Analysis of zz-www.sudokuoftheday.co.uk-20060809-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006
level: medium
position: ..6...1..8.1..6..32...........35..9.6.5...42......4......4..53...9.678..4...1.97. initial
Autosolve
position: 5.6.3.1..8.1..62532.31.576...435.69.635...42.9..6.43.5...4..53.3.9.678..4...1397. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 4,9 => CTR => B1: 7 * DIS # E3: 4,9 => CTR => E3: 8 * DIS # D1: 7,9 => CTR => D1: 2,8 * DIS # E2: 7,9 => CTR => E2: 4 * DIS # B2: 4 => CTR => B2: 7,9 * DIS # D5: 8 => CTR => D5: 7,9 * DIS # I4: 8 => CTR => I4: 1,7 * DIS # I4: 1,8 => CTR => I4: 7 * PRF # I4: 7 => SOL * PRF # I5: 1,8 => SOL * DIS # I5: 7 => CTR => I5: 1,8 * DIS # B6: 2 => CTR => B6: 1,8 * DIS # B7: 2,8 => CTR => B7: 1,6 * PRF # C7: 2,8 => SOL * DIS # C7: 7 => CTR => C7: 2,8 * DIS # B9: 2,8 => CTR => B9: 5,6 * DIS # D9: 5 => CTR => D9: 2,8 * DIS # C6: 2,8 => CTR => C6: 7 * PRF # C6: 7 => SOL * DIS # D9: 2,5 => CTR => D9: 8 * PRF # D9: 8 => SOL * PRF # B8: 1 => SOL * PRF # I8: 2 => SOL * PRF # I7: 1 => SOL * DIS # B9: 2,6 => CTR => B9: 5,8 * CNT 25 HDP CHAINS / 44 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B1: 4,9 => CTR => B1: 7 * DIS B1: 7 # E3: 4,9 => CTR => E3: 8 * DIS B1: 7 + E3: 8 # I4: 8 => CTR => I4: 1,7 * DIS B1: 7 + E3: 8 + I4: 1,7 # B6: 2 => CTR => B6: 1,8 * PRF B1: 7 + E3: 8 + I4: 1,7 + B6: 1,8 # C7: 2,8 => SOL * STA B1: 7 + E3: 8 + I4: 1,7 + B6: 1,8 + C7: 2,8 * CNT 5 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..6...1..8.1..6..32...........35..9.6.5...42......4......4..53...9.678..4...1.97. | initial |
| 5.6.3.1..8.1..62532.31.576...435.69.635...42.9..6.43.5...4..53.3.9.678..4...1397. | autosolve |
| 576239184891746253243185769124358697635971428987624315768492531319567842452813976 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) B3: 4,9 D2: 7,9 H1: 4,8 A4: 1,7 H6: 1,8 A7: 1,7 C9: 2,8 D8: 2,5 H8: 1,4 I9: 2,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F4,F5: 1.. / F4 = 1 => 0 pairs (X) / F5 = 1 => 12 pairs (_) F5,I5: 1.. / F5 = 1 => 12 pairs (_) / I5 = 1 => 0 pairs (X) B6,H6: 1.. / B6 = 1 => 0 pairs (X) / H6 = 1 => 21 pairs (_) A4,A7: 1.. / A4 = 1 => 0 pairs (*) / A7 = 1 => 0 pairs (X) H6,H8: 1.. / H6 = 1 => 21 pairs (_) / H8 = 1 => 0 pairs (X) D1,F1: 2.. / D1 = 2 => 0 pairs (*) / F1 = 2 => 0 pairs (X) F4,E6: 2.. / F4 = 2 => 0 pairs (X) / E6 = 2 => 0 pairs (_) B4,F4: 2.. / B4 = 2 => 0 pairs (*) / F4 = 2 => 0 pairs (X) E6,E7: 2.. / E6 = 2 => 0 pairs (*) / E7 = 2 => 0 pairs (X) E2,E3: 4.. / E2 = 4 => 13 pairs (_) / E3 = 4 => 0 pairs (X) H8,I8: 4.. / H8 = 4 => 21 pairs (_) / I8 = 4 => 0 pairs (X) B2,E2: 4.. / B2 = 4 => 0 pairs (X) / E2 = 4 => 13 pairs (_) H1,H8: 4.. / H1 = 4 => 0 pairs (X) / H8 = 4 => 21 pairs (_) B8,B9: 5.. / B8 = 5 => 0 pairs (X) / B9 = 5 => 12 pairs (_) D8,D9: 5.. / D8 = 5 => 12 pairs (_) / D9 = 5 => 0 pairs (X) B8,D8: 5.. / B8 = 5 => 0 pairs (X) / D8 = 5 => 12 pairs (_) B9,D9: 5.. / B9 = 5 => 12 pairs (_) / D9 = 5 => 0 pairs (X) B7,B9: 6.. / B7 = 6 => 10 pairs (_) / B9 = 6 => 0 pairs (X) I7,I9: 6.. / I7 = 6 => 0 pairs (X) / I9 = 6 => 10 pairs (_) B7,I7: 6.. / B7 = 6 => 10 pairs (_) / I7 = 6 => 0 pairs (X) B9,I9: 6.. / B9 = 6 => 0 pairs (X) / I9 = 6 => 10 pairs (_) B1,B2: 7.. / B1 = 7 => 12 pairs (_) / B2 = 7 => 0 pairs (X) A4,C6: 7.. / A4 = 7 => 0 pairs (X) / C6 = 7 => 0 pairs (_) I4,I5: 7.. / I4 = 7 => 0 pairs (*) / I5 = 7 => 0 pairs (X) A7,C7: 7.. / A7 = 7 => 0 pairs (*) / C7 = 7 => 0 pairs (X) B1,D1: 7.. / B1 = 7 => 12 pairs (_) / D1 = 7 => 0 pairs (X) A4,I4: 7.. / A4 = 7 => 0 pairs (X) / I4 = 7 => 0 pairs (_) C6,E6: 7.. / C6 = 7 => 0 pairs (*) / E6 = 7 => 0 pairs (X) A4,A7: 7.. / A4 = 7 => 0 pairs (X) / A7 = 7 => 0 pairs (_) C6,C7: 7.. / C6 = 7 => 0 pairs (*) / C7 = 7 => 0 pairs (X) E3,I3: 8.. / E3 = 8 => 17 pairs (_) / I3 = 8 => 0 pairs (X) H1,H6: 8.. / H1 = 8 => 21 pairs (_) / H6 = 8 => 0 pairs (X) I1,I3: 9.. / I1 = 9 => 13 pairs (_) / I3 = 9 => 17 pairs (_) E7,F7: 9.. / E7 = 9 => 0 pairs (*) / F7 = 9 => 0 pairs (X) * DURATION: 0:00:38.492148 START: 01:40:05.241576 END: 01:40:43.733724 2019-05-01 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A7,B3,C9,D2,D8,H1,H6,H8,I9) * 5.6.3.1..8.1..62532.31.576...435.69.635...42.9..6.43.5...4..53.3.9.678..4...1397. * PAIR B3: 4,9 BLK 1 B1: 4,9,7 # reduction candidate for 4,9 B1: 4,9 => CTR * 5.67321..8719462532.318576..2435169863587.42.9..6243.5...49853.3.9.678..4...1397. B1: 7 # 12 pairs B2: 4,9,7 # reduction candidate for 4,9 B2: 4,9 # 12 pairs * PAIR B3: 4,9 ROW 3 E3: 4,9,8 # reduction candidate for 4,9 E3: 4,9 => CTR * 5.6.3.1498.1..62532.31.5768.8435269.635..14279126743851.742.53.3.9.678144...1397. E3: 8 # 17 pairs I3: 4,9,8 # reduction candidate for 4,9 I3: 4,9 # 17 pairs * PAIR D2: 7,9 BLK 2 D1: 7,9,2,8 # reduction candidate for 7,9 D1: 7,9 => CTR * 5.6.321..8.1.462532.318576..243516986358..42.9..6243.5...49853.3.9.678..4...1397. D1: 2,8 # 14 pairs E2: 7,9,4 # reduction candidate for 7,9 E2: 7,9 => CTR * 576.3.149841..6253293145768.8435269.635..14279126743851.742.53.3.9.678144...1397. E2: 4 # 13 pairs * PAIR D2: 7,9 ROW 2 B2: 7,9,4 # reduction candidate for 7,9 B2: 4 => CTR * 576.3.149841..6253293145768.8435269.635..14279126743851.742.53.3.9.678144...1397. B2: 7,9 # 13 pairs * PAIR D2: 7,9 COL D D5: 7,9,8 # reduction candidate for 7,9 D5: 8 => CTR * 5.6.321..8.1.462532.318576..243516986358.942.9..6.43.5...4.853.3.9.678..4...1397. D5: 7,9 # 14 pairs * PAIR H1: 4,8 BLK 3 I1: 4,8,9 # reduction candidate for 4,8 I1: 4,8 # 17 pairs I3: 4,8,9 # reduction candidate for 4,8 I3: 4,8 # 13 pairs * PAIR A4: 1,7 ROW 4 I4: 1,7,8 # reduction candidate for 1,7 I4: 8 => CTR * 5.6.3.1..8.1..62532.31.576.7.435.698635...4279..6743151.74295363.95678414...1397. I4: 1,7 # 14 pairs * PAIR H6: 1,8 BLK 6 I4: 1,8,7 # reduction candidate for 1,8 I4: 1,8 => CTR * 5.6.3.1..8.1..62532.31.576.7.435.69.635...4279..6743.51.74295363.95678..4...1397. I4: 7 => SOLVED * 576239184891746253243185769124358697635971428987624315768492531319567842452813976 I5: 1,8,7 # reduction candidate for 1,8 I5: 1,8 => SOLVED * 576239184891746253243185769124358697635971428987624315768492531319567842452813976 I5: 7 => CTR * 5.6.3.1..8.1..62532.31.576...435.69.635..14279..6743.5..742953.3.95678..45.813976 * PAIR H6: 1,8 ROW 6 B6: 1,8,2 # reduction candidate for 1,8 B6: 2 => CTR * 5.62381..8.1..62532.31.576...435.69.635...42.92.6.4315...42953.3.9567842452813976 B6: 1,8 # 13 pairs * PAIR C9: 2,8 BLK 7 B7: 2,8,1,6 # reduction candidate for 2,8 B7: 2,8 => CTR * 5.6.3.1..8.1..62532.31.576...435.69.635...42.9..6.43.51.74..5363592678..468513972 B7: 1,6 # 11 pairs C7: 2,8,7 # reduction candidate for 2,8 C7: 2,8 => SOLVED * 576239184891746253243185769124358697635971428987624315768492531319567842452813976 C7: 7 => CTR * 5.6.3.1..8.1..62532.31.576.7.435.69.635...4279..6743.51.74295363.95678..4...1397. B9: 2,8,5,6 # reduction candidate for 2,8 B9: 2,8 => CTR * 5.6.321..8.1..62532.31.576..2435.69.635...42.9186.43.5.6.4..53.3592678..4..513976 B9: 5,6 # 11 pairs * PAIR C9: 2,8 ROW 9 D9: 2,8,5 # reduction candidate for 2,8 D9: 5 => CTR * 5.6.321..8.1..62532.31.576.124358697635..1428987624315712489536359267841468513972 D9: 2,8 # 12 pairs * PAIR C9: 2,8 COL C C6: 2,8,7 # reduction candidate for 2,8 C6: 2,8 => CTR * 5.6.3.1..8.1..62532.31.576.7.435.69.635...4279..6743.51.74295363.95678..4...1397. C6: 7 => SOLVED * 576239184891746253243185769124358697635971428987624315768492531319567842452813976 * PAIR D8: 2,5 BLK 8 D9: 2,5,8 # reduction candidate for 2,5 D9: 2,5 => CTR * 5.6.321..8.1..62532.31.576.124358697635..14289876243157.248953.3.9.6784.4.8.1397. D9: 8 => SOLVED * 576239184891746253243185769124358697635971428987624315768492531319567842452813976 * PAIR D8: 2,5 ROW 8 B8: 2,5,1 # reduction candidate for 2,5 B8: 1 => SOLVED * 576239184891746253243185769124358697635971428987624315768492531319567842452813976 B8: 2,5 # 13 pairs * PAIR H8: 1,4 BLK 9 I8: 1,4,2 # reduction candidate for 1,4 I8: 2 => SOLVED * 576239184891746253243185769124358697635971428987624315768492531319567842452813976 I8: 1,4 # 13 pairs * PAIR I9: 2,6 BLK 9 I7: 2,6,1 # reduction candidate for 2,6 I7: 1 => SOLVED * 576239184891746253243185769124358697635971428987624315768492531319567842452813976 I7: 2,6 # 13 pairs * PAIR I9: 2,6 ROW 9 B9: 2,6,5,8 # reduction candidate for 2,6 B9: 2,6 => CTR * 5.6.3218.8.1..62532.318576.124358697635..142898762431571249.536359267841468513972 B9: 5,8 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060809-absurd-base-pr-000.dot * REASONING * DIS # B1: 4,9 => CTR => B1: 7 * DIS # E3: 4,9 => CTR => E3: 8 * DIS # D1: 7,9 => CTR => D1: 2,8 * DIS # E2: 7,9 => CTR => E2: 4 * DIS # B2: 4 => CTR => B2: 7,9 * DIS # D5: 8 => CTR => D5: 7,9 * DIS # I4: 8 => CTR => I4: 1,7 * DIS # I4: 1,8 => CTR => I4: 7 * PRF # I4: 7 => SOL * PRF # I5: 1,8 => SOL * DIS # I5: 7 => CTR => I5: 1,8 * DIS # B6: 2 => CTR => B6: 1,8 * DIS # B7: 2,8 => CTR => B7: 1,6 * PRF # C7: 2,8 => SOL * DIS # C7: 7 => CTR => C7: 2,8 * DIS # B9: 2,8 => CTR => B9: 5,6 * DIS # D9: 5 => CTR => D9: 2,8 * DIS # C6: 2,8 => CTR => C6: 7 * PRF # C6: 7 => SOL * DIS # D9: 2,5 => CTR => D9: 8 * PRF # D9: 8 => SOL * PRF # B8: 1 => SOL * PRF # I8: 2 => SOL * PRF # I7: 1 => SOL * DIS # B9: 2,6 => CTR => B9: 5,8 * CNT 25 HDP CHAINS / 44 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A7,B3,C9,D2,D8,H1,H6,H8,I9) * 5.6.3.1..8.1..62532.31.576...435.69.635...42.9..6.43.5...4..53.3.9.678..4...1397. * PAIR B3: 4,9 BLK 1 B1: 4,9,7 # reduction candidate for 4,9 B1: 4,9 => CTR * 5.67321..8719462532.318576..2435169863587.42.9..6243.5...49853.3.9.678..4...1397. * RESTART * PAIR B3: 4,9 ROW 3 E3: 4,9,8 # reduction candidate for 4,9 E3: 4,9 => CTR * 576.3.1498.1..62532.31.5768.8435269.635..14279126743851.742.53.3.9.678144...1397. * PAIR RESTART * PAIR A4: 1,7 ROW 4 I4: 1,7,8 # reduction candidate for 1,7 I4: 8 => CTR * 576.3.1..8917462532431857697.435.698635...4279..6743151.74295363.95678..4...1397. * PAIR RESTART * PAIR H6: 1,8 ROW 6 B6: 1,8,2 # reduction candidate for 1,8 B6: 2 => CTR * 576.3.1..8917462532431857691.435.697635.7142892.6.43.5...4..53.3.9.678..4...1397. * PAIR RESTART * PAIR C9: 2,8 BLK 7 C7: 2,8,7 # reduction candidate for 2,8 C7: 2,8 => SOLVED * 576239184891746253243185769124358697635971428987624315768492531319567842452813976 * DURATION: 0:00:06.754159 START: 01:41:12.756020 END: 01:41:19.510179 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060809-absurd-base-pr-001.dot * REASONING * DIS # B1: 4,9 => CTR => B1: 7 * DIS B1: 7 # E3: 4,9 => CTR => E3: 8 * DIS B1: 7 + E3: 8 # I4: 8 => CTR => I4: 1,7 * DIS B1: 7 + E3: 8 + I4: 1,7 # B6: 2 => CTR => B6: 1,8 * PRF B1: 7 + E3: 8 + I4: 1,7 + B6: 1,8 # C7: 2,8 => SOL * STA B1: 7 + E3: 8 + I4: 1,7 + B6: 1,8 + C7: 2,8 * CNT 5 HDP CHAINS / 7 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060809, absurd
Solution
position: 576239184891746253243185769124358697635971428987624315768492531319567842452813976 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:
* DIS # B1: 4,9 => CTR => B1: 7 * INC # B1: 7 => UNS * INC # B2: 4,9 => UNS * DIS # E3: 4,9 => CTR => E3: 8 * INC # E3: 8 => UNS * INC # I3: 4,9 => UNS * DIS # D1: 7,9 => CTR => D1: 2,8 * INC # D1: 2,8 => UNS * DIS # E2: 7,9 => CTR => E2: 4 * INC # E2: 4 => UNS * INC # B2: 7,9 => UNS * DIS # B2: 4 => CTR => B2: 7,9 * INC # D5: 7,9 => UNS * DIS # D5: 8 => CTR => D5: 7,9 * INC # I1: 4,8 => UNS * INC # I3: 4,8 => UNS * INC # I4: 1,7 => UNS * DIS # I4: 8 => CTR => I4: 1,7 * DIS # I4: 1,8 => CTR => I4: 7 * PRF # I4: 7 => SOL * PRF # I5: 1,8 => SOL * DIS # I5: 7 => CTR => I5: 1,8 * INC # B6: 1,8 => UNS * DIS # B6: 2 => CTR => B6: 1,8 * DIS # B7: 2,8 => CTR => B7: 1,6 * INC # B7: 1,6 => UNS * PRF # C7: 2,8 => SOL * DIS # C7: 7 => CTR => C7: 2,8 * DIS # B9: 2,8 => CTR => B9: 5,6 * INC # B9: 5,6 => UNS * INC # D9: 2,8 => UNS * DIS # D9: 5 => CTR => D9: 2,8 * DIS # C6: 2,8 => CTR => C6: 7 * PRF # C6: 7 => SOL * DIS # D9: 2,5 => CTR => D9: 8 * PRF # D9: 8 => SOL * INC # B8: 2,5 => UNS * PRF # B8: 1 => SOL * INC # I8: 1,4 => UNS * PRF # I8: 2 => SOL * INC # I7: 2,6 => UNS * PRF # I7: 1 => SOL * DIS # B9: 2,6 => CTR => B9: 5,8 * INC # B9: 5,8 => UNS * CNT 44 HDP CHAINS / 44 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B1: 4,9 => CTR => B1: 7 * DIS B1: 7 # E3: 4,9 => CTR => E3: 8 * INC B1: 7 + E3: 8 # I4: 1,7 => UNS * DIS B1: 7 + E3: 8 # I4: 8 => CTR => I4: 1,7 * INC B1: 7 + E3: 8 + I4: 1,7 # B6: 1,8 => UNS * DIS B1: 7 + E3: 8 + I4: 1,7 # B6: 2 => CTR => B6: 1,8 * PRF B1: 7 + E3: 8 + I4: 1,7 + B6: 1,8 # C7: 2,8 => SOL * STA B1: 7 + E3: 8 + I4: 1,7 + B6: 1,8 + C7: 2,8 * CNT 7 HDP CHAINS / 7 HYP OPENED