Analysis of zz-www.sudokuoftheday.co.uk-20060708-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: 6.....8....39.6.14492..1.......9...3.......6..46..3.......19..8.1587.3..7.....1.. initial
Autosolve
position: 6.1.3.8....39.6.14492.8163.1..69.4.3....4..6..46..3....64.19..8.1587.3.67...6.1.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B2: 8 => SOL * DIS # D1: 5,7 => CTR => D1: 2,4 * DIS # H1: 5,7 => CTR => H1: 2,9 * DIS # I1: 5,7 => CTR => I1: 2,9 * PRF # B2: 5,8 => SOL * DIS # D1: 2,5 => CTR => D1: 4,7 * PRF # G2: 7 => SOL * DIS # D1: 5,7 => CTR => D1: 2,4 * DIS # H1: 5,7 => CTR => H1: 2,9 * DIS # I1: 5,7 => CTR => I1: 2,9 * DIS # H4: 7,8 => CTR => H4: 2,5 * DIS # F4: 2,5 => CTR => F4: 7,8 * DIS # F5: 2,5 => CTR => F5: 7,8 * DIS # D6: 2,5 => CTR => D6: 1,7 * DIS # H6: 2,5 => CTR => H6: 7,8 * DIS # I6: 2,5 => CTR => I6: 1,7 * PRF # D7: 5 => SOL * PRF # F9: 2,4 => SOL * CNT 18 HDP CHAINS / 67 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B2: 8 => SOL * STA B2: 8 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6.....8....39.6.14492..1.......9...3.......6..46..3.......19..8.1587.3..7.....1.. | initial |
| 6.1.3.8....39.6.14492.8163.1..69.4.3....4..6..46..3....64.19..8.1587.3.67...6.1.. | autosolve |
| 671435892583926714492781635157698423839247561246153987364519278915872346728364159 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) B1: 5,7 A2: 5,8 E2: 2,5 D3: 5,7 I3: 5,7 C4: 7,8 E6: 2,5 A7: 2,3 A8: 2,9 C9: 8,9 F8: 2,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D5,D6: 1.. / D5 = 1 => 11 pairs (_) / D6 = 1 => 11 pairs (_) I5,I6: 1.. / I5 = 1 => 11 pairs (_) / I6 = 1 => 11 pairs (_) D5,I5: 1.. / D5 = 1 => 11 pairs (_) / I5 = 1 => 11 pairs (_) D6,I6: 1.. / D6 = 1 => 11 pairs (_) / I6 = 1 => 11 pairs (_) E2,G2: 2.. / E2 = 2 => 12 pairs (_) / G2 = 2 => 0 pairs (X) E2,E6: 2.. / E2 = 2 => 12 pairs (_) / E6 = 2 => 0 pairs (X) A5,B5: 3.. / A5 = 3 => 12 pairs (_) / B5 = 3 => 12 pairs (_) A7,B9: 3.. / A7 = 3 => 12 pairs (_) / B9 = 3 => 12 pairs (_) D7,D9: 3.. / D7 = 3 => 12 pairs (_) / D9 = 3 => 12 pairs (_) A7,D7: 3.. / A7 = 3 => 12 pairs (_) / D7 = 3 => 12 pairs (_) B9,D9: 3.. / B9 = 3 => 12 pairs (_) / D9 = 3 => 12 pairs (_) A5,A7: 3.. / A5 = 3 => 12 pairs (_) / A7 = 3 => 12 pairs (_) B5,B9: 3.. / B5 = 3 => 12 pairs (_) / B9 = 3 => 12 pairs (_) D1,F1: 4.. / D1 = 4 => 11 pairs (_) / F1 = 4 => 0 pairs (X) H8,H9: 4.. / H8 = 4 => 11 pairs (_) / H9 = 4 => 12 pairs (_) F8,H8: 4.. / F8 = 4 => 12 pairs (_) / H8 = 4 => 11 pairs (_) D1,D9: 4.. / D1 = 4 => 11 pairs (_) / D9 = 4 => 0 pairs (X) D3,I3: 5.. / D3 = 5 => 0 pairs (X) / I3 = 5 => 16 pairs (_) E2,E6: 5.. / E2 = 5 => 0 pairs (X) / E6 = 5 => 12 pairs (_) B1,B2: 7.. / B1 = 7 => 0 pairs (*) / B2 = 7 => 0 pairs (X) C4,C5: 7.. / C4 = 7 => 11 pairs (_) / C5 = 7 => 13 pairs (_) G7,H7: 7.. / G7 = 7 => 14 pairs (_) / H7 = 7 => 12 pairs (_) B2,G2: 7.. / B2 = 7 => 11 pairs (_) / G2 = 7 => 0 pairs (*) D3,I3: 7.. / D3 = 7 => 16 pairs (_) / I3 = 7 => 0 pairs (X) A2,B2: 8.. / A2 = 8 => 12 pairs (_) / B2 = 8 => 0 pairs (*) F4,F5: 8.. / F4 = 8 => 13 pairs (_) / F5 = 8 => 12 pairs (_) H4,H6: 8.. / H4 = 8 => 0 pairs (X) / H6 = 8 => 11 pairs (_) B9,C9: 8.. / B9 = 8 => 14 pairs (_) / C9 = 8 => 10 pairs (_) A6,H6: 8.. / A6 = 8 => 0 pairs (X) / H6 = 8 => 11 pairs (_) H1,I1: 9.. / H1 = 9 => 10 pairs (_) / I1 = 9 => 14 pairs (_) G5,G6: 9.. / G5 = 9 => 12 pairs (_) / G6 = 9 => 11 pairs (_) A8,C9: 9.. / A8 = 9 => 10 pairs (_) / C9 = 9 => 14 pairs (_) A6,G6: 9.. / A6 = 9 => 12 pairs (_) / G6 = 9 => 11 pairs (_) A8,H8: 9.. / A8 = 9 => 10 pairs (_) / H8 = 9 => 14 pairs (_) C5,C9: 9.. / C5 = 9 => 10 pairs (_) / C9 = 9 => 14 pairs (_) I1,I9: 9.. / I1 = 9 => 14 pairs (_) / I9 = 9 => 10 pairs (_) * DURATION: 0:00:39.416843 START: 00:29:03.478841 END: 00:29:42.895684 2019-05-01 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,A8,B1,C4,C9,D3,E2,E6,F8,I3) * 6.1.3.8....39.6.14492.8163.1..69.4.3....4..6..46..3....64.19..8.1587.3.67...6.1.. * PAIR B1: 5,7 BLK 1 B2: 5,7,8 # reduction candidate for 5,7 B2: 8 => SOLVED * 671435892583926714492781635157698423839247561246153987364519278915872346728364159 B2: 5,7 # 12 pairs * PAIR B1: 5,7 ROW 1 D1: 5,7,2,4 # reduction candidate for 5,7 D1: 5,7 => CTR * 6.1.348....3926.14492.8163.1.76984.3389.4..6..46.53....64319..89158723467384651.. D1: 2,4 # 12 pairs F1: 5,7,2,4 # reduction candidate for 5,7 F1: 5,7 # 13 pairs H1: 5,7,2,9 # reduction candidate for 5,7 H1: 5,7 => CTR * 651.3.879873956214492781635187695423.2..4..6..46.23.8..64.19758.1587.3.6738.6.192 H1: 2,9 # 12 pairs I1: 5,7,2,9 # reduction candidate for 5,7 I1: 5,7 => CTR * 6.1.3.89..739562144927816351.769.4.3..9.47562546123....64.19..891587.3.67.8.6.1.9 I1: 2,9 # 12 pairs * PAIR A2: 5,8 BLK 1 B2: 5,8,7 # reduction candidate for 5,8 B2: 5,8 => SOLVED * 671435892583926714492781635157698423839247561246153987364519278915872346728364159 B2: 7 # 11 pairs * PAIR A2: 5,8 COL A A5: 5,8,2,3,9 # reduction candidate for 5,8 A5: 5,8 # 14 pairs A6: 5,8,2,9 # reduction candidate for 5,8 A6: 5,8 # 12 pairs * PAIR E2: 2,5 BLK 2 D1: 2,5,4,7 # reduction candidate for 2,5 D1: 2,5 => CTR * 6.1.348..8.39.6.14492781635127698453389547261546123987264319..89158723467384651.. D1: 4,7 # 12 pairs F1: 2,5,4,7 # reduction candidate for 2,5 F1: 2,5 # 17 pairs * PAIR E2: 2,5 ROW 2 G2: 2,5,7 # reduction candidate for 2,5 G2: 7 => SOLVED * 671435892583926714492781635157698423839247561246153987364519278915872346728364159 G2: 2,5 # 11 pairs * PAIR D3: 5,7 BLK 2 D1: 5,7,2,4 # reduction candidate for 5,7 D1: 5,7 => CTR * 6.1.348....3926.14492.8163.1.76984.3389.4..6..46.53....64319..89158723467384651.. D1: 2,4 # 12 pairs F1: 5,7,2,4 # reduction candidate for 5,7 F1: 5,7 # 13 pairs * PAIR D3: 5,7 COL D D5: 5,7,1,2 # reduction candidate for 5,7 D5: 5,7 # 17 pairs D6: 5,7,1,2 # reduction candidate for 5,7 D6: 5,7 # 17 pairs * PAIR I3: 5,7 BLK 3 H1: 5,7,2,9 # reduction candidate for 5,7 H1: 5,7 => CTR * 651.3.879873956214492781635187695423.2..4..6..46.23.8..64.19758.1587.3.6738.6.192 H1: 2,9 # 12 pairs I1: 5,7,2,9 # reduction candidate for 5,7 I1: 5,7 => CTR * 6.1.3.89..739562144927816351.769.4.3..9.47562546123....64.19..891587.3.67.8.6.1.9 I1: 2,9 # 12 pairs G2: 5,7,2 # reduction candidate for 5,7 G2: 5,7 # 12 pairs * PAIR I3: 5,7 COL I I5: 5,7,1,2 # reduction candidate for 5,7 I5: 5,7 # 14 pairs I6: 5,7,1,2 # reduction candidate for 5,7 I6: 5,7 # 14 pairs * PAIR C4: 7,8 BLK 4 C5: 7,8,9 # reduction candidate for 7,8 C5: 7,8 # 14 pairs C5: 9 # 10 pairs * PAIR C4: 7,8 ROW 4 F4: 7,8,2,5 # reduction candidate for 7,8 F4: 7,8 # 14 pairs H4: 7,8,2,5 # reduction candidate for 7,8 H4: 7,8 => CTR * 65143782987392651449258163712.69.4.3....48.6..46.53....64.19..8.1587.3.6789365142 H4: 2,5 # 12 pairs * PAIR E6: 2,5 BLK 5 F4: 2,5,7,8 # reduction candidate for 2,5 F4: 2,5 => CTR * 6514378..8739265144925816371..69245353..48.6.246.539813642197.8.1587.3.67...651.. F4: 7,8 # 14 pairs D5: 2,5,1,7 # reduction candidate for 2,5 D5: 2,5 # 16 pairs F5: 2,5,7,8 # reduction candidate for 2,5 F5: 2,5 => CTR * 6514378..873926514492581637127698453538.42961946153782364219.78.1587.3.67...651.. F5: 7,8 # 12 pairs D6: 2,5,1,7 # reduction candidate for 2,5 D6: 2,5 => CTR * 651.3.8..8739.6.14492.8163.1..69.4.3...14.96.946..3781.64.19.782158743967.9.6.14. D6: 1,7 # 12 pairs * PAIR E6: 2,5 ROW 6 A6: 2,5,8,9 # reduction candidate for 2,5 A6: 2,5 # 14 pairs G6: 2,5,7,9 # reduction candidate for 2,5 G6: 2,5 # 15 pairs H6: 2,5,7,8 # reduction candidate for 2,5 H6: 2,5 => CTR * 6.1.3.8..5839267144927816351.769.483..9.48.67846.53921.64.19..8.1587.3.67.8.6.1.. H6: 7,8 # 12 pairs I6: 2,5,1,7 # reduction candidate for 2,5 I6: 2,5 => CTR * 65143.8298739265144925816371..69.45353.742961946153782364219.782158743967.9.6.14. I6: 1,7 # 12 pairs * PAIR A7: 2,3 BLK 7 B9: 2,3,8 # reduction candidate for 2,3 B9: 8 # 14 pairs B9: 2,3 # 10 pairs * PAIR A7: 2,3 ROW 7 D7: 2,3,5 # reduction candidate for 2,3 D7: 5 => SOLVED * 671435892583926714492781635157698423839247561246153987364519278915872346728364159 D7: 2,3 # 15 pairs * PAIR A7: 2,3 COL A A5: 2,3,5,8,9 # reduction candidate for 2,3 A5: 5,8,9 # 12 pairs A5: 2,3 # 12 pairs * PAIR A8: 2,9 ROW 8 H8: 2,9,4 # reduction candidate for 2,9 H8: 2,9 # 12 pairs H8: 4 # 11 pairs * PAIR A8: 2,9 COL A A5: 2,9,3,5,8 # reduction candidate for 2,9 A5: 2,9 # 14 pairs A6: 2,9,5,8 # reduction candidate for 2,9 A6: 2,9 # 14 pairs * PAIR C9: 8,9 COL C C5: 8,9,7 # reduction candidate for 8,9 C5: 7 # 13 pairs C5: 8,9 # 11 pairs * PAIR F8: 2,4 BLK 8 D9: 2,4,3,5 # reduction candidate for 2,4 D9: 2,4 # 14 pairs F9: 2,4,5 # reduction candidate for 2,4 F9: 2,4 => SOLVED * 671435892583926714492781635157698423839247561246153987364519278915872346728364159 F9: 5 # 15 pairs * PAIR F8: 2,4 ROW 8 H8: 2,4,9 # reduction candidate for 2,4 H8: 9 # 14 pairs H8: 2,4 # 10 pairs * PAIR F8: 2,4 COL F F1: 2,4,5,7 # reduction candidate for 2,4 F1: 2,4 # 20 pairs F1: 5,7 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060708-absurd-base-pr-000.dot * REASONING * PRF # B2: 8 => SOL * DIS # D1: 5,7 => CTR => D1: 2,4 * DIS # H1: 5,7 => CTR => H1: 2,9 * DIS # I1: 5,7 => CTR => I1: 2,9 * PRF # B2: 5,8 => SOL * DIS # D1: 2,5 => CTR => D1: 4,7 * PRF # G2: 7 => SOL * DIS # D1: 5,7 => CTR => D1: 2,4 * DIS # H1: 5,7 => CTR => H1: 2,9 * DIS # I1: 5,7 => CTR => I1: 2,9 * DIS # H4: 7,8 => CTR => H4: 2,5 * DIS # F4: 2,5 => CTR => F4: 7,8 * DIS # F5: 2,5 => CTR => F5: 7,8 * DIS # D6: 2,5 => CTR => D6: 1,7 * DIS # H6: 2,5 => CTR => H6: 7,8 * DIS # I6: 2,5 => CTR => I6: 1,7 * PRF # D7: 5 => SOL * PRF # F9: 2,4 => SOL * CNT 18 HDP CHAINS / 67 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,A8,B1,C4,C9,D3,E2,E6,F8,I3) * 6.1.3.8....39.6.14492.8163.1..69.4.3....4..6..46..3....64.19..8.1587.3.67...6.1.. * PAIR B1: 5,7 BLK 1 B2: 5,7,8 # reduction candidate for 5,7 B2: 8 => SOLVED * 671435892583926714492781635157698423839247561246153987364519278915872346728364159 * DURATION: 0:00:02.146662 START: 00:30:24.609181 END: 00:30:26.755843 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060708-absurd-base-pr-001.dot * REASONING * PRF # B2: 8 => SOL * STA B2: 8 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060708, absurd
Solution
position: 671435892583926714492781635157698423839247561246153987364519278915872346728364159 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: 5,7 => UNS * PRF # B2: 8 => SOL * DIS # D1: 5,7 => CTR => D1: 2,4 * INC # D1: 2,4 => UNS * INC # F1: 5,7 => UNS * DIS # H1: 5,7 => CTR => H1: 2,9 * INC # H1: 2,9 => UNS * DIS # I1: 5,7 => CTR => I1: 2,9 * INC # I1: 2,9 => UNS * PRF # B2: 5,8 => SOL * INC # B2: 7 => UNS * INC # A5: 5,8 => UNS * INC # A6: 5,8 => UNS * DIS # D1: 2,5 => CTR => D1: 4,7 * INC # D1: 4,7 => UNS * INC # F1: 2,5 => UNS * INC # G2: 2,5 => UNS * PRF # G2: 7 => SOL * DIS # D1: 5,7 => CTR => D1: 2,4 * INC # D1: 2,4 => UNS * INC # F1: 5,7 => UNS * INC # D5: 5,7 => UNS * INC # D6: 5,7 => UNS * DIS # H1: 5,7 => CTR => H1: 2,9 * INC # H1: 2,9 => UNS * DIS # I1: 5,7 => CTR => I1: 2,9 * INC # I1: 2,9 => UNS * INC # G2: 5,7 => UNS * INC # I5: 5,7 => UNS * INC # I6: 5,7 => UNS * INC # C5: 7,8 => UNS * INC # C5: 9 => UNS * INC # F4: 7,8 => UNS * DIS # H4: 7,8 => CTR => H4: 2,5 * INC # H4: 2,5 => UNS * DIS # F4: 2,5 => CTR => F4: 7,8 * INC # F4: 7,8 => UNS * INC # D5: 2,5 => UNS * DIS # F5: 2,5 => CTR => F5: 7,8 * INC # F5: 7,8 => UNS * DIS # D6: 2,5 => CTR => D6: 1,7 * INC # D6: 1,7 => UNS * INC # A6: 2,5 => UNS * INC # G6: 2,5 => UNS * DIS # H6: 2,5 => CTR => H6: 7,8 * INC # H6: 7,8 => UNS * DIS # I6: 2,5 => CTR => I6: 1,7 * INC # I6: 1,7 => UNS * INC # B9: 2,3 => UNS * INC # B9: 8 => UNS * INC # D7: 2,3 => UNS * PRF # D7: 5 => SOL * INC # A5: 2,3 => UNS * INC # A5: 5,8,9 => UNS * INC # H8: 2,9 => UNS * INC # H8: 4 => UNS * INC # A5: 2,9 => UNS * INC # A6: 2,9 => UNS * INC # C5: 8,9 => UNS * INC # C5: 7 => UNS * INC # D9: 2,4 => UNS * PRF # F9: 2,4 => SOL * INC # F9: 5 => UNS * INC # H8: 2,4 => UNS * INC # H8: 9 => UNS * INC # F1: 2,4 => UNS * INC # F1: 5,7 => UNS * CNT 67 HDP CHAINS / 67 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 5,7 => UNS * PRF # B2: 8 => SOL * STA B2: 8 * CNT 2 HDP CHAINS / 2 HYP OPENED