Analysis of zz-www.sudokuoftheday.co.uk-20190106-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: .1...42......1.7....69....4..48....2683.92..19........7...6........39.5...54..6.. initial
Autosolve
position: .1...42......1.7....69....41.48....2683.92..19...4....7...6.....6..39.5...54..6.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B6: 2 => CTR => B6: 5,7 * DIS # B6: 2,7 => CTR => B6: 5 * PRF # E3: 5,7 => SOL * DIS # D1: 5,7 => CTR => D1: 3,6 * DIS # H9: 7,8 => CTR => H9: 1,2,3,9 * CNT 5 HDP CHAINS / 24 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B6: 2 => CTR => B6: 5,7 * PRF B6: 5,7 # E3: 5,7 => SOL * STA B6: 5,7 + E3: 5,7 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .1...42......1.7....69....4..48....2683.92..19........7...6........39.5...54..6.. | initial |
| .1...42......1.7....69....41.48....2683.92..19...4....7...6.....6..39.5...54..6.. | autosolve |
| 517384296439216785826975134174853962683792541952641873741568329268139457395427618 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) B4: 5,7 C6: 2,7 E4: 5,7 F4: 3,6 D5: 5,7 G4: 3,9 G5: 4,5 H5: 4,7 I8: 7,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G3,H3: 1.. / G3 = 1 => 14 pairs (_) / H3 = 1 => 27 pairs (_) D6,F6: 1.. / D6 = 1 => 17 pairs (_) / F6 = 1 => 16 pairs (_) C7,C8: 1.. / C7 = 1 => 12 pairs (_) / C8 = 1 => 11 pairs (_) F9,H9: 1.. / F9 = 1 => 27 pairs (_) / H9 = 1 => 14 pairs (_) D2,E3: 2.. / D2 = 2 => 0 pairs (*) / E3 = 2 => 0 pairs (X) B6,C6: 2.. / B6 = 2 => 0 pairs (X) / C6 = 2 => 13 pairs (_) H7,H9: 2.. / H7 = 2 => 11 pairs (_) / H9 = 2 => 30 pairs (_) E3,E9: 2.. / E3 = 2 => 11 pairs (_) / E9 = 2 => 0 pairs (*) A2,B2: 4.. / A2 = 4 => 14 pairs (_) / B2 = 4 => 10 pairs (_) G5,H5: 4.. / G5 = 4 => 0 pairs (X) / H5 = 4 => 10 pairs (_) B7,A8: 4.. / B7 = 4 => 14 pairs (_) / A8 = 4 => 10 pairs (_) A8,G8: 4.. / A8 = 4 => 10 pairs (_) / G8 = 4 => 14 pairs (_) A2,A8: 4.. / A2 = 4 => 14 pairs (_) / A8 = 4 => 10 pairs (_) B2,B7: 4.. / B2 = 4 => 10 pairs (_) / B7 = 4 => 14 pairs (_) H5,H7: 4.. / H5 = 4 => 10 pairs (_) / H7 = 4 => 0 pairs (X) B4,B6: 5.. / B4 = 5 => 0 pairs (X) / B6 = 5 => 10 pairs (_) E4,D5: 5.. / E4 = 5 => 10 pairs (_) / D5 = 5 => 0 pairs (X) D7,F7: 5.. / D7 = 5 => 12 pairs (_) / F7 = 5 => 11 pairs (_) B4,E4: 5.. / B4 = 5 => 0 pairs (X) / E4 = 5 => 10 pairs (_) D5,G5: 5.. / D5 = 5 => 0 pairs (X) / G5 = 5 => 10 pairs (_) F4,H4: 6.. / F4 = 6 => 12 pairs (_) / H4 = 6 => 9 pairs (_) C1,B3: 7.. / C1 = 7 => 13 pairs (_) / B3 = 7 => 0 pairs (X) E4,D5: 7.. / E4 = 7 => 0 pairs (X) / D5 = 7 => 10 pairs (_) B4,E4: 7.. / B4 = 7 => 10 pairs (_) / E4 = 7 => 0 pairs (X) D5,H5: 7.. / D5 = 7 => 10 pairs (_) / H5 = 7 => 0 pairs (X) D8,I8: 7.. / D8 = 7 => 0 pairs (X) / I8 = 7 => 9 pairs (_) C1,C6: 7.. / C1 = 7 => 13 pairs (_) / C6 = 7 => 0 pairs (X) F3,F9: 7.. / F3 = 7 => 14 pairs (_) / F9 = 7 => 0 pairs (*) G4,H4: 9.. / G4 = 9 => 9 pairs (_) / H4 = 9 => 14 pairs (_) G4,G7: 9.. / G4 = 9 => 9 pairs (_) / G7 = 9 => 14 pairs (_) * DURATION: 0:00:31.402224 START: 02:45:16.091582 END: 02:45:47.493806 2019-05-01 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,C6,D5,E4,F4,G4,G5,H5,I8) * .1...42......1.7....69....41.48....2683.92..19...4....7...6.....6..39.5...54..6.. * PAIR B4: 5,7 BLK 4 B6: 5,7,2 # reduction candidate for 5,7 B6: 2 => CTR * .1.7.42...4..1.7...7692..1415487...2683592471927.4....7...65.4.46..39.57..548.62. B6: 5,7 # 13 pairs * PAIR C6: 2,7 BLK 4 B6: 2,7,5 # reduction candidate for 2,7 B6: 2,7 => CTR * .1..542..24..1.7.55.692781415487...268359247197214....7...65.4.46..39.5...5481627 B6: 5 # 10 pairs * PAIR E4: 5,7 COL E E1: 5,7,8 # reduction candidate for 5,7 E1: 5,7 # 12 pairs E3: 5,7,2,8 # reduction candidate for 5,7 E3: 5,7 => SOLVED * 517384296439216785826975134174853962683792541952641873741568329268139457395427618 E3: 2,8 # 10 pairs * PAIR F4: 3,6 BLK 5 D6: 3,6,1 # reduction candidate for 3,6 D6: 3,6 # 16 pairs F6: 3,6,1 # reduction candidate for 3,6 F6: 3,6 # 17 pairs * PAIR F4: 3,6 ROW 4 H4: 3,6,9 # reduction candidate for 3,6 H4: 9 # 14 pairs H4: 3,6 # 9 pairs * PAIR F4: 3,6 COL F F2: 3,6,5,8 # reduction candidate for 3,6 F2: 3,6 # 18 pairs F2: 5,8 # 11 pairs * PAIR D5: 5,7 COL D D1: 5,7,3,6 # reduction candidate for 5,7 D1: 5,7 => CTR * .175842......1.7.553692.1.41.48....2683.92.419...41.7.7..165.2..61239.57..54..61. D1: 3,6 # 10 pairs * PAIR G4: 3,9 BLK 6 H4: 3,9,6 # reduction candidate for 3,9 H4: 3,9 # 12 pairs H4: 6 # 9 pairs * PAIR G4: 3,9 COL G G7: 3,9,1,4,8 # reduction candidate for 3,9 G7: 3,9 # 13 pairs G7: 1,4,8 # 9 pairs * PAIR I8: 7,8 BLK 9 H9: 7,8,1,2,3,9 # reduction candidate for 7,8 H9: 7,8 => CTR * .17.842.5....157..5.692781417485...268379254195214.3787..568.2..6.239.57..547168. H9: 1,2,3,9 # 9 pairs I9: 7,8,3,9 # reduction candidate for 7,8 I9: 7,8 # 12 pairs * PAIR I8: 7,8 COL I I6: 7,8,3,5,6 # reduction candidate for 7,8 I6: 7,8 # 14 pairs I6: 3,5,6 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190106-absurd-base-pr-000.dot * REASONING * DIS # B6: 2 => CTR => B6: 5,7 * DIS # B6: 2,7 => CTR => B6: 5 * PRF # E3: 5,7 => SOL * DIS # D1: 5,7 => CTR => D1: 3,6 * DIS # H9: 7,8 => CTR => H9: 1,2,3,9 * CNT 5 HDP CHAINS / 24 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,C6,D5,E4,F4,G4,G5,H5,I8) * .1...42......1.7....69....41.48....2683.92..19...4....7...6.....6..39.5...54..6.. * PAIR B4: 5,7 BLK 4 B6: 5,7,2 # reduction candidate for 5,7 B6: 2 => CTR * .1.7.42...4..1.7...7692..1415487...2683592471927.4....7...65.4.46..39.57..548.62. * PAIR E4: 5,7 COL E E3: 5,7,2,8 # reduction candidate for 5,7 E3: 5,7 => SOLVED * 517384296439216785826975134174853962683792541952641873741568329268139457395427618 * DURATION: 0:00:02.998009 START: 02:46:00.831703 END: 02:46:03.829712 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190106-absurd-base-pr-001.dot * REASONING * DIS # B6: 2 => CTR => B6: 5,7 * PRF B6: 5,7 # E3: 5,7 => SOL * STA B6: 5,7 + E3: 5,7 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190106, absurd
Solution
position: 517384296439216785826975134174853962683792541952641873741568329268139457395427618 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 # B6: 5,7 => UNS * DIS # B6: 2 => CTR => B6: 5,7 * DIS # B6: 2,7 => CTR => B6: 5 * INC # B6: 5 => UNS * INC # E1: 5,7 => UNS * PRF # E3: 5,7 => SOL * INC # E3: 2,8 => UNS * INC # D6: 3,6 => UNS * INC # F6: 3,6 => UNS * INC # H4: 3,6 => UNS * INC # H4: 9 => UNS * INC # F2: 3,6 => UNS * INC # F2: 5,8 => UNS * DIS # D1: 5,7 => CTR => D1: 3,6 * INC # D1: 3,6 => UNS * INC # H4: 3,9 => UNS * INC # H4: 6 => UNS * INC # G7: 3,9 => UNS * INC # G7: 1,4,8 => UNS * DIS # H9: 7,8 => CTR => H9: 1,2,3,9 * INC # H9: 1,2,3,9 => UNS * INC # I9: 7,8 => UNS * INC # I6: 7,8 => UNS * INC # I6: 3,5,6 => UNS * CNT 24 HDP CHAINS / 24 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B6: 5,7 => UNS * DIS # B6: 2 => CTR => B6: 5,7 * PRF B6: 5,7 # E3: 5,7 => SOL * STA B6: 5,7 + E3: 5,7 * CNT 3 HDP CHAINS / 3 HYP OPENED