Analysis of zz-www.sudokuoftheday.co.uk-20060316-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006
level: medium
position: .6.....4..47......95..1.6.3.7...3.8.5......9489....7.1..98.61.......1.6..1.37.... initial
Autosolve
position: .6.....4..47....1.95..1.6.3.7...3.865......9489....7.1..98.61...8...1.6.61.37.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A7: 2,3 => SOL * DIS # A8: 2,3 => CTR => A8: 4,7 * DIS # H7: 2,7 => CTR => H7: 3,5 * DIS # C6: 4,6 => CTR => C6: 2,3 * DIS # D5: 7 => CTR => D5: 1,6 * DIS # H6: 2,5 => CTR => H6: 3 * PRF # H6: 3 => SOL * DIS # G1: 2,5 => CTR => G1: 8,9 * DIS # G2: 2,5 => CTR => G2: 8,9 * DIS # G8: 2,5 => CTR => G8: 3,4,9 * DIS # G9: 2,5 => CTR => G9: 4,8,9 * DIS # H6: 5 => CTR => H6: 2,3 * DIS # G8: 4,5,9 => CTR => G8: 2,3 * PRF # A7: 2,3 => SOL * DIS # A8: 2,3 => CTR => A8: 4,7 * PRF # H7: 5,7 => SOL * PRF # H7: 2,5 => SOL * DIS # G8: 2,5 => CTR => G8: 3,4,9 * DIS # I8: 2,5 => CTR => I8: 7,9 * DIS # G9: 2,5 => CTR => G9: 4,8,9 * DIS # I9: 2,5 => CTR => I9: 8,9 * DIS # F9: 2,5 => CTR => F9: 4,9 * DIS # H6: 2,5 => CTR => H6: 3 * PRF # H6: 3 => SOL * CNT 24 HDP CHAINS / 65 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A7: 2,3 => SOL * STA A7: 2,3 * CNT 1 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .6.....4..47......95..1.6.3.7...3.8.5......9489....7.1..98.61.......1.6..1.37.... | initial |
| .6.....4..47....1.95..1.6.3.7...3.865......9489....7.1..98.61...8...1.6.61.37.... | autosolve |
| 163795842247638915958412673471923586536187294892564731329846157784251369615379428 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) A2: 2,3 C3: 2,8 H3: 2,7 B5: 2,3 C5: 1,6 E5: 6,8 F5: 7,8 G4: 2,5 G5: 2,3 B7: 2,3 H9: 2,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,C1: 1.. / A1 = 1 => 12 pairs (_) / C1 = 1 => 15 pairs (_) D4,D5: 1.. / D4 = 1 => 0 pairs (X) / D5 = 1 => 8 pairs (_) C5,D5: 1.. / C5 = 1 => 0 pairs (X) / D5 = 1 => 8 pairs (_) A1,A4: 1.. / A1 = 1 => 12 pairs (_) / A4 = 1 => 15 pairs (_) B5,G5: 2.. / B5 = 2 => 0 pairs (X) / G5 = 2 => 0 pairs (_) B5,B7: 2.. / B5 = 2 => 0 pairs (X) / B7 = 2 => 0 pairs (_) E1,E2: 3.. / E1 = 3 => 11 pairs (_) / E2 = 3 => 13 pairs (_) B5,C6: 3.. / B5 = 3 => 0 pairs (*) / C6 = 3 => 0 pairs (X) G5,H6: 3.. / G5 = 3 => 0 pairs (X) / H6 = 3 => 0 pairs (_) H7,G8: 3.. / H7 = 3 => 0 pairs (X) / G8 = 3 => 0 pairs (_) A2,E2: 3.. / A2 = 3 => 11 pairs (_) / E2 = 3 => 13 pairs (_) B5,G5: 3.. / B5 = 3 => 0 pairs (*) / G5 = 3 => 0 pairs (X) C6,H6: 3.. / C6 = 3 => 0 pairs (X) / H6 = 3 => 0 pairs (_) B5,B7: 3.. / B5 = 3 => 0 pairs (*) / B7 = 3 => 0 pairs (X) G5,G8: 3.. / G5 = 3 => 0 pairs (X) / G8 = 3 => 0 pairs (_) H6,H7: 3.. / H6 = 3 => 0 pairs (*) / H7 = 3 => 0 pairs (X) D3,F3: 4.. / D3 = 4 => 11 pairs (_) / F3 = 4 => 12 pairs (_) G8,G9: 4.. / G8 = 4 => 0 pairs (X) / G9 = 4 => 12 pairs (_) A7,E7: 4.. / A7 = 4 => 16 pairs (_) / E7 = 4 => 17 pairs (_) G4,H6: 5.. / G4 = 5 => 12 pairs (_) / H6 = 5 => 0 pairs (X) C8,C9: 5.. / C8 = 5 => 12 pairs (_) / C9 = 5 => 15 pairs (_) D2,E2: 6.. / D2 = 6 => 12 pairs (_) / E2 = 6 => 10 pairs (_) C5,C6: 6.. / C5 = 6 => 8 pairs (_) / C6 = 6 => 0 pairs (X) I1,H3: 7.. / I1 = 7 => 0 pairs (X) / H3 = 7 => 11 pairs (_) D5,F5: 7.. / D5 = 7 => 0 pairs (X) / F5 = 7 => 10 pairs (_) A7,A8: 7.. / A7 = 7 => 0 pairs (X) / A8 = 7 => 11 pairs (_) A8,I8: 7.. / A8 = 7 => 11 pairs (_) / I8 = 7 => 0 pairs (X) H3,H7: 7.. / H3 = 7 => 11 pairs (_) / H7 = 7 => 0 pairs (X) C1,C3: 8.. / C1 = 8 => 10 pairs (_) / C3 = 8 => 10 pairs (_) E5,F5: 8.. / E5 = 8 => 10 pairs (_) / F5 = 8 => 0 pairs (X) G9,I9: 8.. / G9 = 8 => 0 pairs (X) / I9 = 8 => 11 pairs (_) C3,F3: 8.. / C3 = 8 => 10 pairs (_) / F3 = 8 => 10 pairs (_) D4,E4: 9.. / D4 = 9 => 8 pairs (_) / E4 = 9 => 11 pairs (_) * DURATION: 0:00:31.678973 START: 19:50:25.020085 END: 19:50:56.699058 2019-04-30 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B5,B7,C3,C5,E5,F5,G4,G5,H3,H9) * .6.....4..47....1.95..1.6.3.7...3.865......9489....7.1..98.61...8...1.6.61.37.... * PAIR A2: 2,3 BLK 1 A1: 2,3,1 # reduction candidate for 2,3 A1: 2,3 # 15 pairs C1: 2,3,1,8 # reduction candidate for 2,3 C1: 2,3 # 12 pairs * PAIR A2: 2,3 ROW 2 E2: 2,3,5,6,8,9 # reduction candidate for 2,3 E2: 2,3 # 13 pairs E2: 5,6,8,9 # 11 pairs * PAIR A2: 2,3 COL A A7: 2,3,4,7 # reduction candidate for 2,3 A7: 2,3 => SOLVED * 163795842247638915958412673471923586536187294892564731329846157784251369615379428 A7: 4,7 # 12 pairs A8: 2,3,4,7 # reduction candidate for 2,3 A8: 2,3 => CTR * 16.....4..47....1.95..1.67347...3.865......9489....7.172984613538...1.6761.37..2. A8: 4,7 # 12 pairs * PAIR C3: 2,8 BLK 1 C1: 2,8,1,3 # reduction candidate for 2,8 C1: 2,8 # 14 pairs C1: 1,3 # 12 pairs * PAIR C3: 2,8 ROW 3 F3: 2,8,4,7 # reduction candidate for 2,8 F3: 4,7 # 11 pairs F3: 2,8 # 11 pairs * PAIR H3: 2,7 BLK 3 I1: 2,7,5,8,9 # reduction candidate for 2,7 I1: 2,7 # 12 pairs I1: 5,8,9 # 11 pairs * PAIR H3: 2,7 ROW 3 D3: 2,7,4 # reduction candidate for 2,7 D3: 2,7 # 12 pairs F3: 2,7,4,8 # reduction candidate for 2,7 F3: 2,7 # 11 pairs * PAIR H3: 2,7 COL H H7: 2,7,3,5 # reduction candidate for 2,7 H7: 2,7 => CTR * .63....4.247.3..1.958.1.6.3.7...358653....29489....7313298.61...8...136.61.37.458 H7: 3,5 # 12 pairs * PAIR B5: 2,3 BLK 4 C6: 2,3,4,6 # reduction candidate for 2,3 C6: 4,6 => CTR * 163....4224763.915958.1.673472193586531768294896...7313298461..784..1369615379428 C6: 2,3 # 11 pairs * PAIR C5: 1,6 ROW 5 D5: 1,6,7 # reduction candidate for 1,6 D5: 7 => CTR * 163....4.24763.81.958.1.6.3472193586531768294896...7313298461..784..1369615379428 D5: 1,6 # 10 pairs * PAIR E5: 6,8 COL E E2: 6,8,2,3,5,9 # reduction candidate for 6,8 E2: 6,8 # 12 pairs E2: 2,3,5,9 # 12 pairs * PAIR F5: 7,8 COL F F1: 7,8,2,5,9 # reduction candidate for 7,8 F1: 7,8 # 12 pairs F3: 7,8,2,4 # reduction candidate for 7,8 F3: 7,8 # 12 pairs * PAIR G4: 2,5 BLK 6 H6: 2,5,3 # reduction candidate for 2,5 H6: 2,5 => CTR * .6.....4..47....1.95..1.6.3.7...3.865.....394893...7.1.398.61...8...1.6.61.37.... H6: 3 => SOLVED * 163795842247638915958412673471923586536187294892564731329846157784251369615379428 * PAIR G4: 2,5 ROW 4 D4: 2,5,1,4,9 # reduction candidate for 2,5 D4: 2,5 # 12 pairs E4: 2,5,4,9 # reduction candidate for 2,5 E4: 2,5 # 12 pairs * PAIR G4: 2,5 COL G G1: 2,5,8,9 # reduction candidate for 2,5 G1: 2,5 => CTR * .6.....4..47....1.95..1.6.3.7...3.8652....394893...7.1.398.61...8...1.6.61.37.... G1: 8,9 # 12 pairs G2: 2,5,8,9 # reduction candidate for 2,5 G2: 2,5 => CTR * .6.....4..47....1.95..1.6.3.7...3.8652....394893...7.1.398.61...8...1.6.61.37.... G2: 8,9 # 12 pairs G8: 2,5,3,4,9 # reduction candidate for 2,5 G8: 2,5 => CTR * .6.....4..47....1.95..1.6.3.7...3.865.....394893...7.1.398.61...8...1.6.61.37.4.8 G8: 3,4,9 # 11 pairs G9: 2,5,4,8,9 # reduction candidate for 2,5 G9: 2,5 => CTR * .6.....4..47....1.95..1.6.3.7...3.865.....394893...7.1.398.61...8...146961.379..8 G9: 4,8,9 # 11 pairs * PAIR G5: 2,3 BLK 6 H6: 2,3,5 # reduction candidate for 2,3 H6: 5 => CTR * .6.....4..47....1.95..1.6.3.7...3.865.....394893...751.398.61...8...1.6.61.37..2. H6: 2,3 # 12 pairs * PAIR G5: 2,3 COL G G8: 2,3,4,5,9 # reduction candidate for 2,3 G8: 4,5,9 => CTR * .6.....4..47....1.95..1.6.3.7...3.865.....394893...7.1.398.61...8...1.6.61.37.... G8: 2,3 # 17 pairs * PAIR B7: 2,3 BLK 7 A7: 2,3,4,7 # reduction candidate for 2,3 A7: 2,3 => SOLVED * 163795842247638915958412673471923586536187294892564731329846157784251369615379428 A7: 4,7 # 12 pairs A8: 2,3,4,7 # reduction candidate for 2,3 A8: 2,3 => CTR * 16.....4..47....1.95..1.67347...3.865......9489....7.172984613538...1.6761.37..2. A8: 4,7 # 12 pairs C8: 2,3,4,5 # reduction candidate for 2,3 C8: 2,3 # 19 pairs * PAIR B7: 2,3 ROW 7 H7: 2,3,5,7 # reduction candidate for 2,3 H7: 5,7 => SOLVED * 163795842247638915958412673471923586536187294892564731329846157784251369615379428 H7: 2,3 # 15 pairs * PAIR H9: 2,5 BLK 9 H7: 2,5,3,7 # reduction candidate for 2,5 H7: 2,5 => SOLVED * 163795842247638915958412673471923586536187294892564731329846157784251369615379428 H7: 3,7 # 12 pairs I7: 2,5,7 # reduction candidate for 2,5 I7: 2,5 # 15 pairs G8: 2,5,3,4,9 # reduction candidate for 2,5 G8: 2,5 => CTR * .6.....4..47....1.95..1.6.3.7...3.865.....394893...7.1.398.61...8...1.6.61.37.4.8 G8: 3,4,9 # 11 pairs I8: 2,5,7,9 # reduction candidate for 2,5 I8: 2,5 => CTR * .6.....4..47....1.95..1.673.7...3.865.....394893...7.1.398.61..78...1.6.61.37.... I8: 7,9 # 12 pairs G9: 2,5,4,8,9 # reduction candidate for 2,5 G9: 2,5 => CTR * .6.....4..47....1.95..1.6.3.7...3.865.....394893...7.1.398.61...8...146961.379..8 G9: 4,8,9 # 11 pairs I9: 2,5,8,9 # reduction candidate for 2,5 I9: 2,5 => CTR * .6.....4..47....1.95..1.6.3.7...3.865.....394893...7.1.398.61...8...146961.3798.. I9: 8,9 # 12 pairs * PAIR H9: 2,5 ROW 9 C9: 2,5,4 # reduction candidate for 2,5 C9: 2,5 # 14 pairs F9: 2,5,4,9 # reduction candidate for 2,5 F9: 2,5 => CTR * .6.....4..47....1.95..1.673.7...3.865.....394893...7.1..98.61...8...1.6.61.37.... F9: 4,9 # 12 pairs * PAIR H9: 2,5 COL H H6: 2,5,3 # reduction candidate for 2,5 H6: 2,5 => CTR * .6.....4..47....1.95..1.6.3.7...3.865.....394893...7.1.398.61...8...1.6.61.37.... H6: 3 => SOLVED * 163795842247638915958412673471923586536187294892564731329846157784251369615379428 * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060316-absurd-base-pr-000.dot * REASONING * PRF # A7: 2,3 => SOL * DIS # A8: 2,3 => CTR => A8: 4,7 * DIS # H7: 2,7 => CTR => H7: 3,5 * DIS # C6: 4,6 => CTR => C6: 2,3 * DIS # D5: 7 => CTR => D5: 1,6 * DIS # H6: 2,5 => CTR => H6: 3 * PRF # H6: 3 => SOL * DIS # G1: 2,5 => CTR => G1: 8,9 * DIS # G2: 2,5 => CTR => G2: 8,9 * DIS # G8: 2,5 => CTR => G8: 3,4,9 * DIS # G9: 2,5 => CTR => G9: 4,8,9 * DIS # H6: 5 => CTR => H6: 2,3 * DIS # G8: 4,5,9 => CTR => G8: 2,3 * PRF # A7: 2,3 => SOL * DIS # A8: 2,3 => CTR => A8: 4,7 * PRF # H7: 5,7 => SOL * PRF # H7: 2,5 => SOL * DIS # G8: 2,5 => CTR => G8: 3,4,9 * DIS # I8: 2,5 => CTR => I8: 7,9 * DIS # G9: 2,5 => CTR => G9: 4,8,9 * DIS # I9: 2,5 => CTR => I9: 8,9 * DIS # F9: 2,5 => CTR => F9: 4,9 * DIS # H6: 2,5 => CTR => H6: 3 * PRF # H6: 3 => SOL * CNT 24 HDP CHAINS / 65 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B5,B7,C3,C5,E5,F5,G4,G5,H3,H9) * .6.....4..47....1.95..1.6.3.7...3.865......9489....7.1..98.61...8...1.6.61.37.... * PAIR A2: 2,3 BLK 1 A1: 2,3,1 # reduction candidate for 2,3 A1: 2,3 # 15 pairs C1: 2,3,1,8 # reduction candidate for 2,3 C1: 2,3 # 12 pairs * PAIR A2: 2,3 ROW 2 E2: 2,3,5,6,8,9 # reduction candidate for 2,3 E2: 2,3 # 13 pairs E2: 5,6,8,9 # 11 pairs * PAIR A2: 2,3 COL A A7: 2,3,4,7 # reduction candidate for 2,3 A7: 2,3 => SOLVED * 163795842247638915958412673471923586536187294892564731329846157784251369615379428 * DURATION: 0:00:03.646258 START: 19:51:29.486223 END: 19:51:33.132481 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060316-absurd-base-pr-001.dot * REASONING * PRF # A7: 2,3 => SOL * STA A7: 2,3 * CNT 1 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006, 20060316, absurd
Solution
position: 163795842247638915958412673471923586536187294892564731329846157784251369615379428 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: 2,3 => UNS * INC # C1: 2,3 => UNS * INC # E2: 2,3 => UNS * INC # E2: 5,6,8,9 => UNS * PRF # A7: 2,3 => SOL * INC # A7: 4,7 => UNS * DIS # A8: 2,3 => CTR => A8: 4,7 * INC # A8: 4,7 => UNS * INC # C1: 2,8 => UNS * INC # C1: 1,3 => UNS * INC # F3: 2,8 => UNS * INC # F3: 4,7 => UNS * INC # I1: 2,7 => UNS * INC # I1: 5,8,9 => UNS * INC # D3: 2,7 => UNS * INC # F3: 2,7 => UNS * DIS # H7: 2,7 => CTR => H7: 3,5 * INC # H7: 3,5 => UNS * INC # C6: 2,3 => UNS * DIS # C6: 4,6 => CTR => C6: 2,3 * INC # D5: 1,6 => UNS * DIS # D5: 7 => CTR => D5: 1,6 * INC # E2: 6,8 => UNS * INC # E2: 2,3,5,9 => UNS * INC # F1: 7,8 => UNS * INC # F3: 7,8 => UNS * DIS # H6: 2,5 => CTR => H6: 3 * PRF # H6: 3 => SOL * INC # D4: 2,5 => UNS * INC # E4: 2,5 => UNS * DIS # G1: 2,5 => CTR => G1: 8,9 * INC # G1: 8,9 => UNS * DIS # G2: 2,5 => CTR => G2: 8,9 * INC # G2: 8,9 => UNS * DIS # G8: 2,5 => CTR => G8: 3,4,9 * INC # G8: 3,4,9 => UNS * DIS # G9: 2,5 => CTR => G9: 4,8,9 * INC # G9: 4,8,9 => UNS * INC # H6: 2,3 => UNS * DIS # H6: 5 => CTR => H6: 2,3 * INC # G8: 2,3 => UNS * DIS # G8: 4,5,9 => CTR => G8: 2,3 * PRF # A7: 2,3 => SOL * INC # A7: 4,7 => UNS * DIS # A8: 2,3 => CTR => A8: 4,7 * INC # A8: 4,7 => UNS * INC # C8: 2,3 => UNS * INC # H7: 2,3 => UNS * PRF # H7: 5,7 => SOL * PRF # H7: 2,5 => SOL * INC # H7: 3,7 => UNS * INC # I7: 2,5 => UNS * DIS # G8: 2,5 => CTR => G8: 3,4,9 * INC # G8: 3,4,9 => UNS * DIS # I8: 2,5 => CTR => I8: 7,9 * INC # I8: 7,9 => UNS * DIS # G9: 2,5 => CTR => G9: 4,8,9 * INC # G9: 4,8,9 => UNS * DIS # I9: 2,5 => CTR => I9: 8,9 * INC # I9: 8,9 => UNS * INC # C9: 2,5 => UNS * DIS # F9: 2,5 => CTR => F9: 4,9 * INC # F9: 4,9 => UNS * DIS # H6: 2,5 => CTR => H6: 3 * PRF # H6: 3 => SOL * CNT 65 HDP CHAINS / 65 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 2,3 => UNS * INC # C1: 2,3 => UNS * INC # E2: 2,3 => UNS * INC # E2: 5,6,8,9 => UNS * PRF # A7: 2,3 => SOL * STA A7: 2,3 * CNT 5 HDP CHAINS / 5 HYP OPENED