Analysis of zz-www.sudokuoftheday.co.uk-20190427-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019

level: medium

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019

position: .......5...9.1....3..5...48.2..6.....153..6..6...97......9.....4...365....2.4.37. initial

Autosolve

position: .......5..59.1....3..5.9.48.2..65....153..6..6...97..5...952...4..7365..5.284137. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C3: 1 => CTR => C3: 6,7
* PRF # B7: 6,7 => SOL
* DIS # D2: 2,6 => CTR => D2: 4
* DIS # I1: 2,6 => CTR => I1: 1,3,7,9
* DIS # F2: 4 => CTR => F2: 3,8
* DIS # E1: 8 => CTR => E1: 2,7
* DIS # G3: 2,7 => CTR => G3: 1
* PRF # G1: 2,7 => SOL
* DIS # I1: 2,7 => CTR => I1: 1,3,6,9
* DIS # I2: 2,7 => CTR => I2: 3,6
* DIS # G3: 2,7 => CTR => G3: 1
* DIS # A2: 8 => CTR => A2: 2,7
* DIS # A4: 7,9 => CTR => A4: 8
* DIS # I5: 2,4 => CTR => I5: 7,9
* DIS # D6: 1,4 => CTR => D6: 2
* DIS # E1: 2,8 => CTR => E1: 7
* DIS # F2: 3 => CTR => F2: 4,8
* DIS # I5: 2,9 => CTR => I5: 4,7
* DIS # H8: 1,8 => CTR => H8: 2,9
* PRF # H8: 8,9 => SOL
* DIS # A7: 1,8 => CTR => A7: 7
* PRF # A7: 7 => SOL
* DIS # C7: 1,8 => CTR => C7: 3,6,7
* DIS # H8: 1,8 => CTR => H8: 2,9
* CNT  24 HDP CHAINS /  52 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: 1 => CTR => C3: 6,7
* PRF C3: 6,7 # B7: 6,7 => SOL
* STA C3: 6,7 + B7: 6,7
* CNT   2 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

.......5...9.1....3..5...48.2..6.....153..6..6...97......9.....4...365....2.4.37. initial
.......5..59.1....3..5.9.48.2..65....153..6..6...97..5...952...4..7365..5.284137. autosolve
148673259259418763376529148827165934915384627634297815763952481481736592592841376 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
B3: 6,7
D1: 2,6
F1: 3,8
E3: 2,7
G2: 2,7
A5: 7,9
D4: 1,4
E5: 2,8
F5: 4,8
H5: 2,9
B8: 8,9
C8: 1,8
B9: 6,9
I9: 6,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D4,D6: 1.. / D4 = 1  => 14 pairs (_) / D6 = 1  =>  0 pairs (X)
C3,G3: 1.. / C3 = 1  =>  0 pairs (X) / G3 = 1  => 24 pairs (_)
A1,A7: 1.. / A1 = 1  =>  0 pairs (*) / A7 = 1  =>  0 pairs (X)
A1,A2: 2.. / A1 = 2  =>  0 pairs (X) / A2 = 2  => 13 pairs (_)
E5,D6: 2.. / E5 = 2  =>  0 pairs (X) / D6 = 2  => 13 pairs (_)
H8,I8: 2.. / H8 = 2  =>  0 pairs (X) / I8 = 2  => 14 pairs (_)
E3,G3: 2.. / E3 = 2  => 13 pairs (_) / G3 = 2  =>  0 pairs (X)
F1,F2: 3.. / F1 = 3  => 14 pairs (_) / F2 = 3  =>  0 pairs (X)
B7,C7: 3.. / B7 = 3  => 18 pairs (_) / C7 = 3  =>  0 pairs (*)
F1,I1: 3.. / F1 = 3  => 14 pairs (_) / I1 = 3  =>  0 pairs (X)
B6,B7: 3.. / B6 = 3  =>  0 pairs (*) / B7 = 3  =>  0 pairs (X)
B1,C1: 4.. / B1 = 4  => 15 pairs (_) / C1 = 4  => 20 pairs (_)
D2,F2: 4.. / D2 = 4  => 13 pairs (_) / F2 = 4  =>  0 pairs (X)
G7,I7: 4.. / G7 = 4  => 15 pairs (_) / I7 = 4  => 14 pairs (_)
F5,I5: 4.. / F5 = 4  => 13 pairs (_) / I5 = 4  =>  0 pairs (X)
B1,B6: 4.. / B1 = 4  => 15 pairs (_) / B6 = 4  => 20 pairs (_)
F2,F5: 4.. / F2 = 4  =>  0 pairs (X) / F5 = 4  => 13 pairs (_)
B3,C3: 6.. / B3 = 6  =>  0 pairs (X) / C3 = 6  => 23 pairs (_)
D1,D2: 6.. / D1 = 6  => 14 pairs (_) / D2 = 6  =>  0 pairs (X)
D1,I1: 6.. / D1 = 6  => 14 pairs (_) / I1 = 6  =>  0 pairs (X)
B9,I9: 6.. / B9 = 6  =>  0 pairs (X) / I9 = 6  =>  0 pairs (_)
C3,C7: 6.. / C3 = 6  => 23 pairs (_) / C7 = 6  =>  0 pairs (X)
H2,H7: 6.. / H2 = 6  => 15 pairs (_) / H7 = 6  =>  0 pairs (X)
E1,E3: 7.. / E1 = 7  => 13 pairs (_) / E3 = 7  =>  0 pairs (X)
A5,I5: 7.. / A5 = 7  =>  0 pairs (X) / I5 = 7  => 13 pairs (_)
E5,F5: 8.. / E5 = 8  => 13 pairs (_) / F5 = 8  =>  0 pairs (X)
A2,F2: 8.. / A2 = 8  =>  0 pairs (X) / F2 = 8  => 13 pairs (_)
E1,E5: 8.. / E1 = 8  =>  0 pairs (X) / E5 = 8  => 13 pairs (_)
G1,I1: 9.. / G1 = 9  => 14 pairs (_) / I1 = 9  =>  0 pairs (*)
A4,A5: 9.. / A4 = 9  =>  0 pairs (X) / A5 = 9  => 13 pairs (_)
B8,B9: 9.. / B8 = 9  =>  0 pairs (X) / B9 = 9  =>  0 pairs (_)
B9,I9: 9.. / B9 = 9  =>  0 pairs (*) / I9 = 9  =>  0 pairs (X)
G1,G4: 9.. / G1 = 9  => 14 pairs (_) / G4 = 9  =>  0 pairs (*)
* DURATION: 0:00:36.475378  START: 05:38:14.105481  END: 05:38:50.580859 2019-05-01
* CP COUNT: (33)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B3,B8,B9,C8,D1,D4,E3,E5,F1,F5,G2,H5,I9)
* .......5..59.1....3..5.9.48.2..65....153..6..6...97..5...952...4..7365..5.284137.
* PAIR B3: 6,7 BLK 1
C3: 6,7,1                                # reduction candidate for 6,7
C3: 1 => CTR
* .......5..59.1....3615.9.48.2..65....153..6..6...97..51.6952.8.4..7365..5.284137.
C3: 6,7                                  # 24 pairs
* PAIR B3: 6,7 COL B
B7: 6,7,3,8                              # reduction candidate for 6,7
B7: 6,7 => SOLVED
* 148673259259418763376529148827165934915384627634297815763952481481736592592841376
B7: 3,8                                  # 18 pairs
* PAIR D1: 2,6 BLK 2
D2: 2,6,4                                # reduction candidate for 2,6
D2: 2,6 => CTR
* ....83.5.859.14...3..579248.2..65...7153286946...97.251..9524.64.87365..5.284137.
D2: 4                                    # 13 pairs
* PAIR D1: 2,6 ROW 1
I1: 2,6,1,3,7,9                          # reduction candidate for 2,6
I1: 2,6 => CTR
* ...6739522594187..3..529148.2.165....1538462.6..297.15...952...4..7365..5.284137.
I1: 1,3,7,9                              # 14 pairs
* PAIR F1: 3,8 BLK 2
F2: 3,8,4                                # reduction candidate for 3,8
F2: 4 => CTR
* 2..683.5.8592147..3..579248.2..65..77153286946...97.251..9524.64.87365..5.284137.
F2: 3,8                                  # 13 pairs
* PAIR E3: 2,7 BLK 2
E1: 2,7,8                                # reduction candidate for 2,7
E1: 8 => CTR
* ....83.5.859.14...3..579248.2..65....153286946...97.25...9524..4..7365.25.2841379
E1: 2,7                                  # 13 pairs
* PAIR E3: 2,7 ROW 3
G3: 2,7,1                                # reduction candidate for 2,7
G3: 2,7 => CTR
* .......5..59.1....3.15.9.48.2..65....153..6..6...97..51.6952.8.4..7365..5.284137.
G3: 1                                    # 24 pairs
* PAIR G2: 2,7 BLK 3
G1: 2,7,1,9                              # reduction candidate for 2,7
G1: 2,7 => SOLVED
* 148673259259418763376529148827165934915384627634297815763952481481736592592841376
G1: 1,9                                  # 15 pairs
I1: 2,7,1,3,6,9                          # reduction candidate for 2,7
I1: 2,7 => CTR
* ...6739522594187..3..529148.2.165....1538462.6..297.15...952...4..7365..5.284137.
I1: 1,3,6,9                              # 14 pairs
I2: 2,7,3,6                              # reduction candidate for 2,7
I2: 2,7 => CTR
* 2416789538594132673..529148.2.165....153846..6..297.151..952.8.4.87365.15.284137.
I2: 3,6                                  # 15 pairs
G3: 2,7,1                                # reduction candidate for 2,7
G3: 2,7 => CTR
* .......5..59.1....3.15.9.48.2..65....153..6..6...97..51.6952.8.4..7365..5.284137.
G3: 1                                    # 24 pairs
* PAIR G2: 2,7 ROW 2
A2: 2,7,8                                # reduction candidate for 2,7
A2: 8 => CTR
* 2416..95.859.1....376529148.2..65....153846..68.297415137952864498736521562841379
A2: 2,7                                  # 13 pairs
* PAIR A5: 7,9 BLK 4
A4: 7,9,8                                # reduction candidate for 7,9
A4: 7,9 => CTR
* 2.167.9538594132673765291489241657..7153846926.3297.15.37952..649.736521562841379
A4: 8                                    # 22 pairs
* PAIR A5: 7,9 ROW 5
I5: 7,9,2,4                              # reduction candidate for 7,9
I5: 2,4 => CTR
* 2.167.95385941326737652914892.16573471538469268.297.15.37952...49.736521562841379
I5: 7,9                                  # 13 pairs
* PAIR D4: 1,4 BLK 5
D6: 1,4,2                                # reduction candidate for 1,4
D6: 1,4 => CTR
* ....8395.859.14...3..57924892..65...7153286946...97.251..9524.64.87365..5.284137.
D6: 2                                    # 13 pairs
* PAIR D4: 1,4 ROW 4
G4: 1,4,7,8,9                            # reduction candidate for 1,4
G4: 1,4                                  # 16 pairs
I4: 1,4,3,7,9                            # reduction candidate for 1,4
I4: 1,4                                  # 19 pairs
* PAIR E5: 2,8 COL E
E1: 2,8,7                                # reduction candidate for 2,8
E1: 2,8 => CTR
* .......5..59.1.7..361579248.2..65....153..6..6...97..51.6952.8.4..7365..5.284137.
E1: 7                                    # 13 pairs
* PAIR F5: 4,8 COL F
F2: 4,8,3                                # reduction candidate for 4,8
F2: 3 => CTR
* 2..6789538594132673..529148.2.16578..153846..6..297..51..952...4.87365.15.284137.
F2: 4,8                                  # 14 pairs
* PAIR H5: 2,9 BLK 6
I5: 2,9,4,7                              # reduction candidate for 2,9
I5: 2,9 => CTR
* ..167.953.5941326737652914892.1657..7153846..6..297.15.37952...498736521562841379
I5: 4,7                                  # 15 pairs
* PAIR H5: 2,9 COL H
H8: 2,9,1,8                              # reduction candidate for 2,9
H8: 1,8 => CTR
* ......95..59.1....376529148.2..65....153846276..297.15...952..1491736582562841379
H8: 2,9                                  # 17 pairs
* PAIR B8: 8,9 ROW 8
H8: 8,9,1,2                              # reduction candidate for 8,9
H8: 8,9 => SOLVED
* 148673259259418763376529148827165934915384627634297815763952481481736592592841376
H8: 1,2                                  # 16 pairs
* PAIR C8: 1,8 BLK 7
A7: 1,8,7                                # reduction candidate for 1,8
A7: 1,8 => CTR
* 2.167.9538594132673765291489241657..7153846926.3297.15.37952..649.736521562841379
A7: 7 => SOLVED
* 148673259259418763376529148827165934915384627634297815763952481481736592592841376
C7: 1,8,3,6,7                            # reduction candidate for 1,8
C7: 1,8 => CTR
* ......95..59.1....376529148.27.65...9153846276.3297.1573.952...49.736582562841379
C7: 3,6,7                                # 14 pairs
* PAIR C8: 1,8 ROW 8
H8: 1,8,2,9                              # reduction candidate for 1,8
H8: 1,8 => CTR
* ......95..59.1....376529148.2..65....153846276..297.15...952..1491736582562841379
H8: 2,9                                  # 17 pairs
* PAIR C8: 1,8 COL C
C1: 1,8,4,7                              # reduction candidate for 1,8
C1: 1,8                                  # 27 pairs
C1: 4,7                                  # 15 pairs
* PAIR I9: 6,9 COL I
I1: 6,9,1,2,3,7                          # reduction candidate for 6,9
I1: 6,9                                  # 18 pairs
I1: 1,2,3,7                              # 14 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190427-absurd-base-pr-000.dot
* REASONING
* DIS # C3: 1 => CTR => C3: 6,7
* PRF # B7: 6,7 => SOL
* DIS # D2: 2,6 => CTR => D2: 4
* DIS # I1: 2,6 => CTR => I1: 1,3,7,9
* DIS # F2: 4 => CTR => F2: 3,8
* DIS # E1: 8 => CTR => E1: 2,7
* DIS # G3: 2,7 => CTR => G3: 1
* PRF # G1: 2,7 => SOL
* DIS # I1: 2,7 => CTR => I1: 1,3,6,9
* DIS # I2: 2,7 => CTR => I2: 3,6
* DIS # G3: 2,7 => CTR => G3: 1
* DIS # A2: 8 => CTR => A2: 2,7
* DIS # A4: 7,9 => CTR => A4: 8
* DIS # I5: 2,4 => CTR => I5: 7,9
* DIS # D6: 1,4 => CTR => D6: 2
* DIS # E1: 2,8 => CTR => E1: 7
* DIS # F2: 3 => CTR => F2: 4,8
* DIS # I5: 2,9 => CTR => I5: 4,7
* DIS # H8: 1,8 => CTR => H8: 2,9
* PRF # H8: 8,9 => SOL
* DIS # A7: 1,8 => CTR => A7: 7
* PRF # A7: 7 => SOL
* DIS # C7: 1,8 => CTR => C7: 3,6,7
* DIS # H8: 1,8 => CTR => H8: 2,9
* CNT  24 HDP CHAINS /  52 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B3,B8,B9,C8,D1,D4,E3,E5,F1,F5,G2,H5,I9)
* .......5..59.1....3..5.9.48.2..65....153..6..6...97..5...952...4..7365..5.284137.
* PAIR B3: 6,7 BLK 1
C3: 6,7,1                                # reduction candidate for 6,7
C3: 1 => CTR
* .......5..59.1....3615.9.48.2..65....153..6..6...97..51.6952.8.4..7365..5.284137.
* PAIR B3: 6,7 COL B
B7: 6,7,3                                # reduction candidate for 6,7
B7: 6,7 => SOLVED
* 148673259259418763376529148827165934915384627634297815763952481481736592592841376
* DURATION: 0:00:02.998335  START: 05:39:22.271352  END: 05:39:25.269687 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190427-absurd-base-pr-001.dot
* REASONING
* DIS # C3: 1 => CTR => C3: 6,7
* PRF C3: 6,7 # B7: 6,7 => SOL
* STA C3: 6,7 + B7: 6,7
* CNT   2 HDP CHAINS /   3 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190427, absurd

Solution

position: 148673259259418763376529148827165934915384627634297815763952481481736592592841376 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 # C3: 6,7 => UNS
* DIS # C3: 1 => CTR => C3: 6,7
* PRF # B7: 6,7 => SOL
* INC # B7: 3,8 => UNS
* DIS # D2: 2,6 => CTR => D2: 4
* INC # D2: 4 => UNS
* DIS # I1: 2,6 => CTR => I1: 1,3,7,9
* INC # I1: 1,3,7,9 => UNS
* INC # F2: 3,8 => UNS
* DIS # F2: 4 => CTR => F2: 3,8
* INC # E1: 2,7 => UNS
* DIS # E1: 8 => CTR => E1: 2,7
* DIS # G3: 2,7 => CTR => G3: 1
* INC # G3: 1 => UNS
* PRF # G1: 2,7 => SOL
* INC # G1: 1,9 => UNS
* DIS # I1: 2,7 => CTR => I1: 1,3,6,9
* INC # I1: 1,3,6,9 => UNS
* DIS # I2: 2,7 => CTR => I2: 3,6
* INC # I2: 3,6 => UNS
* DIS # G3: 2,7 => CTR => G3: 1
* INC # G3: 1 => UNS
* INC # A2: 2,7 => UNS
* DIS # A2: 8 => CTR => A2: 2,7
* DIS # A4: 7,9 => CTR => A4: 8
* INC # A4: 8 => UNS
* INC # I5: 7,9 => UNS
* DIS # I5: 2,4 => CTR => I5: 7,9
* DIS # D6: 1,4 => CTR => D6: 2
* INC # D6: 2 => UNS
* INC # G4: 1,4 => UNS
* INC # I4: 1,4 => UNS
* DIS # E1: 2,8 => CTR => E1: 7
* INC # E1: 7 => UNS
* INC # F2: 4,8 => UNS
* DIS # F2: 3 => CTR => F2: 4,8
* DIS # I5: 2,9 => CTR => I5: 4,7
* INC # I5: 4,7 => UNS
* INC # H8: 2,9 => UNS
* DIS # H8: 1,8 => CTR => H8: 2,9
* PRF # H8: 8,9 => SOL
* INC # H8: 1,2 => UNS
* DIS # A7: 1,8 => CTR => A7: 7
* PRF # A7: 7 => SOL
* DIS # C7: 1,8 => CTR => C7: 3,6,7
* INC # C7: 3,6,7 => UNS
* DIS # H8: 1,8 => CTR => H8: 2,9
* INC # H8: 2,9 => UNS
* INC # C1: 1,8 => UNS
* INC # C1: 4,7 => UNS
* INC # I1: 6,9 => UNS
* INC # I1: 1,2,3,7 => UNS
* CNT  52 HDP CHAINS /  52 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C3: 6,7 => UNS
* DIS # C3: 1 => CTR => C3: 6,7
* PRF C3: 6,7 # B7: 6,7 => SOL
* STA C3: 6,7 + B7: 6,7
* CNT   3 HDP CHAINS /   3 HYP OPENED