Analysis of zz-www.sudokuoftheday.co.uk-20060726-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006
level: medium
position: .....8....7...15...2.7...1...8.......15.8472.7....3..4...3...71..9..5....3..198.. initial
Autosolve
position: .51..8..7.7...15...2.756.1...8127....15.8472.7.25.318458.3.29711.9875...237.198.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 4,6 => CTR => A2: 8,9 * PRF # C2: 3,4 => SOL * DIS # C2: 6 => CTR => C2: 3,4 * DIS # I2: 8,9 => CTR => I2: 2,3,6 * DIS # A4: 3,6 => CTR => A4: 4 * PRF # A4: 4 => SOL * PRF # I5: 3,6 => SOL * DIS # I5: 9 => CTR => I5: 3,6 * PRF # B4: 6,9 => SOL * DIS # B4: 4 => CTR => B4: 6,9 * DIS # I5: 3 => CTR => I5: 6,9 * DIS # H4: 3,6 => CTR => H4: 5,9 * DIS # I4: 3,6 => CTR => I4: 5,9 * PRF # I5: 3,6 => SOL * DIS # I5: 9 => CTR => I5: 3,6 * DIS # A4: 3,6 => CTR => A4: 4 * PRF # A4: 4 => SOL * DIS # C2: 3 => CTR => C2: 4,6 * PRF # B4: 4,6 => SOL * DIS # B4: 9 => CTR => B4: 4,6 * DIS # H9: 5 => CTR => H9: 4,6 * DIS # H9: 5,6 => CTR => H9: 4 * PRF # H9: 4 => SOL * CNT 23 HDP CHAINS / 41 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A2: 4,6 => CTR => A2: 8,9 * PRF A2: 8,9 # C2: 3,4 => SOL * STA A2: 8,9 + C2: 3,4 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....8....7...15...2.7...1...8.......15.8472.7....3..4...3...71..9..5....3..198.. | initial |
| .51..8..7.7...15...2.756.1...8127....15.8472.7.25.318458.3.29711.9875...237.198.. | autosolve |
| 651438297874291563923756418468127359315984726792563184586342971149875632237619845 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) A3: 8,9 C3: 3,4 G3: 3,4 I3: 8,9 A5: 3,6 B6: 6,9 D5: 6,9 E6: 6,9 G4: 3,6 C7: 4,6 B8: 4,6 E7: 4,6 D9: 4,6 I9: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,D2: 2.. / D1 = 2 => 15 pairs (_) / D2 = 2 => 15 pairs (_) G1,I2: 2.. / G1 = 2 => 15 pairs (_) / I2 = 2 => 15 pairs (_) G8,I8: 2.. / G8 = 2 => 15 pairs (_) / I8 = 2 => 15 pairs (_) D1,G1: 2.. / D1 = 2 => 15 pairs (_) / G1 = 2 => 15 pairs (_) D2,I2: 2.. / D2 = 2 => 15 pairs (_) / I2 = 2 => 15 pairs (_) G1,G8: 2.. / G1 = 2 => 15 pairs (_) / G8 = 2 => 15 pairs (_) I2,I8: 2.. / I2 = 2 => 15 pairs (_) / I8 = 2 => 15 pairs (_) C2,C3: 3.. / C2 = 3 => 0 pairs (X) / C3 = 3 => 13 pairs (_) E1,E2: 3.. / E1 = 3 => 15 pairs (_) / E2 = 3 => 15 pairs (_) A4,A5: 3.. / A4 = 3 => 0 pairs (X) / A5 = 3 => 15 pairs (_) C3,G3: 3.. / C3 = 3 => 13 pairs (_) / G3 = 3 => 0 pairs (X) A5,I5: 3.. / A5 = 3 => 15 pairs (_) / I5 = 3 => 0 pairs (X) A4,B4: 4.. / A4 = 4 => 0 pairs (*) / B4 = 4 => 0 pairs (X) C7,B8: 4.. / C7 = 4 => 0 pairs (X) / B8 = 4 => 0 pairs (_) E7,D9: 4.. / E7 = 4 => 0 pairs (*) / D9 = 4 => 0 pairs (X) C3,G3: 4.. / C3 = 4 => 0 pairs (X) / G3 = 4 => 13 pairs (_) C7,E7: 4.. / C7 = 4 => 0 pairs (X) / E7 = 4 => 0 pairs (_) D9,H9: 4.. / D9 = 4 => 0 pairs (X) / H9 = 4 => 0 pairs (_) B4,B8: 4.. / B4 = 4 => 0 pairs (X) / B8 = 4 => 0 pairs (_) H4,I4: 5.. / H4 = 5 => 13 pairs (_) / I4 = 5 => 0 pairs (X) H9,I9: 5.. / H9 = 5 => 0 pairs (X) / I9 = 5 => 13 pairs (_) H4,H9: 5.. / H4 = 5 => 13 pairs (_) / H9 = 5 => 0 pairs (X) I4,I9: 5.. / I4 = 5 => 0 pairs (X) / I9 = 5 => 13 pairs (_) D5,E6: 6.. / D5 = 6 => 0 pairs (X) / E6 = 6 => 0 pairs (_) C7,B8: 6.. / C7 = 6 => 0 pairs (*) / B8 = 6 => 0 pairs (X) E7,D9: 6.. / E7 = 6 => 0 pairs (X) / D9 = 6 => 0 pairs (_) B6,E6: 6.. / B6 = 6 => 0 pairs (X) / E6 = 6 => 0 pairs (_) C7,E7: 6.. / C7 = 6 => 0 pairs (*) / E7 = 6 => 0 pairs (X) C2,C7: 6.. / C2 = 6 => 0 pairs (X) / C7 = 6 => 0 pairs (_) D5,D9: 6.. / D5 = 6 => 0 pairs (X) / D9 = 6 => 0 pairs (_) E6,E7: 6.. / E6 = 6 => 0 pairs (*) / E7 = 6 => 0 pairs (X) A2,A3: 8.. / A2 = 8 => 13 pairs (_) / A3 = 8 => 0 pairs (X) I2,I3: 8.. / I2 = 8 => 0 pairs (X) / I3 = 8 => 13 pairs (_) A2,I2: 8.. / A2 = 8 => 13 pairs (_) / I2 = 8 => 0 pairs (X) A3,I3: 8.. / A3 = 8 => 0 pairs (X) / I3 = 8 => 13 pairs (_) B4,B6: 9.. / B4 = 9 => 0 pairs (X) / B6 = 9 => 0 pairs (_) D5,E6: 9.. / D5 = 9 => 0 pairs (*) / E6 = 9 => 0 pairs (X) A3,I3: 9.. / A3 = 9 => 13 pairs (_) / I3 = 9 => 0 pairs (X) D5,I5: 9.. / D5 = 9 => 0 pairs (*) / I5 = 9 => 0 pairs (X) B6,E6: 9.. / B6 = 9 => 0 pairs (*) / E6 = 9 => 0 pairs (X) * DURATION: 0:00:49.434727 START: 01:18:13.515773 END: 01:19:02.950500 2019-05-01 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,B6,B8,C3,C7,D5,D9,E6,E7,G3,G4,I3,I9) * .51..8..7.7...15...2.756.1...8127....15.8472.7.25.318458.3.29711.9875...237.198.. * PAIR A3: 8,9 BLK 1 A2: 8,9,4,6 # reduction candidate for 8,9 A2: 4,6 => CTR * .51..8..7.7...15.882.756.19..8127.95.1598472.792563184586342971149875..2237.198.. A2: 8,9 # 16 pairs * PAIR C3: 3,4 BLK 1 C2: 3,4,6 # reduction candidate for 3,4 C2: 3,4 => SOLVED * 651438297874291563923756418468127359315984726792563184586342971149875632237619845 C2: 6 => CTR * .51..8..7.76..15...2375641...8127....15.8472.7.25.3184584362971169875.4.2374198.. * PAIR G3: 3,4 BLK 3 G1: 3,4,2,6 # reduction candidate for 3,4 G1: 3,4 # 23 pairs H1: 3,4,6,9 # reduction candidate for 3,4 H1: 3,4 # 17 pairs H2: 3,4,6,9 # reduction candidate for 3,4 H2: 3,4 # 18 pairs * PAIR G3: 3,4 COL G G8: 3,4,2,6 # reduction candidate for 3,4 G8: 3,4 # 18 pairs G8: 2,6 # 15 pairs * PAIR I3: 8,9 BLK 3 I2: 8,9,2,3,6 # reduction candidate for 8,9 I2: 8,9 => CTR * .51..82.7.762.15...2375641..481276.56159847237925631845843.2971169875..2237.198.6 I2: 2,3,6 # 13 pairs * PAIR A5: 3,6 BLK 4 A4: 3,6,4 # reduction candidate for 3,6 A4: 3,6 => CTR * .51..8..7.7...15...2.756.1..48127....15.8472.79256318458.3.29711.9875...237.198.. A4: 4 => SOLVED * 651438297874291563923756418468127359315984726792563184586342971149875632237619845 * PAIR A5: 3,6 ROW 5 I5: 3,6,9 # reduction candidate for 3,6 I5: 3,6 => SOLVED * 651438297874291563923756418468127359315984726792563184586342971149875632237619845 I5: 9 => CTR * .51..8..7.7...15...2.756.1...8127...3156847297625931845863429711.9875...237.198.. * PAIR B6: 6,9 BLK 4 B4: 6,9,4 # reduction candidate for 6,9 B4: 6,9 => SOLVED * 651438297874291563923756418468127359315984726792563184586342971149875632237619845 B4: 4 => CTR * .51..8..7.7...15...2.756.1..48127....15.8472.79256318458.3.29711.9875...237.198.. * PAIR D5: 6,9 ROW 5 I5: 6,9,3 # reduction candidate for 6,9 I5: 3 => CTR * .51..8..7.7...15...2.756.1...8127....15984723792563184586342971149875...237619845 I5: 6,9 # 15 pairs * PAIR G4: 3,6 BLK 6 H4: 3,6,5,9 # reduction candidate for 3,6 H4: 3,6 => CTR * .51..8..7.7...15...2.756.1...8127..5.15.847297.259318458.362971169875...237.198.. H4: 5,9 # 15 pairs I4: 3,6,5,9 # reduction candidate for 3,6 I4: 3,6 => CTR * .51..8..7.7...15...2.756.1...8127.5..15.847297.259318458.362971169875...237.198.. I4: 5,9 # 15 pairs I5: 3,6,9 # reduction candidate for 3,6 I5: 3,6 => SOLVED * 651438297874291563923756418468127359315984726792563184586342971149875632237619845 I5: 9 => CTR * .51..8..7.7...15...2.756.1...8127...3156847297625931845863429711.9875...237.198.. * PAIR G4: 3,6 ROW 4 A4: 3,6,4 # reduction candidate for 3,6 A4: 3,6 => CTR * .51..8..7.7...15...2.756.1..48127....15.8472.79256318458.3.29711.9875...237.198.. A4: 4 => SOLVED * 651438297874291563923756418468127359315984726792563184586342971149875632237619845 * PAIR G4: 3,6 COL G G1: 3,6,2,4 # reduction candidate for 3,6 G1: 3,6 # 15 pairs G8: 3,6,2,4 # reduction candidate for 3,6 G8: 3,6 # 15 pairs * PAIR C7: 4,6 COL C C2: 4,6,3 # reduction candidate for 4,6 C2: 3 => CTR * .51..8..7.73..15...2475631.4.81276..31568472976259318458.3.29711.9875...237.198.. C2: 4,6 # 13 pairs * PAIR B8: 4,6 ROW 8 G8: 4,6,2,3 # reduction candidate for 4,6 G8: 4,6 # 17 pairs H8: 4,6,3 # reduction candidate for 4,6 H8: 4,6 # 17 pairs * PAIR B8: 4,6 COL B B4: 4,6,9 # reduction candidate for 4,6 B4: 4,6 => SOLVED * 651438297874291563923756418468127359315984726792563184586342971149875632237619845 B4: 9 => CTR * .51..8..7.7...15...2.756.1.498127...315.84729762593184586342971149875...2376198.. * PAIR D9: 4,6 ROW 9 H9: 4,6,5 # reduction candidate for 4,6 H9: 5 => CTR * .51..8..7.7...15...2.756.1...8127..5.1568472976259318458.3.29711.9875...237419856 H9: 4,6 # 13 pairs * PAIR I9: 5,6 BLK 9 H9: 5,6,4 # reduction candidate for 5,6 H9: 5,6 => CTR * .51..8..7.7...15...2.756.1...8127....1568472976259318458.3.29711.9875...2374198.. H9: 4 => SOLVED * 651438297874291563923756418468127359315984726792563184586342971149875632237619845 * PAIR I9: 5,6 COL I I4: 5,6,3,9 # reduction candidate for 5,6 I4: 5,6 # 19 pairs I4: 3,9 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060726-absurd-base-pr-000.dot * REASONING * DIS # A2: 4,6 => CTR => A2: 8,9 * PRF # C2: 3,4 => SOL * DIS # C2: 6 => CTR => C2: 3,4 * DIS # I2: 8,9 => CTR => I2: 2,3,6 * DIS # A4: 3,6 => CTR => A4: 4 * PRF # A4: 4 => SOL * PRF # I5: 3,6 => SOL * DIS # I5: 9 => CTR => I5: 3,6 * PRF # B4: 6,9 => SOL * DIS # B4: 4 => CTR => B4: 6,9 * DIS # I5: 3 => CTR => I5: 6,9 * DIS # H4: 3,6 => CTR => H4: 5,9 * DIS # I4: 3,6 => CTR => I4: 5,9 * PRF # I5: 3,6 => SOL * DIS # I5: 9 => CTR => I5: 3,6 * DIS # A4: 3,6 => CTR => A4: 4 * PRF # A4: 4 => SOL * DIS # C2: 3 => CTR => C2: 4,6 * PRF # B4: 4,6 => SOL * DIS # B4: 9 => CTR => B4: 4,6 * DIS # H9: 5 => CTR => H9: 4,6 * DIS # H9: 5,6 => CTR => H9: 4 * PRF # H9: 4 => SOL * CNT 23 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,B6,B8,C3,C7,D5,D9,E6,E7,G3,G4,I3,I9) * .51..8..7.7...15...2.756.1...8127....15.8472.7.25.318458.3.29711.9875...237.198.. * PAIR A3: 8,9 BLK 1 A2: 8,9,4,6 # reduction candidate for 8,9 A2: 4,6 => CTR * .51..8..7.7...15.882.756.19..8127.95.1598472.792563184586342971149875..2237.198.. * PAIR C3: 3,4 BLK 1 C2: 3,4,6 # reduction candidate for 3,4 C2: 3,4 => SOLVED * 651438297874291563923756418468127359315984726792563184586342971149875632237619845 * DURATION: 0:00:02.908419 START: 01:19:31.749721 END: 01:19:34.658140 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060726-absurd-base-pr-001.dot * REASONING * DIS # A2: 4,6 => CTR => A2: 8,9 * PRF A2: 8,9 # C2: 3,4 => SOL * STA A2: 8,9 + C2: 3,4 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060726, absurd
Solution
position: 651438297874291563923756418468127359315984726792563184586342971149875632237619845 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 # A2: 8,9 => UNS * DIS # A2: 4,6 => CTR => A2: 8,9 * PRF # C2: 3,4 => SOL * DIS # C2: 6 => CTR => C2: 3,4 * INC # G1: 3,4 => UNS * INC # H1: 3,4 => UNS * INC # H2: 3,4 => UNS * INC # G8: 3,4 => UNS * INC # G8: 2,6 => UNS * DIS # I2: 8,9 => CTR => I2: 2,3,6 * INC # I2: 2,3,6 => UNS * DIS # A4: 3,6 => CTR => A4: 4 * PRF # A4: 4 => SOL * PRF # I5: 3,6 => SOL * DIS # I5: 9 => CTR => I5: 3,6 * PRF # B4: 6,9 => SOL * DIS # B4: 4 => CTR => B4: 6,9 * INC # I5: 6,9 => UNS * DIS # I5: 3 => CTR => I5: 6,9 * DIS # H4: 3,6 => CTR => H4: 5,9 * INC # H4: 5,9 => UNS * DIS # I4: 3,6 => CTR => I4: 5,9 * INC # I4: 5,9 => UNS * PRF # I5: 3,6 => SOL * DIS # I5: 9 => CTR => I5: 3,6 * DIS # A4: 3,6 => CTR => A4: 4 * PRF # A4: 4 => SOL * INC # G1: 3,6 => UNS * INC # G8: 3,6 => UNS * INC # C2: 4,6 => UNS * DIS # C2: 3 => CTR => C2: 4,6 * INC # G8: 4,6 => UNS * INC # H8: 4,6 => UNS * PRF # B4: 4,6 => SOL * DIS # B4: 9 => CTR => B4: 4,6 * INC # H9: 4,6 => UNS * DIS # H9: 5 => CTR => H9: 4,6 * DIS # H9: 5,6 => CTR => H9: 4 * PRF # H9: 4 => SOL * INC # I4: 5,6 => UNS * INC # I4: 3,9 => UNS * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A2: 8,9 => UNS * DIS # A2: 4,6 => CTR => A2: 8,9 * PRF A2: 8,9 # C2: 3,4 => SOL * STA A2: 8,9 + C2: 3,4 * CNT 3 HDP CHAINS / 3 HYP OPENED