Analysis of zz-www.sudokuoftheday.co.uk-20060423-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006
level: medium
position: .37...8..6........9..1...562.1...47...3..56.9.......1....2.4...4.6.3.1....27..... initial
Autosolve
position: .37...8..6........9..1...562.1...47.7.3.15629.......1....2.4...47653.1.2..27.1... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 2,4,8 => CTR => B2: 1,5 * PRF # A7: 3,8 => SOL * DIS # B2: 4,8 => CTR => B2: 1,2,5 * DIS # B3: 4,8 => CTR => B3: 2 * DIS # F1: 6,9 => CTR => F1: 2 * DIS # D4: 6,9 => CTR => D4: 3,8 * DIS # D6: 6,9 => CTR => D6: 4 * PRF # E2: 4,7 => SOL * DIS # H2: 4,9 => CTR => H2: 3 * DIS # H9: 3,6,8 => CTR => H9: 4,9 * PRF # I2: 1,4 => SOL * DIS # I2: 3,7 => CTR => I2: 1,4 * DIS # B2: 4,8 => CTR => B2: 1,2,5 * DIS # B3: 4,8 => CTR => B3: 2 * DIS # B4: 6,9 => CTR => B4: 5,8 * DIS # A7: 5,8 => CTR => A7: 1,3 * PRF # A9: 5,8 => SOL * DIS # B6: 4,9 => CTR => B6: 6 * DIS # D6: 6 => CTR => D6: 4,9 * DIS # D4: 8,9 => CTR => D4: 3,6 * DIS # F4: 8,9 => CTR => F4: 3,6 * PRF # B4: 8,9 => SOL * DIS # E9: 8,9 => CTR => E9: 6 * DIS # B4: 6,9 => CTR => B4: 5,8 * PRF # I6: 8 => SOL * DIS # E9: 8,9 => CTR => E9: 6 * DIS # F4: 8,9 => CTR => F4: 3,6 * DIS # H7: 8,9 => CTR => H7: 3,6 * DIS # H9: 8,9 => CTR => H9: 3,4,6 * CNT 29 HDP CHAINS / 66 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 2,4,8 => CTR => B2: 1,5 * PRF B2: 1,5 # E2: 4,7 => SOL * STA B2: 1,5 + E2: 4,7 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .37...8..6........9..1...562.1...47...3..56.9.......1....2.4...4.6.3.1....27..... | initial |
| .37...8..6........9..1...562.1...47.7.3.15629.......1....2.4...47653.1.2..27.1... | autosolve |
| 137652894654978231928143756281396475743815629569427318315284967476539182892761543 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) A1: 1,5 C3: 4,8 D1: 6,9 E3: 4,7 H1: 4,9 I1: 1,4 B5: 4,8 A6: 5,8 C6: 4,9 E4: 8,9 D5: 4,8 E6: 2,7 F6: 2,7 I4: 5,8 G6: 3,5 F8: 8,9 H8: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,B2: 1.. / A1 = 1 => 0 pairs (*) / B2 = 1 => 0 pairs (X) I1,I2: 1.. / I1 = 1 => 24 pairs (_) / I2 = 1 => 0 pairs (*) A7,B7: 1.. / A7 = 1 => 24 pairs (_) / B7 = 1 => 0 pairs (*) A1,I1: 1.. / A1 = 1 => 0 pairs (*) / I1 = 1 => 0 pairs (X) B2,I2: 1.. / B2 = 1 => 24 pairs (_) / I2 = 1 => 0 pairs (*) A1,A7: 1.. / A1 = 1 => 0 pairs (*) / A7 = 1 => 0 pairs (X) B2,B7: 1.. / B2 = 1 => 24 pairs (_) / B7 = 1 => 0 pairs (*) B2,B3: 2.. / B2 = 2 => 0 pairs (X) / B3 = 2 => 20 pairs (_) E1,F1: 2.. / E1 = 2 => 0 pairs (X) / F1 = 2 => 17 pairs (_) G2,G3: 2.. / G2 = 2 => 20 pairs (_) / G3 = 2 => 0 pairs (X) E6,F6: 2.. / E6 = 2 => 17 pairs (_) / F6 = 2 => 0 pairs (X) B2,G2: 2.. / B2 = 2 => 0 pairs (X) / G2 = 2 => 20 pairs (_) B3,G3: 2.. / B3 = 2 => 20 pairs (_) / G3 = 2 => 0 pairs (X) E1,E6: 2.. / E1 = 2 => 0 pairs (X) / E6 = 2 => 17 pairs (_) F1,F6: 2.. / F1 = 2 => 17 pairs (_) / F6 = 2 => 0 pairs (X) D4,F4: 3.. / D4 = 3 => 18 pairs (_) / F4 = 3 => 0 pairs (X) G6,I6: 3.. / G6 = 3 => 23 pairs (_) / I6 = 3 => 21 pairs (_) A7,A9: 3.. / A7 = 3 => 0 pairs (*) / A9 = 3 => 0 pairs (X) F3,G3: 3.. / F3 = 3 => 20 pairs (_) / G3 = 3 => 0 pairs (X) D2,D4: 3.. / D2 = 3 => 0 pairs (X) / D4 = 3 => 18 pairs (_) D5,D6: 4.. / D5 = 4 => 0 pairs (X) / D6 = 4 => 20 pairs (_) H9,I9: 4.. / H9 = 4 => 0 pairs (*) / I9 = 4 => 0 pairs (X) B5,D5: 4.. / B5 = 4 => 20 pairs (_) / D5 = 4 => 0 pairs (X) E1,E2: 5.. / E1 = 5 => 0 pairs (*) / E2 = 5 => 0 pairs (X) B4,A6: 5.. / B4 = 5 => 20 pairs (_) / A6 = 5 => 0 pairs (*) A1,E1: 5.. / A1 = 5 => 24 pairs (_) / E1 = 5 => 0 pairs (*) B4,I4: 5.. / B4 = 5 => 20 pairs (_) / I4 = 5 => 0 pairs (*) C2,C7: 5.. / C2 = 5 => 0 pairs (X) / C7 = 5 => 25 pairs (_) D1,F1: 6.. / D1 = 6 => 19 pairs (_) / F1 = 6 => 0 pairs (X) B4,B6: 6.. / B4 = 6 => 0 pairs (X) / B6 = 6 => 20 pairs (_) E7,E9: 6.. / E7 = 6 => 0 pairs (X) / E9 = 6 => 18 pairs (_) H7,H9: 6.. / H7 = 6 => 18 pairs (_) / H9 = 6 => 0 pairs (X) B6,D6: 6.. / B6 = 6 => 20 pairs (_) / D6 = 6 => 0 pairs (X) E7,H7: 6.. / E7 = 6 => 0 pairs (X) / H7 = 6 => 18 pairs (_) E9,H9: 6.. / E9 = 6 => 18 pairs (_) / H9 = 6 => 0 pairs (X) F1,F4: 6.. / F1 = 6 => 0 pairs (X) / F4 = 6 => 19 pairs (_) E6,F6: 7.. / E6 = 7 => 0 pairs (X) / F6 = 7 => 17 pairs (_) G7,I7: 7.. / G7 = 7 => 0 pairs (X) / I7 = 7 => 25 pairs (_) I2,I7: 7.. / I2 = 7 => 0 pairs (X) / I7 = 7 => 25 pairs (_) I4,I6: 8.. / I4 = 8 => 20 pairs (_) / I6 = 8 => 0 pairs (*) B5,D5: 8.. / B5 = 8 => 0 pairs (X) / D5 = 8 => 20 pairs (_) A6,I6: 8.. / A6 = 8 => 20 pairs (_) / I6 = 8 => 0 pairs (*) F8,H8: 8.. / F8 = 8 => 0 pairs (X) / H8 = 8 => 18 pairs (_) F8,H8: 9.. / F8 = 9 => 18 pairs (_) / H8 = 9 => 0 pairs (X) C6,C7: 9.. / C6 = 9 => 20 pairs (_) / C7 = 9 => 0 pairs (X) * DURATION: 0:01:04.154153 START: 22:35:32.653967 END: 22:36:36.808120 2019-04-30 * CP COUNT: (45) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B5,C3,C6,D1,D5,E3,E4,E6,F6,F8,G6,H1,H8,I1,I4) * .37...8..6........9..1...562.1...47.7.3.15629.......1....2.4...47653.1.2..27.1... * PAIR A1: 1,5 BLK 1 B2: 1,5,2,4,8 # reduction candidate for 1,5 B2: 2,4,8 => CTR * 1376528946.59.8.319..1.3.562.139647.7.3815629.69427.1..182.4.67476539182..2761.4. B2: 1,5 # 25 pairs * PAIR A1: 1,5 COL A A7: 1,5,3,8 # reduction candidate for 1,5 A7: 3,8 => SOLVED * 137652894654978231928143756281396475743815629569427318315284967476539182892761543 A7: 1,5 # 23 pairs * PAIR C3: 4,8 BLK 1 B2: 4,8,1,2,5 # reduction candidate for 4,8 B2: 4,8 => CTR * 1376528946.5.7.23192.1437562.13.647.7.3.15629.64927.1..192.4.674765391.2..27.1.4. B2: 1,2,5 # 17 pairs C2: 4,8,5 # reduction candidate for 4,8 C2: 4,8 # 25 pairs B3: 4,8,2 # reduction candidate for 4,8 B3: 4,8 => CTR * 1376528946259487319..1732562.139647.7.3815629.69427.1..182.4.67476539182..2761.4. B3: 2 # 20 pairs * PAIR D1: 6,9 BLK 2 F1: 6,9,2 # reduction candidate for 6,9 F1: 6,9 => CTR * 537.2.841614.58297928147356251.9347874381562986947251.1.52.4...47653.1.23.27.1..4 F1: 2 # 17 pairs * PAIR D1: 6,9 COL D D4: 6,9,3,8 # reduction candidate for 6,9 D4: 6,9 => CTR * .37..68..6..3..2.792.1..3562516934787438156298694.2513.9.2.47.54765391825827.19.. D4: 3,8 # 18 pairs D6: 6,9,4 # reduction candidate for 6,9 D6: 6,9 => CTR * 137.528.46.......19..1.3.562.13.6475783415629564927318.192.45.747653.1.2.52791... D6: 4 # 20 pairs * PAIR E3: 4,7 BLK 2 E2: 4,7,5 # reduction candidate for 4,7 E2: 4,7 => SOLVED * 137652894654978231928143756281396475743815629569427318315284967476539182892761543 E2: 5 # 24 pairs * PAIR H1: 4,9 BLK 3 H2: 4,9,3 # reduction candidate for 4,9 H2: 4,9 => CTR * 537...8.161..572.392.14..56251.9.4787.38156298694...1.1.5264.374765391823.2781564 H2: 3 # 20 pairs * PAIR H1: 4,9 COL H H9: 4,9,3,6,8 # reduction candidate for 4,9 H9: 3,6,8 => CTR * 537...8.161..572.392.14..56251.9.4787438156298694..3151.52.49.7476539182392781564 H9: 4,9 # 23 pairs * PAIR I1: 1,4 BLK 3 I2: 1,4,3,7 # reduction candidate for 1,4 I2: 1,4 => SOLVED * 137652894654978231928143756281396475743815629569427318315284967476539182892761543 I2: 3,7 => CTR * 537...8.161..572.392.14..56251.9.4787438156298694..3151.52.49.7476539182392781564 * PAIR B5: 4,8 COL B B2: 4,8,1,2,5 # reduction candidate for 4,8 B2: 4,8 => CTR * 1376528946.5.7.23192.1437562.13.647.7.3.15629.64927.1..192.4.674765391.2..27.1.4. B2: 1,2,5 # 17 pairs B3: 4,8,2 # reduction candidate for 4,8 B3: 4,8 => CTR * 1376528946259487319..1732562.139647.7.3815629.69427.1..182.4.67476539182..2761.4. B3: 2 # 20 pairs * PAIR A6: 5,8 BLK 4 B4: 5,8,6,9 # reduction candidate for 5,8 B4: 6,9 => CTR * 137.528.46.......19..1.3.562.13.6475783415629564927318.192.45.747653.1.2.52791... B4: 5,8 # 20 pairs * PAIR A6: 5,8 ROW 6 I6: 5,8,3 # reduction candidate for 5,8 I6: 5,8 # 23 pairs I6: 3 # 21 pairs * PAIR A6: 5,8 COL A A7: 5,8,1,3 # reduction candidate for 5,8 A7: 5,8 => CTR * 1376528946......319..1.3.562513964787.381562986942751..1.2.4..747653.1.23.27.1.45 A7: 1,3 # 18 pairs A9: 5,8,3 # reduction candidate for 5,8 A9: 5,8 => SOLVED * 137652894654978231928143756281396475743815629569427318315284967476539182892761543 A9: 3 # 19 pairs * PAIR C6: 4,9 BLK 4 B6: 4,9,6 # reduction candidate for 4,9 B6: 4,9 => CTR * 13795.8..6........9..1...56261...4757.3.156295..6..318...2.4...47653.1.2..27.1... B6: 6 # 20 pairs * PAIR C6: 4,9 ROW 6 D6: 4,9,6 # reduction candidate for 4,9 D6: 6 => CTR * .379.684161....29.92.1...56261...4757834156295..6...1....2.4...47653.1.2..27.1... D6: 4,9 # 20 pairs * PAIR E4: 8,9 BLK 5 D4: 8,9,3,6 # reduction candidate for 8,9 D4: 8,9 => CTR * .37...8..6..3.....9..1..3562.1..347.7.3.15629...6..513...2.4...47653.1.2..27.19.. D4: 3,6 # 18 pairs F4: 8,9,3,6 # reduction candidate for 8,9 F4: 8,9 => CTR * .3792684161.85.29.92814..562613..4757834156295..6.2.1....2.4...47653.1.2..27.1... F4: 3,6 # 18 pairs * PAIR E4: 8,9 ROW 4 B4: 8,9,5,6 # reduction candidate for 8,9 B4: 8,9 => SOLVED * 137652894654978231928143756281396475743815629569427318315284967476539182892761543 B4: 5,6 # 19 pairs * PAIR E4: 8,9 COL E E7: 8,9,6 # reduction candidate for 8,9 E7: 8,9 # 18 pairs E9: 8,9,6 # reduction candidate for 8,9 E9: 8,9 => CTR * 537...8.161..572.392.14..56251.9.4787438156298694..315185264937476539182392781564 E9: 6 # 18 pairs * PAIR I4: 5,8 BLK 6 I6: 5,8,3 # reduction candidate for 5,8 I6: 5,8 # 23 pairs I6: 3 # 21 pairs * PAIR I4: 5,8 ROW 4 B4: 5,8,6,9 # reduction candidate for 5,8 B4: 6,9 => CTR * 137.528.46.......19..1.3.562.13.6475783415629564927318.192.45.747653.1.2.52791... B4: 5,8 # 20 pairs * PAIR G6: 3,5 BLK 6 I6: 3,5,8 # reduction candidate for 3,5 I6: 8 => SOLVED * 137652894654978231928143756281396475743815629569427318315284967476539182892761543 I6: 3,5 # 20 pairs * PAIR G6: 3,5 COL G G7: 3,5,7,9 # reduction candidate for 3,5 G7: 3,5 # 27 pairs G9: 3,5,9 # reduction candidate for 3,5 G9: 3,5 # 22 pairs * PAIR F8: 8,9 BLK 8 E7: 8,9,6 # reduction candidate for 8,9 E7: 8,9 # 18 pairs E9: 8,9,6 # reduction candidate for 8,9 E9: 8,9 => CTR * 537...8.161..572.392.14..56251.9.4787438156298694..315185264937476539182392781564 E9: 6 # 18 pairs * PAIR F8: 8,9 COL F F2: 8,9,3,7 # reduction candidate for 8,9 F2: 8,9 # 22 pairs F4: 8,9,3,6 # reduction candidate for 8,9 F4: 8,9 => CTR * .3792684161.85.29.92814..562613..4757834156295..6.2.1....2.4...47653.1.2..27.1... F4: 3,6 # 18 pairs * PAIR H8: 8,9 BLK 9 H7: 8,9,3,6 # reduction candidate for 8,9 H7: 8,9 => CTR * .37...8.161....2379..1...562.1...47.7.3.15629.......1....264...47653.1.2..27.1.64 H7: 3,6 # 18 pairs H9: 8,9,3,4,6 # reduction candidate for 8,9 H9: 8,9 => CTR * .37...8.161....2379..1...562.1...47.7.3.15629.......1....2.4.6.47653.1.2..2761..4 H9: 3,4,6 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060423-absurd-base-pr-000.dot * REASONING * DIS # B2: 2,4,8 => CTR => B2: 1,5 * PRF # A7: 3,8 => SOL * DIS # B2: 4,8 => CTR => B2: 1,2,5 * DIS # B3: 4,8 => CTR => B3: 2 * DIS # F1: 6,9 => CTR => F1: 2 * DIS # D4: 6,9 => CTR => D4: 3,8 * DIS # D6: 6,9 => CTR => D6: 4 * PRF # E2: 4,7 => SOL * DIS # H2: 4,9 => CTR => H2: 3 * DIS # H9: 3,6,8 => CTR => H9: 4,9 * PRF # I2: 1,4 => SOL * DIS # I2: 3,7 => CTR => I2: 1,4 * DIS # B2: 4,8 => CTR => B2: 1,2,5 * DIS # B3: 4,8 => CTR => B3: 2 * DIS # B4: 6,9 => CTR => B4: 5,8 * DIS # A7: 5,8 => CTR => A7: 1,3 * PRF # A9: 5,8 => SOL * DIS # B6: 4,9 => CTR => B6: 6 * DIS # D6: 6 => CTR => D6: 4,9 * DIS # D4: 8,9 => CTR => D4: 3,6 * DIS # F4: 8,9 => CTR => F4: 3,6 * PRF # B4: 8,9 => SOL * DIS # E9: 8,9 => CTR => E9: 6 * DIS # B4: 6,9 => CTR => B4: 5,8 * PRF # I6: 8 => SOL * DIS # E9: 8,9 => CTR => E9: 6 * DIS # F4: 8,9 => CTR => F4: 3,6 * DIS # H7: 8,9 => CTR => H7: 3,6 * DIS # H9: 8,9 => CTR => H9: 3,4,6 * CNT 29 HDP CHAINS / 66 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B5,C3,C6,D1,D5,E3,E4,E6,F6,F8,G6,H1,H8,I1,I4) * .37...8..6........9..1...562.1...47.7.3.15629.......1....2.4...47653.1.2..27.1... * PAIR A1: 1,5 BLK 1 B2: 1,5,2,4,8 # reduction candidate for 1,5 B2: 2,4,8 => CTR * 1376528946.59.8.319..1.3.562.139647.7.3815629.69427.1..182.4.67476539182..2761.4. * PAIR E3: 4,7 BLK 2 E2: 4,7,5 # reduction candidate for 4,7 E2: 4,7 => SOLVED * 137652894654978231928143756281396475743815629569427318315284967476539182892761543 * DURATION: 0:00:03.560617 START: 22:37:25.114358 END: 22:37:28.674975 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060423-absurd-base-pr-001.dot * REASONING * DIS # B2: 2,4,8 => CTR => B2: 1,5 * PRF B2: 1,5 # E2: 4,7 => SOL * STA B2: 1,5 + E2: 4,7 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060423, absurd
Solution
position: 137652894654978231928143756281396475743815629569427318315284967476539182892761543 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 # B2: 1,5 => UNS * DIS # B2: 2,4,8 => CTR => B2: 1,5 * INC # A7: 1,5 => UNS * PRF # A7: 3,8 => SOL * DIS # B2: 4,8 => CTR => B2: 1,2,5 * INC # B2: 1,2,5 => UNS * INC # C2: 4,8 => UNS * DIS # B3: 4,8 => CTR => B3: 2 * INC # B3: 2 => UNS * DIS # F1: 6,9 => CTR => F1: 2 * INC # F1: 2 => UNS * DIS # D4: 6,9 => CTR => D4: 3,8 * INC # D4: 3,8 => UNS * DIS # D6: 6,9 => CTR => D6: 4 * INC # D6: 4 => UNS * PRF # E2: 4,7 => SOL * INC # E2: 5 => UNS * DIS # H2: 4,9 => CTR => H2: 3 * INC # H2: 3 => UNS * INC # H9: 4,9 => UNS * DIS # H9: 3,6,8 => CTR => H9: 4,9 * PRF # I2: 1,4 => SOL * DIS # I2: 3,7 => CTR => I2: 1,4 * DIS # B2: 4,8 => CTR => B2: 1,2,5 * INC # B2: 1,2,5 => UNS * DIS # B3: 4,8 => CTR => B3: 2 * INC # B3: 2 => UNS * INC # B4: 5,8 => UNS * DIS # B4: 6,9 => CTR => B4: 5,8 * INC # I6: 5,8 => UNS * INC # I6: 3 => UNS * DIS # A7: 5,8 => CTR => A7: 1,3 * INC # A7: 1,3 => UNS * PRF # A9: 5,8 => SOL * INC # A9: 3 => UNS * DIS # B6: 4,9 => CTR => B6: 6 * INC # B6: 6 => UNS * INC # D6: 4,9 => UNS * DIS # D6: 6 => CTR => D6: 4,9 * DIS # D4: 8,9 => CTR => D4: 3,6 * INC # D4: 3,6 => UNS * DIS # F4: 8,9 => CTR => F4: 3,6 * INC # F4: 3,6 => UNS * PRF # B4: 8,9 => SOL * INC # B4: 5,6 => UNS * INC # E7: 8,9 => UNS * DIS # E9: 8,9 => CTR => E9: 6 * INC # E9: 6 => UNS * INC # I6: 5,8 => UNS * INC # I6: 3 => UNS * INC # B4: 5,8 => UNS * DIS # B4: 6,9 => CTR => B4: 5,8 * INC # I6: 3,5 => UNS * PRF # I6: 8 => SOL * INC # G7: 3,5 => UNS * INC # G9: 3,5 => UNS * INC # E7: 8,9 => UNS * DIS # E9: 8,9 => CTR => E9: 6 * INC # E9: 6 => UNS * INC # F2: 8,9 => UNS * DIS # F4: 8,9 => CTR => F4: 3,6 * INC # F4: 3,6 => UNS * DIS # H7: 8,9 => CTR => H7: 3,6 * INC # H7: 3,6 => UNS * DIS # H9: 8,9 => CTR => H9: 3,4,6 * INC # H9: 3,4,6 => UNS * CNT 66 HDP CHAINS / 66 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 1,5 => UNS * DIS # B2: 2,4,8 => CTR => B2: 1,5 * PRF B2: 1,5 # E2: 4,7 => SOL * STA B2: 1,5 + E2: 4,7 * CNT 3 HDP CHAINS / 3 HYP OPENED