Analysis of zz-www.sudokuoftheday.co.uk-20060703-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: 12....5........1374.7...........38.6.6.....2..5.9..3...46..1.......58..28...6.... initial
Autosolve
position: 12....5..6.5..21374.7...2.......38.6.6.....2..5.9.63..546..1.......586.28.2.6.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 3,9 => CTR => B3: 8 * DIS # B3: 3 => CTR => B3: 8,9 * DIS # E2: 8,9 => CTR => E2: 4 * DIS # F9: 4 => CTR => F9: 7,9 * DIS # E2: 9 => CTR => E2: 4,8 * DIS # D5: 4,8 => CTR => D5: 1,5,7 * DIS # H3: 8,9 => CTR => H3: 6 * DIS # E3: 8,9 => CTR => E3: 1,3 * PRF # I7: 8,9 => SOL * PRF # H4: 1,4 => SOL * DIS # I5: 1,4 => CTR => I5: 5,9 * DIS # I9: 1,4 => CTR => I9: 3,5,9 * PRF # H7: 7,9 => SOL * DIS # H8: 7,9 => CTR => H8: 1,4 * DIS # G9: 7,9 => CTR => G9: 4 * DIS # H9: 7,9 => CTR => H9: 1,4,5 * DIS # G5: 4 => CTR => G5: 7,9 * CNT 17 HDP CHAINS / 52 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B3: 3,9 => CTR => B3: 8 * DIS B3: 8 # F9: 4 => CTR => F9: 7,9 * DIS B3: 8 + F9: 7,9 # A4: 2,7 => CTR => A4: 9 * DIS B3: 8 + F9: 7,9 + A4: 9 # C6: 8 => CTR => C6: 1,4 * DIS B3: 8 + F9: 7,9 + A4: 9 + C6: 1,4 # D4: 1,2 => CTR => D4: 5 * PRF B3: 8 + F9: 7,9 + A4: 9 + C6: 1,4 + D4: 5 => SOL * STA B3: 8 + F9: 7,9 + A4: 9 + C6: 1,4 + D4: 5 * CNT 6 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 12....5........1374.7...........38.6.6.....2..5.9..3...46..1.......58..28...6.... | initial |
| 12....5..6.5..21374.7...2.......38.6.6.....2..5.9.63..546..1.......586.28.2.6.... | autosolve |
| 123697584695842137487315269971523846368174925254986371546231798739458612812769453 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) C1: 3,9 B2: 8,9 F1: 7,9 D2: 4,8 F3: 5,9 I3: 8,9 A6: 2,7 I6: 1,4 G7: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D3,E3: 1.. / D3 = 1 => 9 pairs (_) / E3 = 1 => 9 pairs (_) A4,A6: 2.. / A4 = 2 => 0 pairs (X) / A6 = 2 => 9 pairs (_) D7,E7: 2.. / D7 = 2 => 9 pairs (_) / E7 = 2 => 0 pairs (X) A6,E6: 2.. / A6 = 2 => 9 pairs (_) / E6 = 2 => 0 pairs (X) D4,D7: 2.. / D4 = 2 => 0 pairs (X) / D7 = 2 => 9 pairs (_) C1,B3: 3.. / C1 = 3 => 14 pairs (_) / B3 = 3 => 0 pairs (X) A5,C5: 3.. / A5 = 3 => 10 pairs (_) / C5 = 3 => 0 pairs (X) I7,I9: 3.. / I7 = 3 => 11 pairs (_) / I9 = 3 => 0 pairs (*) A5,A8: 3.. / A5 = 3 => 10 pairs (_) / A8 = 3 => 0 pairs (X) D2,E2: 4.. / D2 = 4 => 0 pairs (X) / E2 = 4 => 14 pairs (_) H1,I1: 4.. / H1 = 4 => 19 pairs (_) / I1 = 4 => 11 pairs (_) D8,H8: 4.. / D8 = 4 => 19 pairs (_) / H8 = 4 => 0 pairs (X) F5,F9: 4.. / F5 = 4 => 19 pairs (_) / F9 = 4 => 0 pairs (X) G5,G9: 4.. / G5 = 4 => 0 pairs (X) / G9 = 4 => 19 pairs (_) D3,F3: 5.. / D3 = 5 => 0 pairs (X) / F3 = 5 => 9 pairs (_) H4,I5: 5.. / H4 = 5 => 13 pairs (_) / I5 = 5 => 9 pairs (_) H9,I9: 5.. / H9 = 5 => 9 pairs (_) / I9 = 5 => 13 pairs (_) D4,H4: 5.. / D4 = 5 => 9 pairs (_) / H4 = 5 => 13 pairs (_) F3,F5: 5.. / F3 = 5 => 9 pairs (_) / F5 = 5 => 0 pairs (X) H4,H9: 5.. / H4 = 5 => 13 pairs (_) / H9 = 5 => 9 pairs (_) I5,I9: 5.. / I5 = 5 => 9 pairs (_) / I9 = 5 => 13 pairs (_) D1,D3: 6.. / D1 = 6 => 9 pairs (_) / D3 = 6 => 0 pairs (X) H1,H3: 6.. / H1 = 6 => 0 pairs (X) / H3 = 6 => 9 pairs (_) D1,H1: 6.. / D1 = 6 => 9 pairs (_) / H1 = 6 => 0 pairs (X) D3,H3: 6.. / D3 = 6 => 0 pairs (X) / H3 = 6 => 9 pairs (_) B2,B3: 8.. / B2 = 8 => 0 pairs (X) / B3 = 8 => 16 pairs (_) C5,C6: 8.. / C5 = 8 => 18 pairs (_) / C6 = 8 => 9 pairs (_) H7,I7: 8.. / H7 = 8 => 11 pairs (_) / I7 = 8 => 0 pairs (*) C6,E6: 8.. / C6 = 8 => 9 pairs (_) / E6 = 8 => 18 pairs (_) E7,F9: 9.. / E7 = 9 => 0 pairs (X) / F9 = 9 => 16 pairs (_) B2,E2: 9.. / B2 = 9 => 16 pairs (_) / E2 = 9 => 0 pairs (X) * DURATION: 0:00:30.677789 START: 00:17:53.906591 END: 00:18:24.584380 2019-05-01 * CP COUNT: (31) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B2,C1,D2,F1,F3,G7,I3,I6) * 12....5..6.5..21374.7...2.......38.6.6.....2..5.9.63..546..1.......586.28.2.6.... * PAIR C1: 3,9 BLK 1 B3: 3,9,8 # reduction candidate for 3,9 B3: 3,9 => CTR * 12....5..6854921374.7..52.......38.6.6.....2..5.9.63..546..1.......586.28.2.6.... B3: 8 # 16 pairs * PAIR C1: 3,9 ROW 1 E1: 3,9,7,8 # reduction candidate for 3,9 E1: 3,9 # 16 pairs E1: 7,8 # 12 pairs * PAIR C1: 3,9 COL C C5: 3,9,1,4,8 # reduction candidate for 3,9 C5: 3,9 # 16 pairs C8: 3,9,1 # reduction candidate for 3,9 C8: 3,9 # 13 pairs * PAIR B2: 8,9 BLK 1 B3: 8,9,3 # reduction candidate for 8,9 B3: 3 => CTR * 12....5..685492137437..52.......38.6.6.....2..5.9.63..546..1.......586.28.2.6.... B3: 8,9 # 14 pairs * PAIR B2: 8,9 ROW 2 E2: 8,9,4 # reduction candidate for 8,9 E2: 8,9 => CTR * 12....5.4695482137487...2.9.....38.6.6....42..5.9.63.1546.91783....586428.2.64915 E2: 4 # 14 pairs * PAIR F1: 7,9 BLK 2 E1: 7,9,3,8 # reduction candidate for 7,9 E1: 7,9 # 16 pairs E1: 3,8 # 10 pairs * PAIR F1: 7,9 COL F F9: 7,9,4 # reduction candidate for 7,9 F9: 4 => CTR * 12....5..695..2137487...2.9.....3896.6....425.5.9.63..546.91783....586.28.2.649.. F9: 7,9 # 19 pairs * PAIR D2: 4,8 BLK 2 E2: 4,8,9 # reduction candidate for 4,8 E2: 9 => CTR * 12....5..6.54921374.7..52.......38.6.6.....2..5.9.63..546..1.......586.28.2.6.... E2: 4,8 # 16 pairs * PAIR D2: 4,8 COL D D5: 4,8,1,5,7 # reduction candidate for 4,8 D5: 4,8 => CTR * 12.6875946.5..21374.7...26......38.6.6....42..5.9.63.1546291783....586428.2.64915 D5: 1,5,7 # 14 pairs * PAIR I3: 8,9 BLK 3 H1: 8,9,4,6 # reduction candidate for 8,9 H1: 8,9 # 12 pairs I1: 8,9,4 # reduction candidate for 8,9 I1: 8,9 # 19 pairs H3: 8,9,6 # reduction candidate for 8,9 H3: 8,9 => CTR * 129..75646854921374376152.......38.6.6...4.2..5.9.63.1546..1.......586.28.2.6.... H3: 6 # 9 pairs * PAIR I3: 8,9 ROW 3 B3: 8,9,3 # reduction candidate for 8,9 B3: 8,9 # 14 pairs E3: 8,9,1,3 # reduction candidate for 8,9 E3: 8,9 => CTR * 1296375..685..21374371.526......38.6.6...4.2..5.9.63..546..1.......586.28.2.694.. E3: 1,3 # 10 pairs * PAIR I3: 8,9 COL I I7: 8,9,3 # reduction candidate for 8,9 I7: 8,9 => SOLVED * 123697584695842137487315269971523846368174925254986371546231798739458612812769453 I7: 3 # 11 pairs * PAIR A6: 2,7 BLK 4 A4: 2,7,9 # reduction candidate for 2,7 A4: 2,7 # 13 pairs A4: 9 # 12 pairs * PAIR A6: 2,7 ROW 6 E6: 2,7,1,4,8 # reduction candidate for 2,7 E6: 2,7 # 22 pairs E6: 1,4,8 # 11 pairs * PAIR I6: 1,4 BLK 6 H4: 1,4,5,7,9 # reduction candidate for 1,4 H4: 1,4 => SOLVED * 123697584695842137487315269971523846368174925254986371546231798739458612812769453 H4: 5,7,9 # 9 pairs I5: 1,4,5,9 # reduction candidate for 1,4 I5: 1,4 => CTR * 12.679548695842137487.35269..4..3856.6.584921258916374546291783.3.4586.28.23674.5 I5: 5,9 # 10 pairs H6: 1,4,7 # reduction candidate for 1,4 H6: 1,4 # 22 pairs * PAIR I6: 1,4 ROW 6 C6: 1,4,8 # reduction candidate for 1,4 C6: 1,4 # 18 pairs E6: 1,4,2,7,8 # reduction candidate for 1,4 E6: 1,4 # 12 pairs * PAIR I6: 1,4 COL I I9: 1,4,3,5,9 # reduction candidate for 1,4 I9: 1,4 => CTR * 12.6..54.6.5842137487135269..45.38.6.6.7.4925.5.9.63.4546291783.3.45869289236..5. I9: 3,5,9 # 10 pairs * PAIR G7: 7,9 BLK 9 H7: 7,9,8 # reduction candidate for 7,9 H7: 7,9 => SOLVED * 123697584695842137487315269971523846368174925254986371546231798739458612812769453 H7: 8 # 11 pairs H8: 7,9,1,4 # reduction candidate for 7,9 H8: 7,9 => CTR * 123697548695842137487135269.14..3896369584721.5.9.63.4546..19839314586728723694.. H8: 1,4 # 10 pairs G9: 7,9,4 # reduction candidate for 7,9 G9: 7,9 => CTR * 12....5.4695..2137487...2.9.....38.6.6....42..5.9.6371546.91783....586428.2.64915 G9: 4 # 19 pairs H9: 7,9,1,4,5 # reduction candidate for 7,9 H9: 7,9 => CTR * 12....5..6.5842137487.352.9..4..3856.6.5.4921.51986374546.91783.39458612812367495 H9: 1,4,5 # 9 pairs * PAIR G7: 7,9 ROW 7 E7: 7,9,2,3 # reduction candidate for 7,9 E7: 2,3 # 20 pairs E7: 7,9 # 11 pairs * PAIR G7: 7,9 COL G G5: 7,9,4 # reduction candidate for 7,9 G5: 4 => CTR * 12....5.4695..2137487...2.9.....38.6.6....42..5.9.6371546.91783....586428.2.64915 G5: 7,9 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060703-absurd-base-pr-000.dot * REASONING * DIS # B3: 3,9 => CTR => B3: 8 * DIS # B3: 3 => CTR => B3: 8,9 * DIS # E2: 8,9 => CTR => E2: 4 * DIS # F9: 4 => CTR => F9: 7,9 * DIS # E2: 9 => CTR => E2: 4,8 * DIS # D5: 4,8 => CTR => D5: 1,5,7 * DIS # H3: 8,9 => CTR => H3: 6 * DIS # E3: 8,9 => CTR => E3: 1,3 * PRF # I7: 8,9 => SOL * PRF # H4: 1,4 => SOL * DIS # I5: 1,4 => CTR => I5: 5,9 * DIS # I9: 1,4 => CTR => I9: 3,5,9 * PRF # H7: 7,9 => SOL * DIS # H8: 7,9 => CTR => H8: 1,4 * DIS # G9: 7,9 => CTR => G9: 4 * DIS # H9: 7,9 => CTR => H9: 1,4,5 * DIS # G5: 4 => CTR => G5: 7,9 * CNT 17 HDP CHAINS / 52 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B2,C1,D2,F1,F3,G7,I3,I6) * 12....5..6.5..21374.7...2.......38.6.6.....2..5.9.63..546..1.......586.28.2.6.... * PAIR C1: 3,9 BLK 1 B3: 3,9,8 # reduction candidate for 3,9 B3: 3,9 => CTR * 12....5..6854921374.7..52.......38.6.6.....2..5.9.63..546..1.......586.28.2.6.... * PAIR F1: 7,9 COL F F9: 7,9,4 # reduction candidate for 7,9 F9: 4 => CTR * 123679548695..2137487.35269.....3896369..7425.58946371546.91783....586.28.2.649.. * PAIR RESTART * PAIR A6: 2,7 BLK 4 A4: 2,7,9 # reduction candidate for 2,7 A4: 2,7 => CTR * 123697548695842137487135269.14..3896369584721.5.9.63..546..19839314586728723694.. * PAIR I6: 1,4 ROW 6 C6: 1,4,8 # reduction candidate for 1,4 C6: 8 => CTR * 1236..5..695842137487..5269974..3856361..492.25.9.637.546..17..739458612812.6.4.. * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (C4,C6,D3,D7,D9,E1,E3,E4,E5,F1,F9,H1,H4,H7,H9,I1,I5,I6,I7,I9) * 1236..5..695842137487..526997...38.6368..492.25.98637.546..17..739458612812.6.4.. * PAIR E4: 1,2 BLK 5 D4: 1,2,5 # reduction candidate for 1,2 D4: 1,2 => CTR * 1236..5..695842137487..526997...3856368574921251986374546..17..7394586128127694.. D4: 5 => SOLVED * 123697584695842137487315269971523846368174925254986371546231798739458612812769453 * DURATION: 0:00:08.189382 START: 00:18:54.191484 END: 00:19:02.380866 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060703-absurd-base-pr-001.dot * REASONING * DIS # B3: 3,9 => CTR => B3: 8 * DIS B3: 8 # F9: 4 => CTR => F9: 7,9 * DIS B3: 8 + F9: 7,9 # A4: 2,7 => CTR => A4: 9 * DIS B3: 8 + F9: 7,9 + A4: 9 # C6: 8 => CTR => C6: 1,4 * DIS B3: 8 + F9: 7,9 + A4: 9 + C6: 1,4 # D4: 1,2 => CTR => D4: 5 * PRF B3: 8 + F9: 7,9 + A4: 9 + C6: 1,4 + D4: 5 => SOL * STA B3: 8 + F9: 7,9 + A4: 9 + C6: 1,4 + D4: 5 * CNT 6 HDP CHAINS / 7 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060703, absurd
Solution
position: 123697584695842137487315269971523846368174925254986371546231798739458612812769453 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 # B3: 3,9 => CTR => B3: 8 * INC # B3: 8 => UNS * INC # E1: 3,9 => UNS * INC # E1: 7,8 => UNS * INC # C5: 3,9 => UNS * INC # C8: 3,9 => UNS * INC # B3: 8,9 => UNS * DIS # B3: 3 => CTR => B3: 8,9 * DIS # E2: 8,9 => CTR => E2: 4 * INC # E2: 4 => UNS * INC # E1: 7,9 => UNS * INC # E1: 3,8 => UNS * INC # F9: 7,9 => UNS * DIS # F9: 4 => CTR => F9: 7,9 * INC # E2: 4,8 => UNS * DIS # E2: 9 => CTR => E2: 4,8 * DIS # D5: 4,8 => CTR => D5: 1,5,7 * INC # D5: 1,5,7 => UNS * INC # H1: 8,9 => UNS * INC # I1: 8,9 => UNS * DIS # H3: 8,9 => CTR => H3: 6 * INC # H3: 6 => UNS * INC # B3: 8,9 => UNS * DIS # E3: 8,9 => CTR => E3: 1,3 * INC # E3: 1,3 => UNS * PRF # I7: 8,9 => SOL * INC # I7: 3 => UNS * INC # A4: 2,7 => UNS * INC # A4: 9 => UNS * INC # E6: 2,7 => UNS * INC # E6: 1,4,8 => UNS * PRF # H4: 1,4 => SOL * INC # H4: 5,7,9 => UNS * DIS # I5: 1,4 => CTR => I5: 5,9 * INC # I5: 5,9 => UNS * INC # H6: 1,4 => UNS * INC # C6: 1,4 => UNS * INC # E6: 1,4 => UNS * DIS # I9: 1,4 => CTR => I9: 3,5,9 * INC # I9: 3,5,9 => UNS * PRF # H7: 7,9 => SOL * INC # H7: 8 => UNS * DIS # H8: 7,9 => CTR => H8: 1,4 * INC # H8: 1,4 => UNS * DIS # G9: 7,9 => CTR => G9: 4 * INC # G9: 4 => UNS * DIS # H9: 7,9 => CTR => H9: 1,4,5 * INC # H9: 1,4,5 => UNS * INC # E7: 7,9 => UNS * INC # E7: 2,3 => UNS * INC # G5: 7,9 => UNS * DIS # G5: 4 => CTR => G5: 7,9 * CNT 52 HDP CHAINS / 52 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B3: 3,9 => CTR => B3: 8 * INC B3: 8 # F9: 7,9 => UNS * DIS B3: 8 # F9: 4 => CTR => F9: 7,9 * DIS B3: 8 + F9: 7,9 # A4: 2,7 => CTR => A4: 9 * INC B3: 8 + F9: 7,9 + A4: 9 # C6: 1,4 => UNS * DIS B3: 8 + F9: 7,9 + A4: 9 # C6: 8 => CTR => C6: 1,4 * DIS B3: 8 + F9: 7,9 + A4: 9 + C6: 1,4 # D4: 1,2 => CTR => D4: 5 * PRF B3: 8 + F9: 7,9 + A4: 9 + C6: 1,4 + D4: 5 => SOL * STA B3: 8 + F9: 7,9 + A4: 9 + C6: 1,4 + D4: 5 * CNT 8 HDP CHAINS / 7 HYP OPENED