Analysis of zz-www.sudokuoftheday.co.uk-20060510-absurd-base.sdk

Contents

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

level: medium

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

position: ...8...31...3.2...9..6..827.8..1..924........2....416.1.....7...32......7....9.8. initial

Autosolve

position: .2.8...31...3.2...9.36.182738..1.4924.....3752...341681....37...32....1.7..1.9283 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C1: 5,6 => CTR => C1: 4,7
* DIS # A2: 5,6 => CTR => A2: 8
* DIS # B2: 5,6 => CTR => B2: 1,7
* DIS # C2: 5,6 => CTR => C2: 1,7,8
* DIS # G1: 5,6 => CTR => G1: 9
* DIS # A8: 8 => CTR => A8: 5,6
* PRF # C1: 4,5 => SOL
* DIS # C1: 6,7 => CTR => C1: 4,5
* DIS # B9: 6 => CTR => B9: 4,5
* PRF # E1: 5,7 => SOL
* DIS # E2: 5,7 => CTR => E2: 9
* DIS # C1: 5,7 => CTR => C1: 4,6
* DIS # E1: 4,5 => CTR => E1: 7,9
* PRF # E1: 7,9 => SOL
* DIS # D8: 5,7 => CTR => D8: 4
* PRF # E7: 5,6 => SOL
* DIS # E8: 5,6 => CTR => E8: 7,8
* DIS # B9: 5,6 => CTR => B9: 4
* PRF # B9: 4 => SOL
* PRF # C9: 5,6 => SOL
* DIS # C9: 4 => CTR => C9: 5,6
* DIS # I8: 4,6 => CTR => I8: 9
* DIS # I2: 9 => CTR => I2: 4,6
* CNT  23 HDP CHAINS /  51 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 # C1: 5,6 => CTR => C1: 4,7
* DIS C1: 4,7 # A2: 5,6 => CTR => A2: 8
* DIS C1: 4,7 + A2: 8 # B2: 5,6 => CTR => B2: 1,7
* DIS C1: 4,7 + A2: 8 + B2: 1,7 # C2: 5,6 => CTR => C2: 1,7
* PRF C1: 4,7 + A2: 8 + B2: 1,7 + C2: 1,7 => SOL
* STA C1: 4,7 + A2: 8 + B2: 1,7 + C2: 1,7
* CNT   5 HDP CHAINS /   4 HYP OPENED

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

Details

Positions

...8...31...3.2...9..6..827.8..1..924........2....416.1.....7...32......7....9.8. initial
.2.8...31...3.2...9.36.182738..1.4924.....3752...341681....37...32....1.7..1.9283 autosolve
624875931817392546953641827385716492461928375279534168198263754532487619746159283 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (11)
A1: 5,6
B3: 4,5
F1: 5,7
E3: 4,5
H2: 4,5
D4: 5,7
D5: 2,9
F5: 6,8
E9: 5,6
H7: 4,5
I7: 4,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B2,C2: 1.. / B2 = 1  => 16 pairs (_) / C2 = 1  => 15 pairs (_)
B5,C5: 1.. / B5 = 1  => 15 pairs (_) / C5 = 1  => 16 pairs (_)
B2,B5: 1.. / B2 = 1  => 16 pairs (_) / B5 = 1  => 15 pairs (_)
C2,C5: 1.. / C2 = 1  => 15 pairs (_) / C5 = 1  => 16 pairs (_)
D5,E5: 2.. / D5 = 2  => 20 pairs (_) / E5 = 2  => 15 pairs (_)
D7,E7: 2.. / D7 = 2  => 15 pairs (_) / E7 = 2  => 20 pairs (_)
D5,D7: 2.. / D5 = 2  => 20 pairs (_) / D7 = 2  => 15 pairs (_)
E5,E7: 2.. / E5 = 2  => 15 pairs (_) / E7 = 2  => 20 pairs (_)
C1,B3: 4.. / C1 = 4  =>  0 pairs (*) / B3 = 4  =>  0 pairs (X)
E1,E3: 4.. / E1 = 4  =>  0 pairs (X) / E3 = 4  =>  0 pairs (_)
H2,I2: 4.. / H2 = 4  => 13 pairs (_) / I2 = 4  =>  0 pairs (X)
B9,C9: 4.. / B9 = 4  =>  0 pairs (*) / C9 = 4  =>  0 pairs (X)
D7,D8: 4.. / D7 = 4  =>  0 pairs (X) / D8 = 4  => 14 pairs (_)
C1,E1: 4.. / C1 = 4  =>  0 pairs (*) / E1 = 4  =>  0 pairs (X)
B3,E3: 4.. / B3 = 4  =>  0 pairs (X) / E3 = 4  =>  0 pairs (_)
D8,I8: 4.. / D8 = 4  => 14 pairs (_) / I8 = 4  =>  0 pairs (X)
B3,B9: 4.. / B3 = 4  =>  0 pairs (X) / B9 = 4  =>  0 pairs (_)
C1,C9: 4.. / C1 = 4  =>  0 pairs (*) / C9 = 4  =>  0 pairs (X)
H2,H7: 4.. / H2 = 4  => 13 pairs (_) / H7 = 4  =>  0 pairs (X)
H7,G8: 5.. / H7 = 5  => 13 pairs (_) / G8 = 5  =>  0 pairs (X)
B3,E3: 5.. / B3 = 5  =>  0 pairs (*) / E3 = 5  =>  0 pairs (X)
H2,H7: 5.. / H2 = 5  =>  0 pairs (X) / H7 = 5  => 13 pairs (_)
C4,F4: 6.. / C4 = 6  => 20 pairs (_) / F4 = 6  => 15 pairs (_)
B2,B6: 7.. / B2 = 7  =>  0 pairs (X) / B6 = 7  => 15 pairs (_)
A2,C2: 8.. / A2 = 8  => 14 pairs (_) / C2 = 8  =>  0 pairs (X)
E5,F5: 8.. / E5 = 8  => 17 pairs (_) / F5 = 8  => 11 pairs (_)
C7,A8: 8.. / C7 = 8  => 14 pairs (_) / A8 = 8  =>  0 pairs (X)
C7,E7: 8.. / C7 = 8  => 14 pairs (_) / E7 = 8  =>  0 pairs (X)
A2,A8: 8.. / A2 = 8  => 14 pairs (_) / A8 = 8  =>  0 pairs (X)
C2,C7: 8.. / C2 = 8  =>  0 pairs (X) / C7 = 8  => 14 pairs (_)
F5,F8: 8.. / F5 = 8  => 11 pairs (_) / F8 = 8  => 17 pairs (_)
E1,E2: 9.. / E1 = 9  =>  0 pairs (X) / E2 = 9  => 24 pairs (_)
D5,D6: 9.. / D5 = 9  => 15 pairs (_) / D6 = 9  => 20 pairs (_)
B7,C7: 9.. / B7 = 9  => 13 pairs (_) / C7 = 9  =>  0 pairs (X)
G8,I8: 9.. / G8 = 9  =>  0 pairs (X) / I8 = 9  => 15 pairs (_)
E1,G1: 9.. / E1 = 9  =>  0 pairs (X) / G1 = 9  => 24 pairs (_)
I2,I8: 9.. / I2 = 9  =>  0 pairs (X) / I8 = 9  => 15 pairs (_)
* DURATION: 0:00:44.838188  START: 23:03:00.779982  END: 23:03:45.618170 2019-04-30
* CP COUNT: (37)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B3,D4,D5,E3,E9,F1,F5,H2,H7,I7)
* .2.8...31...3.2...9.36.182738..1.4924.....3752...341681....37...32....1.7..1.9283
* PAIR A1: 5,6 BLK 1
C1: 5,6,4,7                              # reduction candidate for 5,6
C1: 5,6 => CTR
* 5268479318..392...94365182738..164924619283752...341681....37...3247..19754169283
C1: 4,7                                  # 12 pairs
A2: 5,6,8                                # reduction candidate for 5,6
A2: 5,6 => CTR
* .278...31.18372...9.36.182738..1.4924.1.2837527..341681..2837..8324.7.1.7..1.9283
A2: 8                                    # 14 pairs
B2: 5,6,1,7                              # reduction candidate for 5,6
B2: 5,6 => CTR
* .278...31..1372...9.36.182738..1.49241....37527..34168198..37...32....1.7..1.9283
B2: 1,7                                  # 12 pairs
C2: 5,6,1,7,8                            # reduction candidate for 5,6
C2: 5,6 => CTR
* .278...3181.372...9.36.182738..1.4924.1...37527..341681.8..37...32....1.7..1.9283
C2: 1,7,8                                # 11 pairs
* PAIR A1: 5,6 ROW 1
G1: 5,6,9                                # reduction candidate for 5,6
G1: 5,6 => CTR
* .24897.31...352.4.95364182738..1.4924.....3752...341681....375.532.78.1.7461.9283
G1: 9                                    # 24 pairs
* PAIR A1: 5,6 COL A
A8: 5,6,8                                # reduction candidate for 5,6
A8: 8 => CTR
* .278...31.18372...9.36.182738..1.4924.1.2837527..341681..2837..8324.7.1.7..1.9283
A8: 5,6                                  # 14 pairs
* PAIR B3: 4,5 BLK 1
C1: 4,5,6,7                              # reduction candidate for 4,5
C1: 4,5 => SOLVED
* 624875931817392546953641827385716492461928375279534168198263754532487619746159283
C1: 6,7 => CTR
* 5268479318..392...94365182738..164924619283752...341681....37...32.7..197.4169283
* PAIR B3: 4,5 COL B
B9: 4,5,6                                # reduction candidate for 4,5
B9: 6 => CTR
* .2.8...31...3.2...94365182738..1.4924.....3752...341681....37...32....1.76.1.9283
B9: 4,5                                  # 15 pairs
* PAIR F1: 5,7 BLK 2
E1: 5,7,4,9                              # reduction candidate for 5,7
E1: 5,7 => SOLVED
* 624875931817392546953641827385716492461928375279534168198263754532487619746159283
E1: 4,9                                  # 12 pairs
E2: 5,7,9                                # reduction candidate for 5,7
E2: 5,7 => CTR
* .24897.31...352.4.95364182738..1.4924.....3752...341681....375.532.78.1.7461.9283
E2: 9                                    # 24 pairs
* PAIR F1: 5,7 ROW 1
C1: 5,7,4,6                              # reduction candidate for 5,7
C1: 5,7 => CTR
* 6258479318..392...94365182738..1.4924.....37525..341681....37...32.7..197.4169283
C1: 4,6                                  # 19 pairs
* PAIR F1: 5,7 COL F
F4: 5,7,6                                # reduction candidate for 5,7
F4: 5,7                                  # 20 pairs
F8: 5,7,6,8                              # reduction candidate for 5,7
F8: 5,7                                  # 15 pairs
* PAIR E3: 4,5 BLK 2
E1: 4,5,7,9                              # reduction candidate for 4,5
E1: 4,5 => CTR
* .2.8.79318..392...9.36.182738..154924...863752...341681.8..37...32478.197..169283
E1: 7,9 => SOLVED
* 624875931817392546953641827385716492461928375279534168198263754532487619746159283
* PAIR D4: 5,7 BLK 5
F4: 5,7,6                                # reduction candidate for 5,7
F4: 5,7                                  # 20 pairs
D6: 5,7,9                                # reduction candidate for 5,7
D6: 5,7                                  # 15 pairs
* PAIR D4: 5,7 ROW 4
C4: 5,7,6                                # reduction candidate for 5,7
C4: 6                                    # 20 pairs
C4: 5,7                                  # 15 pairs
* PAIR D4: 5,7 COL D
D8: 5,7,4                                # reduction candidate for 5,7
D8: 5,7 => CTR
* .24897.318..35264995364182738.71549246.2..3752..934168198423756.32...91474.1.9283
D8: 4                                    # 14 pairs
* PAIR F5: 6,8 BLK 5
E5: 6,8,2                                # reduction candidate for 6,8
E5: 6,8                                  # 20 pairs
E5: 2                                    # 15 pairs
* PAIR F5: 6,8 COL F
F8: 6,8,5,7                              # reduction candidate for 6,8
F8: 6,8                                  # 20 pairs
F8: 5,7                                  # 15 pairs
* PAIR E9: 5,6 BLK 8
E7: 5,6,2,8                              # reduction candidate for 5,6
E7: 5,6 => SOLVED
* 624875931817392546953641827385716492461928375279534168198263754532487619746159283
E7: 2,8                                  # 12 pairs
E8: 5,6,7,8                              # reduction candidate for 5,6
E8: 5,6 => CTR
* .2.8.5.31...3.2...95364182738..1.4924.....3752...341681....37..532.68914746159283
E8: 7,8                                  # 12 pairs
F8: 5,6,7,8                              # reduction candidate for 5,6
F8: 5,6                                  # 17 pairs
* PAIR E9: 5,6 ROW 9
B9: 5,6,4                                # reduction candidate for 5,6
B9: 5,6 => CTR
* 5268479318..392...94365182738..164924619283752...341681....37...3247..19754169283
B9: 4 => SOLVED
* 624875931817392546953641827385716492461928375279534168198263754532487619746159283
C9: 5,6,4                                # reduction candidate for 5,6
C9: 5,6 => SOLVED
* 624875931817392546953641827385716492461928375279534168198263754532487619746159283
C9: 4 => CTR
* 5268479318..392...94365182738..164924619283752...341681....37...3247..19754169283
* PAIR H7: 4,5 ROW 7
D7: 4,5,2                                # reduction candidate for 4,5
D7: 4,5                                  # 20 pairs
D7: 2                                    # 15 pairs
* PAIR I7: 4,6 BLK 9
I8: 4,6,9                                # reduction candidate for 4,6
I8: 4,6 => CTR
* .24897.31...35264995364182738..1.4924.....3752...341681....375.532.789167461.9283
I8: 9                                    # 15 pairs
* PAIR I7: 4,6 COL I
I2: 4,6,9                                # reduction candidate for 4,6
I2: 9 => CTR
* .24897.31...35264995364182738..1.4924.....3752...341681....375.532.789167461.9283
I2: 4,6                                  # 15 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060510-absurd-base-pr-000.dot
* REASONING
* DIS # C1: 5,6 => CTR => C1: 4,7
* DIS # A2: 5,6 => CTR => A2: 8
* DIS # B2: 5,6 => CTR => B2: 1,7
* DIS # C2: 5,6 => CTR => C2: 1,7,8
* DIS # G1: 5,6 => CTR => G1: 9
* DIS # A8: 8 => CTR => A8: 5,6
* PRF # C1: 4,5 => SOL
* DIS # C1: 6,7 => CTR => C1: 4,5
* DIS # B9: 6 => CTR => B9: 4,5
* PRF # E1: 5,7 => SOL
* DIS # E2: 5,7 => CTR => E2: 9
* DIS # C1: 5,7 => CTR => C1: 4,6
* DIS # E1: 4,5 => CTR => E1: 7,9
* PRF # E1: 7,9 => SOL
* DIS # D8: 5,7 => CTR => D8: 4
* PRF # E7: 5,6 => SOL
* DIS # E8: 5,6 => CTR => E8: 7,8
* DIS # B9: 5,6 => CTR => B9: 4
* PRF # B9: 4 => SOL
* PRF # C9: 5,6 => SOL
* DIS # C9: 4 => CTR => C9: 5,6
* DIS # I8: 4,6 => CTR => I8: 9
* DIS # I2: 9 => CTR => I2: 4,6
* CNT  23 HDP CHAINS /  51 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B3,D4,D5,E3,E9,F1,F5,H2,H7,I7)
* .2.8...31...3.2...9.36.182738..1.4924.....3752...341681....37...32....1.7..1.9283
* PAIR A1: 5,6 BLK 1
C1: 5,6,4,7                              # reduction candidate for 5,6
C1: 5,6 => CTR
* 5268479318..392...94365182738..164924619283752...341681....37...3247..19754169283
A2: 5,6,8                                # reduction candidate for 5,6
A2: 5,6 => CTR
* .278...31.18372...9.36.182738..1.4924.1.2837527..341681..2837..8324.7.1.7..1.9283
B2: 5,6,1,7                              # reduction candidate for 5,6
B2: 5,6 => CTR
* .278...318.1372...9.36.182738..1.49241....37527..34168198..37...32....1.7..1.9283
C2: 5,6,1,7                              # reduction candidate for 5,6
C2: 5,6 => CTR
* .278...3181.372...9.36.182738..1.4924619283752795341681982.37...32487.1.7..1.9283
C2: 1,7 => SOLVED
* 624875931817392546953641827385716492461928375279534168198263754532487619746159283
* DURATION: 0:00:03.581312  START: 23:04:20.225367  END: 23:04:23.806679 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060510-absurd-base-pr-001.dot
* REASONING
* DIS # C1: 5,6 => CTR => C1: 4,7
* DIS C1: 4,7 # A2: 5,6 => CTR => A2: 8
* DIS C1: 4,7 + A2: 8 # B2: 5,6 => CTR => B2: 1,7
* DIS C1: 4,7 + A2: 8 + B2: 1,7 # C2: 5,6 => CTR => C2: 1,7
* PRF C1: 4,7 + A2: 8 + B2: 1,7 + C2: 1,7 => SOL
* STA C1: 4,7 + A2: 8 + B2: 1,7 + C2: 1,7
* CNT   5 HDP CHAINS /   4 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060510, absurd

Solution

position: 624875931817392546953641827385716492461928375279534168198263754532487619746159283 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:

* DIS # C1: 5,6 => CTR => C1: 4,7
* INC # C1: 4,7 => UNS
* DIS # A2: 5,6 => CTR => A2: 8
* INC # A2: 8 => UNS
* DIS # B2: 5,6 => CTR => B2: 1,7
* INC # B2: 1,7 => UNS
* DIS # C2: 5,6 => CTR => C2: 1,7,8
* INC # C2: 1,7,8 => UNS
* DIS # G1: 5,6 => CTR => G1: 9
* INC # G1: 9 => UNS
* INC # A8: 5,6 => UNS
* DIS # A8: 8 => CTR => A8: 5,6
* PRF # C1: 4,5 => SOL
* DIS # C1: 6,7 => CTR => C1: 4,5
* INC # B9: 4,5 => UNS
* DIS # B9: 6 => CTR => B9: 4,5
* PRF # E1: 5,7 => SOL
* INC # E1: 4,9 => UNS
* DIS # E2: 5,7 => CTR => E2: 9
* INC # E2: 9 => UNS
* DIS # C1: 5,7 => CTR => C1: 4,6
* INC # C1: 4,6 => UNS
* INC # F4: 5,7 => UNS
* INC # F8: 5,7 => UNS
* DIS # E1: 4,5 => CTR => E1: 7,9
* PRF # E1: 7,9 => SOL
* INC # F4: 5,7 => UNS
* INC # D6: 5,7 => UNS
* INC # C4: 5,7 => UNS
* INC # C4: 6 => UNS
* DIS # D8: 5,7 => CTR => D8: 4
* INC # D8: 4 => UNS
* INC # E5: 6,8 => UNS
* INC # E5: 2 => UNS
* INC # F8: 6,8 => UNS
* INC # F8: 5,7 => UNS
* PRF # E7: 5,6 => SOL
* INC # E7: 2,8 => UNS
* DIS # E8: 5,6 => CTR => E8: 7,8
* INC # E8: 7,8 => UNS
* INC # F8: 5,6 => UNS
* DIS # B9: 5,6 => CTR => B9: 4
* PRF # B9: 4 => SOL
* PRF # C9: 5,6 => SOL
* DIS # C9: 4 => CTR => C9: 5,6
* INC # D7: 4,5 => UNS
* INC # D7: 2 => UNS
* DIS # I8: 4,6 => CTR => I8: 9
* INC # I8: 9 => UNS
* INC # I2: 4,6 => UNS
* DIS # I2: 9 => CTR => I2: 4,6
* CNT  51 HDP CHAINS /  51 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # C1: 5,6 => CTR => C1: 4,7
* DIS C1: 4,7 # A2: 5,6 => CTR => A2: 8
* DIS C1: 4,7 + A2: 8 # B2: 5,6 => CTR => B2: 1,7
* DIS C1: 4,7 + A2: 8 + B2: 1,7 # C2: 5,6 => CTR => C2: 1,7
* PRF C1: 4,7 + A2: 8 + B2: 1,7 + C2: 1,7 => SOL
* STA C1: 4,7 + A2: 8 + B2: 1,7 + C2: 1,7
* CNT   5 HDP CHAINS /   4 HYP OPENED