259
F4: 3 => CTR
* .7.435..2.5.926..442.781635847163529192548.67536297481264359178.15872.4678961425.
I4: 7,9,3,4                              # reduction candidate for 7,9
I4: 7,9 => CTR
* .7.435..2.5.926..442.781635847163529192548.67536297481264359178.15872.4678961425.
I4: 3,4                                  # 12 pairs
* PAIR C4: 7,9 COL C
C9: 7,9,3,8                              # reduction candidate for 7,9
C9: 7,9 => CTR
* .7.435..245.926....2.7...3.8.716352...25483.7536297481264359178315872...789614253
C9: 3,8                                  # 13 pairs
* PAIR B5: 5,9 BLK 4
A5: 5,9,1,7                              # reduction candidate for 5,9
A5: 5,9 => SOLVED
* 671435892358926417429781635847169523592348761136257984264593178915872346783614259
A5: 1,7                                  # 12 pairs
A6: 5,9,1,4,7                            # reduction candidate for 5,9
A6: 5,9                                  # 17 pairs
* PAIR D5: 3,5 COL D
D1: 3,5,4                                # reduction candidate for 3,5
D1: 3,5 => CTR
* .7......2...926....2.7...3.8..16352...25483..536297481294...178.1.872......419253
D1: 4                                    # 11 pairs
D7: 3,5,6                                # reduction candidate for 3,5
D7: 3,5                                  # 11 pairs
* PAIR E6: 5,9 BLK 5
F6: 5,9,7                                # reduction candidate for 5,9
F6: 5,9 => CTR
* .7......2..3926....2.7...3.849167523.52348....362...8.2946..17851.8723....7.1.259
F6: 7                                    # 13 pairs
* PAIR E6: 5,9 ROW 6
A6: 5,9,1,4,7                            # reduction candidate for 5,9
A6: 1,4,7 => SOLVED
* 671435892358926417429781635847169523592348761136257984264593178915872346783614259
A6: 5,9                                  # 17 pairs
* PAIR E6: 5,9 COL E
E7: 5,9,3                                # reduction candidate for 5,9
E7: 3                                    # 18 pairs
E7: 5,9                                  # 12 pairs
* PAIR B7: 6,9 BLK 7
B9: 6,9,8                                # reduction candidate for 6,9
B9: 6,9 => CTR
* .7......2.8.926....2.7...3.84.16.52..52348....362...8.2.4...178.1.8723....8.1.259
B9: 8                                    # 14 pairs
* PAIR I9: 3,9 BLK 9
G8: 3,9,4,6                              # reduction candidate for 3,9
G8: 3,9                                  # 14 pairs
I8: 3,9,4,6                              # reduction candidate for 3,9
I8: 3,9 => CTR
* .7......2.5.926714.2.7...3584916352...25483..5362974812.4...178.1587264.....1.25.
I8: 4,6                                  # 12 pairs
* PAIR I9: 3,9 ROW 9
A9: 3,9,7                                # reduction candidate for 3,9
A9: 3,9 => CTR
* .7......2...926....2.7...3.8.916.52..52348....362...8.2.4...178.1.8723..387614259
A9: 7                                    # 12 pairs
C9: 3,9,7,8                              # reduction candidate for 3,9
C9: 3,9                                  # 14 pairs
* PAIR I9: 3,9 COL I
I4: 3,9,4,7                              # reduction candidate for 3,9
I4: 3,9                                  # 13 pairs
I5: 3,9,1,6,7                            # reduction candidate for 3,9
I5: 3,9 => CTR
* .7......2...926....2.7...3.8..16352...2548..35362974812.4...178.158723......1.259
I5: 1,6,7                                # 11 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060315-absurd-base-pr-000.dot
* REASONING
* DIS # C3: 5,8 => CTR => C3: 1,9
* DIS # I3: 1,4 => CTR => I3: 5,6,9
* DIS # A6: 4,9 => CTR => A6: 1,5,7
* DIS # I4: 4,9 => CTR => I4: 3,7
* DIS # A5: 7,9 => CTR => A5: 1,5
* DIS # A6: 7,9 => CTR => A6: 1,4,5
* PRF # F4: 7,9 => SOL
* DIS # F4: 3 => CTR => F4: 7,9
* DIS # I4: 7,9 => CTR => I4: 3,4
* DIS # C9: 7,9 => CTR => C9: 3,8
* PRF # A5: 5,9 => SOL
* DIS # D1: 3,5 => CTR => D1: 4
* DIS # F6: 5,9 => CTR => F6: 7
* PRF # A6: 1,4,7 => SOL
* DIS # B9: 6,9 => CTR => B9: 8
* DIS # I8: 3,9 => CTR => I8: 4,6
* DIS # A9: 3,9 => CTR => A9: 7
* DIS # I5: 3,9 => CTR => I5: 1,6,7
* CNT  18 HDP CHAINS /  45 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B5,B7,C4,D5,D9,E3,E6,F9,H2,I9)
* .7......2...926....2.7...3.8..16.52...2.48....362...8.2.4...178.1.872.......1.25.
* PAIR E3: 5,8 BLK 2
E1: 5,8,3                                # reduction candidate for 5,8
E1: 5,8                                  # 18 pairs
E1: 3                                    # 12 pairs
* PAIR E3: 5,8 ROW 3
C3: 5,8,1,9                              # reduction candidate for 5,8
C3: 5,8 => CTR
* .7.4..8.2...9267.5.2.781.3.84.16.523.52348....362...8.294...178.1.8723......14259
* PAIR RESTART
* PAIR E3: 5,8 BLK 2
E1: 5,8,3                                # reduction candidate for 5,8
E1: 5,8                                  # 19 pairs
E1: 3                                    # 13 pairs
* PAIR H2: 1,4 BLK 3
H1: 1,4,6,9                              # reduction candidate for 1,4
H1: 1,4                                  # 17 pairs
I2: 1,4,5,7                              # reduction candidate for 1,4
I2: 1,4                                  # 26 pairs
I3: 1,4,5,6,9                            # reduction candidate for 1,4
I3: 1,4 => CTR
* .7.4....2...9267.5.2.7...3.84.16.523.52348....362...8.294...178.1.8723......14259
* PAIR RESTART
* PAIR H2: 1,4 BLK 3
H1: 1,4,6,9                              # reduction candidate for 1,4
H1: 1,4                                  # 17 pairs
I2: 1,4,5,7                              # reduction candidate for 1,4
I2: 1,4                                  # 26 pairs
* PAIR B4: 4,9 BLK 4
A6: 4,9,1,5,7                            # reduction candidate for 4,9
A6: 4,9 => CTR
* .7......23..926....2.7...3.8.7169523152348...93625748129463517851.8723..7.3.1.259
* PAIR C4: 7,9 BLK 4
A5: 7,9,1,5                              # reduction candidate for 7,9
A5: 7,9 => CTR
* .7......2.8.926....2.7...3.84.16.523.52348...1362...8.2946..17851.8723......1.259
* PAIR C4: 7,9 ROW 4
F4: 7,9,3                                # reduction candidate for 7,9
F4: 7,9 => SOLVED
* 671435892358926417429781635847169523592348761136257984264593178915872346783614259
* DURATION: 0:00:10.339725  START: 19:50:05.586199  END: 19:50:15.925924 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060315-absurd-base-pr-001.dot
* REASONING
* DIS # C3: 5,8 => CTR => C3: 1,9
* DIS C3: 1,9 # I3: 1,4 => CTR => I3: 5,6,9
* DIS C3: 1,9 + I3: 5,6,9 # A6: 4,9 => CTR => A6: 1,5,7
* DIS C3: 1,9 + I3: 5,6,9 + A6: 1,5,7 # A5: 7,9 => CTR => A5: 1,5
* PRF C3: 1,9 + I3: 5,6,9 + A6: 1,5,7 + A5: 1,5 # F4: 7,9 => SOL
* STA C3: 1,9 + I3: 5,6,9 + A6: 1,5,7 + A5: 1,5 + F4: 7,9
* CNT   5 HDP CHAINS /  13 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006, 20060315, absurd

Solution

position: 671435892358926417429781635847169523592348761136257984264593178915872346783614259 solved
Solution

See section Pair Reduction for the HDP chains leading to this result.

Appendix: Full HDP Chains

A1. Pair Reduction Analysis

Full list of HDP chains traversed:

* INC # E1: 5,8 => UNS
* INC # E1: 3 => UNS
* DIS # C3: 5,8 => CTR => C3: 1,9
* INC # C3: 1,9 => UNS
* INC # H1: 1,4 => UNS
* INC # I2: 1,4 => UNS
* DIS # I3: 1,4 => CTR => I3: 5,6,9
* INC # I3: 5,6,9 => UNS
* DIS # A6: 4,9 => CTR => A6: 1,5,7
* INC # A6: 1,5,7 => UNS
* DIS # I4: 4,9 => CTR => I4: 3,7
* INC # I4: 3,7 => UNS
* DIS # A5: 7,9 => CTR => A5: 1,5
* INC # A5: 1,5 => UNS
* DIS # A6: 7,9 => CTR => A6: 1,4,5
* INC # A6: 1,4,5 => UNS
* PRF # F4: 7,9 => SOL
* DIS # F4: 3 => CTR => F4: 7,9
* DIS # I4: 7,9 => CTR => I4: 3,4
* INC # I4: 3,4 => UNS
* DIS # C9: 7,9 => CTR => C9: 3,8
* INC # C9: 3,8 => UNS
* PRF # A5: 5,9 => SOL
* INC # A5: 1,7 => UNS
* INC # A6: 5,9 => UNS
* DIS # D1: 3,5 => CTR => D1: 4
* INC # D1: 4 => UNS
* INC # D7: 3,5 => UNS
* DIS # F6: 5,9 => CTR => F6: 7
* INC # F6: 7 => UNS
* INC # A6: 5,9 => UNS
* PRF # A6: 1,4,7 => SOL
* INC # E7: 5,9 => UNS
* INC # E7: 3 => UNS
* DIS # B9: 6,9 => CTR => B9: 8
* INC # B9: 8 => UNS
* INC # G8: 3,9 => UNS
* DIS # I8: 3,9 => CTR => I8: 4,6
* INC # I8: 4,6 => UNS
* DIS # A9: 3,9 => CTR => A9: 7
* INC # A9: 7 => UNS
* INC # C9: 3,9 => UNS
* INC # I4: 3,9 => UNS
* DIS # I5: 3,9 => CTR => I5: 1,6,7
* INC # I5: 1,6,7 => UNS
* CNT  45 HDP CHAINS /  45 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E1: 5,8 => UNS
* INC # E1: 3 => UNS
* DIS # C3: 5,8 => CTR => C3: 1,9
* INC C3: 1,9 # E1: 5,8 => UNS
* INC C3: 1,9 # E1: 3 => UNS
* INC C3: 1,9 # H1: 1,4 => UNS
* INC C3: 1,9 # I2: 1,4 => UNS
* DIS C3: 1,9 # I3: 1,4 => CTR => I3: 5,6,9
* INC C3: 1,9 + I3: 5,6,9 # H1: 1,4 => UNS
* INC C3: 1,9 + I3: 5,6,9 # I2: 1,4 => UNS
* DIS C3: 1,9 + I3: 5,6,9 # A6: 4,9 => CTR => A6: 1,5,7
* DIS C3: 1,9 + I3: 5,6,9 + A6: 1,5,7 # A5: 7,9 => CTR => A5: 1,5
* PRF C3: 1,9 + I3: 5,6,9 + A6: 1,5,7 + A5: 1,5 # F4: 7,9 => SOL
* STA C3: 1,9 + I3: 5,6,9 + A6: 1,5,7 + A5: 1,5 + F4: 7,9
* CNT  13 HDP CHAINS /  13 HYP OPENED