Analysis of zz-www.sudokuoftheday.co.uk-20190116-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019
level: medium
position: ...34....37...8...294..56.........16.61...3..9...8.......8132.7.2.5........2.7.35 initial
Autosolve
position: ...346...376928...294175683....3..16.61.5.3..93.681......8132.77235.4......2.7.35 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # H1: 7,9 => SOL * DIS # G4: 7,9 => CTR => G4: 8 * PRF # G4: 8 => SOL * DIS # H1: 7 => CTR => H1: 2,9 * PRF # I5: 2,9 => SOL * DIS # I5: 8 => CTR => I5: 2,9 * PRF # G2: 4,5 => SOL * DIS # G2: 1 => CTR => G2: 4,5 * PRF # H6: 2,7 => SOL * DIS # G2: 5 => CTR => G2: 1,4 * PRF # H6: 2,7 => SOL * DIS # H5: 2,9 => CTR => H5: 7 * PRF # H5: 7 => SOL * PRF # I5: 2,9 => SOL * DIS # I5: 8 => CTR => I5: 2,9 * DIS # B4: 8 => CTR => B4: 4,5 * PRF # H7: 4 => SOL * CNT 17 HDP CHAINS / 36 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # H1: 7,9 => SOL * STA H1: 7,9 * CNT 1 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...34....37...8...294..56.........16.61...3..9...8.......8132.7.2.5........2.7.35 | initial |
| ...346...376928...294175683....3..16.61.5.3..93.681......8132.77235.4......2.7.35 | autosolve |
| 185346792376928451294175683542739816861452379937681524659813247723594168418267935 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (22) C1: 5,8 G1: 7,9 I1: 2,9 H2: 4,5 I2: 1,4 C4: 2,7 A5: 4,8 C6: 2,7 D4: 4,7 F4: 2,9 D5: 4,7 F5: 2,9 I6: 2,4 B7: 4,5 C7: 5,9 C9: 8,9 E8: 6,9 E9: 6,9 G8: 1,8 H8: 6,9 I8: 1,8 G9: 4,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,B1: 1.. / A1 = 1 => 23 pairs (_) / B1 = 1 => 23 pairs (_) G2,I2: 1.. / G2 = 1 => 0 pairs (X) / I2 = 1 => 0 pairs (_) A9,B9: 1.. / A9 = 1 => 23 pairs (_) / B9 = 1 => 23 pairs (_) G8,I8: 1.. / G8 = 1 => 0 pairs (*) / I8 = 1 => 0 pairs (X) A1,A9: 1.. / A1 = 1 => 23 pairs (_) / A9 = 1 => 23 pairs (_) B1,B9: 1.. / B1 = 1 => 23 pairs (_) / B9 = 1 => 23 pairs (_) G2,G8: 1.. / G2 = 1 => 0 pairs (X) / G8 = 1 => 0 pairs (_) I2,I8: 1.. / I2 = 1 => 0 pairs (*) / I8 = 1 => 0 pairs (X) H1,I1: 2.. / H1 = 2 => 24 pairs (_) / I1 = 2 => 0 pairs (*) C4,C6: 2.. / C4 = 2 => 22 pairs (_) / C6 = 2 => 0 pairs (X) F4,F5: 2.. / F4 = 2 => 0 pairs (X) / F5 = 2 => 22 pairs (_) C4,F4: 2.. / C4 = 2 => 22 pairs (_) / F4 = 2 => 0 pairs (X) D4,D5: 4.. / D4 = 4 => 0 pairs (X) / D5 = 4 => 0 pairs (_) H7,G9: 4.. / H7 = 4 => 0 pairs (*) / G9 = 4 => 0 pairs (X) A5,D5: 4.. / A5 = 4 => 0 pairs (X) / D5 = 4 => 0 pairs (_) I2,I6: 4.. / I2 = 4 => 0 pairs (X) / I6 = 4 => 0 pairs (_) G2,H2: 5.. / G2 = 5 => 0 pairs (X) / H2 = 5 => 22 pairs (_) A4,B4: 5.. / A4 = 5 => 25 pairs (_) / B4 = 5 => 34 pairs (_) G6,H6: 5.. / G6 = 5 => 22 pairs (_) / H6 = 5 => 0 pairs (X) C1,C7: 5.. / C1 = 5 => 23 pairs (_) / C7 = 5 => 26 pairs (_) G2,G6: 5.. / G2 = 5 => 0 pairs (X) / G6 = 5 => 22 pairs (_) H2,H6: 5.. / H2 = 5 => 22 pairs (_) / H6 = 5 => 0 pairs (X) A7,A9: 6.. / A7 = 6 => 20 pairs (_) / A9 = 6 => 24 pairs (_) E8,E9: 6.. / E8 = 6 => 24 pairs (_) / E9 = 6 => 20 pairs (_) H7,H8: 6.. / H7 = 6 => 24 pairs (_) / H8 = 6 => 20 pairs (_) A7,H7: 6.. / A7 = 6 => 20 pairs (_) / H7 = 6 => 24 pairs (_) E8,H8: 6.. / E8 = 6 => 24 pairs (_) / H8 = 6 => 20 pairs (_) A9,E9: 6.. / A9 = 6 => 24 pairs (_) / E9 = 6 => 20 pairs (_) G1,H1: 7.. / G1 = 7 => 24 pairs (_) / H1 = 7 => 0 pairs (X) C4,C6: 7.. / C4 = 7 => 0 pairs (X) / C6 = 7 => 22 pairs (_) D4,D5: 7.. / D4 = 7 => 0 pairs (*) / D5 = 7 => 0 pairs (X) D5,H5: 7.. / D5 = 7 => 0 pairs (X) / H5 = 7 => 0 pairs (_) G4,I5: 8.. / G4 = 8 => 0 pairs (*) / I5 = 8 => 0 pairs (X) G8,I8: 8.. / G8 = 8 => 0 pairs (X) / I8 = 8 => 0 pairs (_) A5,I5: 8.. / A5 = 8 => 0 pairs (*) / I5 = 8 => 0 pairs (X) C1,C9: 8.. / C1 = 8 => 26 pairs (_) / C9 = 8 => 23 pairs (_) G4,G8: 8.. / G4 = 8 => 0 pairs (*) / G8 = 8 => 0 pairs (X) I5,I8: 8.. / I5 = 8 => 0 pairs (X) / I8 = 8 => 0 pairs (_) F4,F5: 9.. / F4 = 9 => 22 pairs (_) / F5 = 9 => 0 pairs (X) C7,C9: 9.. / C7 = 9 => 23 pairs (_) / C9 = 9 => 26 pairs (_) E8,E9: 9.. / E8 = 9 => 20 pairs (_) / E9 = 9 => 24 pairs (_) F4,G4: 9.. / F4 = 9 => 22 pairs (_) / G4 = 9 => 0 pairs (X) C7,H7: 9.. / C7 = 9 => 23 pairs (_) / H7 = 9 => 26 pairs (_) E8,H8: 9.. / E8 = 9 => 20 pairs (_) / H8 = 9 => 24 pairs (_) I1,I5: 9.. / I1 = 9 => 24 pairs (_) / I5 = 9 => 0 pairs (*) * DURATION: 0:00:57.504767 START: 02:58:57.422590 END: 02:59:54.927357 2019-05-01 * CP COUNT: (45) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B7,C1,C4,C6,C7,C9,D4,D5,E8,E9,F4,F5,G1,G8,G9,H2,H8,I1,I2,I6,I8) * ...346...376928...294175683....3..16.61.5.3..93.681......8132.77235.4......2.7.35 * PAIR C1: 5,8 BLK 1 A1: 5,8,1 # reduction candidate for 5,8 A1: 5,8 # 23 pairs B1: 5,8,1 # reduction candidate for 5,8 B1: 5,8 # 23 pairs * PAIR G1: 7,9 BLK 3 H1: 7,9,2 # reduction candidate for 7,9 H1: 7,9 => SOLVED * 185346792376928451294175683542739816861452379937681524659813247723594168418267935 H1: 2 # 24 pairs * PAIR G1: 7,9 COL G G4: 7,9,8 # reduction candidate for 7,9 G4: 7,9 => CTR * ...346..9376928154294175683....3..1646175.3.893.681542.4.8132.77235.48.1...2.7435 G4: 8 => SOLVED * 185346792376928451294175683542739816861452379937681524659813247723594168418267935 * PAIR I1: 2,9 BLK 3 H1: 2,9,7 # reduction candidate for 2,9 H1: 7 => CTR * ...346.72376928...294175683....3..16.6175.3.993.681..4...8132.77235.4..8...2.7.35 H1: 2,9 # 24 pairs * PAIR I1: 2,9 COL I I5: 2,9,8 # reduction candidate for 2,9 I5: 2,9 => SOLVED * 185346792376928451294175683542739816861452379937681524659813247723594168418267935 I5: 8 => CTR * ...346729376928154294175683..2739.16.61.5.3.893.681..2...8132.77235.48.1...2.7.35 * PAIR H2: 4,5 BLK 3 G2: 4,5,1 # reduction candidate for 4,5 G2: 4,5 => SOLVED * 185346792376928451294175683542739816861452379937681524659813247723594168418267935 G2: 1 => CTR * ...346.29376928154294175683..2.39716.61.5.3..93.681542...8132.77235.48.1...2.7435 * PAIR H2: 4,5 COL H H6: 4,5,2,7 # reduction candidate for 4,5 H6: 2,7 => SOLVED * 185346792376928451294175683542739816861452379937681524659813247723594168418267935 H6: 4,5 # 30 pairs * PAIR I2: 1,4 BLK 3 G2: 1,4,5 # reduction candidate for 1,4 G2: 5 => CTR * ...346...376928541294175683....3.81686145.37.93.681.54...8132.77235.41.8...2.7435 G2: 1,4 # 22 pairs * PAIR A5: 4,8 BLK 4 A4: 4,8,5 # reduction candidate for 4,8 A4: 4,8 # 34 pairs B4: 4,8,5 # reduction candidate for 4,8 B4: 4,8 # 25 pairs * PAIR A5: 4,8 COL A A9: 4,8,1,6 # reduction candidate for 4,8 A9: 4,8 # 23 pairs A9: 1,6 # 23 pairs * PAIR C6: 2,7 ROW 6 H6: 2,7,4,5 # reduction candidate for 2,7 H6: 2,7 => SOLVED * 185346792376928451294175683542739816861452379937681524659813247723594168418267935 H6: 4,5 # 30 pairs * PAIR F5: 2,9 ROW 5 H5: 2,9,7 # reduction candidate for 2,9 H5: 2,9 => CTR * ...346..9376928154294175683...43..1646175.3.893.681542.4.8132.77235.48.1...2.7435 H5: 7 => SOLVED * 185346792376928451294175683542739816861452379937681524659813247723594168418267935 I5: 2,9,8 # reduction candidate for 2,9 I5: 2,9 => SOLVED * 185346792376928451294175683542739816861452379937681524659813247723594168418267935 I5: 8 => CTR * ...346729376928154294175683..2739.16.61.5.3.893.681..2...8132.77235.48.1...2.7.35 * PAIR I6: 2,4 BLK 6 H6: 2,4,5,7 # reduction candidate for 2,4 H6: 5,7 # 23 pairs H6: 2,4 # 22 pairs * PAIR B7: 4,5 BLK 7 A7: 4,5,6 # reduction candidate for 4,5 A7: 4,5 # 24 pairs A7: 6 # 20 pairs * PAIR B7: 4,5 COL B B4: 4,5,8 # reduction candidate for 4,5 B4: 8 => CTR * ...346..937692815429417568358.43..1646175.3.893.6815426458132977235.4861...267.35 B4: 4,5 # 26 pairs * PAIR H8: 6,9 BLK 9 H7: 6,9,4 # reduction candidate for 6,9 H7: 4 => SOLVED * 185346792376928451294175683542739816861452379937681524659813247723594168418267935 H7: 6,9 # 30 pairs * PAIR G9: 4,9 BLK 9 H7: 4,9,6 # reduction candidate for 4,9 H7: 6 # 24 pairs H7: 4,9 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190116-absurd-base-pr-000.dot * REASONING * PRF # H1: 7,9 => SOL * DIS # G4: 7,9 => CTR => G4: 8 * PRF # G4: 8 => SOL * DIS # H1: 7 => CTR => H1: 2,9 * PRF # I5: 2,9 => SOL * DIS # I5: 8 => CTR => I5: 2,9 * PRF # G2: 4,5 => SOL * DIS # G2: 1 => CTR => G2: 4,5 * PRF # H6: 2,7 => SOL * DIS # G2: 5 => CTR => G2: 1,4 * PRF # H6: 2,7 => SOL * DIS # H5: 2,9 => CTR => H5: 7 * PRF # H5: 7 => SOL * PRF # I5: 2,9 => SOL * DIS # I5: 8 => CTR => I5: 2,9 * DIS # B4: 8 => CTR => B4: 4,5 * PRF # H7: 4 => SOL * CNT 17 HDP CHAINS / 36 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B7,C1,C4,C6,C7,C9,D4,D5,E8,E9,F4,F5,G1,G8,G9,H2,H8,I1,I2,I6,I8) * ...346...376928...294175683....3..16.61.5.3..93.681......8132.77235.4......2.7.35 * PAIR C1: 5,8 BLK 1 A1: 5,8,1 # reduction candidate for 5,8 A1: 5,8 # 23 pairs B1: 5,8,1 # reduction candidate for 5,8 B1: 5,8 # 23 pairs * PAIR G1: 7,9 BLK 3 H1: 7,9,2 # reduction candidate for 7,9 H1: 7,9 => SOLVED * 185346792376928451294175683542739816861452379937681524659813247723594168418267935 * DURATION: 0:00:02.952526 START: 03:00:22.683042 END: 03:00:25.635568 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190116-absurd-base-pr-001.dot * REASONING * PRF # H1: 7,9 => SOL * STA H1: 7,9 * CNT 1 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190116, absurd
Solution
position: 185346792376928451294175683542739816861452379937681524659813247723594168418267935 solved
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 # A1: 5,8 => UNS * INC # B1: 5,8 => UNS * PRF # H1: 7,9 => SOL * INC # H1: 2 => UNS * DIS # G4: 7,9 => CTR => G4: 8 * PRF # G4: 8 => SOL * INC # H1: 2,9 => UNS * DIS # H1: 7 => CTR => H1: 2,9 * PRF # I5: 2,9 => SOL * DIS # I5: 8 => CTR => I5: 2,9 * PRF # G2: 4,5 => SOL * DIS # G2: 1 => CTR => G2: 4,5 * INC # H6: 4,5 => UNS * PRF # H6: 2,7 => SOL * INC # G2: 1,4 => UNS * DIS # G2: 5 => CTR => G2: 1,4 * INC # A4: 4,8 => UNS * INC # B4: 4,8 => UNS * INC # A9: 4,8 => UNS * INC # A9: 1,6 => UNS * PRF # H6: 2,7 => SOL * INC # H6: 4,5 => UNS * DIS # H5: 2,9 => CTR => H5: 7 * PRF # H5: 7 => SOL * PRF # I5: 2,9 => SOL * DIS # I5: 8 => CTR => I5: 2,9 * INC # H6: 2,4 => UNS * INC # H6: 5,7 => UNS * INC # A7: 4,5 => UNS * INC # A7: 6 => UNS * INC # B4: 4,5 => UNS * DIS # B4: 8 => CTR => B4: 4,5 * INC # H7: 6,9 => UNS * PRF # H7: 4 => SOL * INC # H7: 4,9 => UNS * INC # H7: 6 => UNS * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 5,8 => UNS * INC # B1: 5,8 => UNS * PRF # H1: 7,9 => SOL * STA H1: 7,9 * CNT 3 HDP CHAINS / 3 HYP OPENED