Analysis of zz-www.sudokuoftheday.co.uk-20060710-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: .1...23...63.9.....9..43.62....3.4218....5..9.....95....1.........25....6.5...2.7 initial
Autosolve
position: .1...239.263.9.....9..43.62.5..3.42183...56791....9583.213.....3..25....6.59..237 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 5,7 => CTR => A1: 4 * DIS # C1: 4 => CTR => C1: 7,8 * DIS # G3: 7,8 => CTR => G3: 1 * DIS # C4: 7,9 => CTR => C4: 6 * DIS # A7: 4 => CTR => A7: 7,9 * PRF # C6: 2,4 => SOL * DIS # C6: 6,7 => CTR => C6: 2,4 * DIS # C6: 4,7 => CTR => C6: 2,6 * DIS # D6: 6 => CTR => D6: 4,7 * PRF # B8: 4,7 => SOL * DIS # B8: 8 => CTR => B8: 4,7 * PRF # B8: 4,8 => SOL * DIS # B8: 7 => CTR => B8: 4,8 * PRF # F9: 4,8 => SOL * DIS # F9: 1 => CTR => F9: 4,8 * DIS # F9: 1,8 => CTR => F9: 4 * PRF # F9: 4 => SOL * DIS # G8: 1 => CTR => G8: 8,9 * DIS # H2: 1 => CTR => H2: 4,5 * CNT 19 HDP CHAINS / 41 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 5,7 => CTR => A1: 4 * DIS A1: 4 # G3: 7,8 => CTR => G3: 1 * PRF A1: 4 + G3: 1 # D1: 6,7 => SOL * STA A1: 4 + G3: 1 + D1: 6,7 * CNT 3 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .1...23...63.9.....9..43.62....3.4218....5..9.....95....1.........25....6.5...2.7 | initial |
| .1...239.263.9.....9..43.62.5..3.42183...56791....9583.213.....3..25....6.59..237 | autosolve |
| 418672395263591748597843162956738421834125679172469583721386954349257816685914237 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) A3: 5,7 C3: 7,8 I1: 5,8 A4: 7,9 C5: 2,4 B6: 4,7 D5: 1,4 E5: 1,2 B9: 4,8 E9: 1,8 G7: 8,9 H7: 4,5 H8: 1,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D5,E5: 1.. / D5 = 1 => 0 pairs (*) / E5 = 1 => 0 pairs (X) E9,F9: 1.. / E9 = 1 => 0 pairs (*) / F9 = 1 => 0 pairs (X) G8,H8: 1.. / G8 = 1 => 0 pairs (X) / H8 = 1 => 17 pairs (_) D3,G3: 1.. / D3 = 1 => 0 pairs (X) / G3 = 1 => 16 pairs (_) E5,E9: 1.. / E5 = 1 => 0 pairs (X) / E9 = 1 => 0 pairs (_) F2,F9: 1.. / F2 = 1 => 0 pairs (*) / F9 = 1 => 0 pairs (X) H2,H8: 1.. / H2 = 1 => 0 pairs (X) / H8 = 1 => 17 pairs (_) C5,C6: 2.. / C5 = 2 => 0 pairs (X) / C6 = 2 => 0 pairs (_) E5,E6: 2.. / E5 = 2 => 0 pairs (*) / E6 = 2 => 0 pairs (X) C5,E5: 2.. / C5 = 2 => 0 pairs (X) / E5 = 2 => 0 pairs (_) C6,E6: 2.. / C6 = 2 => 0 pairs (*) / E6 = 2 => 0 pairs (X) A1,C1: 4.. / A1 = 4 => 16 pairs (_) / C1 = 4 => 0 pairs (X) H2,I2: 4.. / H2 = 4 => 17 pairs (_) / I2 = 4 => 15 pairs (_) D5,D6: 4.. / D5 = 4 => 0 pairs (X) / D6 = 4 => 0 pairs (_) C5,D5: 4.. / C5 = 4 => 0 pairs (*) / D5 = 4 => 0 pairs (X) B9,F9: 4.. / B9 = 4 => 0 pairs (X) / F9 = 4 => 0 pairs (_) A1,A7: 4.. / A1 = 4 => 16 pairs (_) / A7 = 4 => 0 pairs (X) A1,A3: 5.. / A1 = 5 => 0 pairs (X) / A3 = 5 => 13 pairs (_) H7,I7: 5.. / H7 = 5 => 13 pairs (_) / I7 = 5 => 20 pairs (_) A3,D3: 5.. / A3 = 5 => 13 pairs (_) / D3 = 5 => 0 pairs (X) H2,H7: 5.. / H2 = 5 => 20 pairs (_) / H7 = 5 => 13 pairs (_) D1,E1: 6.. / D1 = 6 => 18 pairs (_) / E1 = 6 => 17 pairs (_) C4,C6: 6.. / C4 = 6 => 18 pairs (_) / C6 = 6 => 0 pairs (X) I7,I8: 6.. / I7 = 6 => 19 pairs (_) / I8 = 6 => 13 pairs (_) F8,I8: 6.. / F8 = 6 => 19 pairs (_) / I8 = 6 => 13 pairs (_) G2,G3: 7.. / G2 = 7 => 15 pairs (_) / G3 = 7 => 0 pairs (X) B6,B8: 7.. / B6 = 7 => 0 pairs (*) / B8 = 7 => 0 pairs (X) C1,C3: 8.. / C1 = 8 => 20 pairs (_) / C3 = 8 => 14 pairs (_) D4,F4: 8.. / D4 = 8 => 14 pairs (_) / F4 = 8 => 18 pairs (_) B8,B9: 8.. / B8 = 8 => 0 pairs (X) / B9 = 8 => 0 pairs (_) A4,C4: 9.. / A4 = 9 => 14 pairs (_) / C4 = 9 => 0 pairs (X) A7,C8: 9.. / A7 = 9 => 0 pairs (X) / C8 = 9 => 14 pairs (_) G7,G8: 9.. / G7 = 9 => 14 pairs (_) / G8 = 9 => 0 pairs (X) A7,G7: 9.. / A7 = 9 => 0 pairs (X) / G7 = 9 => 14 pairs (_) C8,G8: 9.. / C8 = 9 => 14 pairs (_) / G8 = 9 => 0 pairs (X) A4,A7: 9.. / A4 = 9 => 14 pairs (_) / A7 = 9 => 0 pairs (X) C4,C8: 9.. / C4 = 9 => 0 pairs (X) / C8 = 9 => 14 pairs (_) * DURATION: 0:00:40.999414 START: 00:35:11.317940 END: 00:35:52.317354 2019-05-01 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B6,B9,C3,C5,D5,E5,E9,G7,H7,H8,I1) * .1...239.263.9.....9..43.62.5..3.42183...56791....9583.213.....3..25....6.59..237 * PAIR A3: 5,7 BLK 1 A1: 5,7,4 # reduction candidate for 5,7 A1: 5,7 => CTR * .14..239.263.9.....98.43.62.5..3.42183241567914..295834213..95.37925....6859..237 A1: 4 # 16 pairs * PAIR A3: 5,7 ROW 3 D3: 5,7,1,8 # reduction candidate for 5,7 D3: 5,7 # 17 pairs D3: 1,8 # 14 pairs * PAIR C3: 7,8 BLK 1 C1: 7,8,4 # reduction candidate for 7,8 C1: 4 => CTR * .14..239.263.9.....98.43.62.5..3.42183241567914..295834213..95.37925....6859..237 C1: 7,8 # 16 pairs * PAIR C3: 7,8 ROW 3 D3: 7,8,1,5 # reduction candidate for 7,8 D3: 7,8 # 17 pairs G3: 7,8,1 # reduction candidate for 7,8 G3: 7,8 => CTR * 41...239.263.9....59.143.62.5..3.42183241567917462958372136....38.25....645981237 G3: 1 # 16 pairs * PAIR I1: 5,8 BLK 3 I2: 5,8,4 # reduction candidate for 5,8 I2: 5,8 # 17 pairs I2: 4 # 15 pairs * PAIR I1: 5,8 ROW 1 D1: 5,8,6,7 # reduction candidate for 5,8 D1: 5,8 # 20 pairs D1: 6,7 # 14 pairs * PAIR I1: 5,8 COL I I7: 5,8,4,6 # reduction candidate for 5,8 I7: 5,8 # 15 pairs I7: 4,6 # 14 pairs * PAIR A4: 7,9 BLK 4 C4: 7,9,6 # reduction candidate for 7,9 C4: 7,9 => CTR * .1...239.263.9.....9..43.62.5..3.421832415679146729583.213.....37.25....6859..237 C4: 6 # 18 pairs * PAIR A4: 7,9 COL A A7: 7,9,4 # reduction candidate for 7,9 A7: 4 => CTR * .14..239.263.91.4..98.4316295..3.421832..56791....95834213..95.3.925....685914237 A7: 7,9 # 16 pairs * PAIR C5: 2,4 BLK 4 C6: 2,4,6,7 # reduction candidate for 2,4 C6: 2,4 => SOLVED * 418672395263591748597843162956738421834125679172469583721386954349257816685914237 C6: 6,7 => CTR * .1...239.263.9.....9..43.62.5..3.42183241567914..29583.213.....37.25....6859..237 * PAIR B6: 4,7 BLK 4 C6: 4,7,2,6 # reduction candidate for 4,7 C6: 4,7 => CTR * .1...239.263.9.....9..43.62956.3.4218324156791..629583.213..9.8389257146645981237 C6: 2,6 # 14 pairs * PAIR B6: 4,7 ROW 6 D6: 4,7,6 # reduction candidate for 4,7 D6: 6 => CTR * .1..6239.263.9.....9..43.62.56.3.4218324156791..629583.2137....38.25....6.5981237 D6: 4,7 # 16 pairs * PAIR B6: 4,7 COL B B8: 4,7,8 # reduction candidate for 4,7 B8: 4,7 => SOLVED * 418672395263591748597843162956738421834125679172469583721386954349257816685914237 B8: 8 => CTR * 41...239.263.9....59..43.62956.3.42183...567917...95837213..9.83892571466459..237 * PAIR B9: 4,8 BLK 7 B8: 4,8,7 # reduction candidate for 4,8 B8: 4,8 => SOLVED * 418672395263591748597843162956738421834125679172469583721386954349257816685914237 B8: 7 => CTR * .1...239.263.91....9..43162.5..3.42183.12567914...9583.213.....37.25....685914237 * PAIR B9: 4,8 ROW 9 F9: 4,8,1 # reduction candidate for 4,8 F9: 4,8 => SOLVED * 418672395263591748597843162956738421834125679172469583721386954349257816685914237 F9: 1 => CTR * 41.672395263598714597143.62.5..3.42183..1567917..29583721364958389257146645981237 * PAIR E9: 1,8 BLK 8 F9: 1,8,4 # reduction candidate for 1,8 F9: 1,8 => CTR * 41..7239.263.9.71459714386295673842183...567917...95837213..9..3892571466459..237 F9: 4 => SOLVED * 418672395263591748597843162956738421834125679172469583721386954349257816685914237 * PAIR G7: 8,9 BLK 9 G8: 8,9,1 # reduction candidate for 8,9 G8: 1 => CTR * 41..72395263598714597143862956.3.4218324156791...29583.213.4958389257146645981237 G8: 8,9 # 17 pairs * PAIR H7: 4,5 BLK 9 I7: 4,5,6,8 # reduction candidate for 4,5 I7: 4,5 # 20 pairs I7: 6,8 # 16 pairs * PAIR H7: 4,5 COL H H2: 4,5,1 # reduction candidate for 4,5 H2: 1 => CTR * 41..72395263598714597143862956.3.4218324156791...29583.213.4958389257146645981237 H2: 4,5 # 17 pairs * PAIR H8: 1,4 COL H H2: 1,4,5 # reduction candidate for 1,4 H2: 5 # 20 pairs H2: 1,4 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060710-absurd-base-pr-000.dot * REASONING * DIS # A1: 5,7 => CTR => A1: 4 * DIS # C1: 4 => CTR => C1: 7,8 * DIS # G3: 7,8 => CTR => G3: 1 * DIS # C4: 7,9 => CTR => C4: 6 * DIS # A7: 4 => CTR => A7: 7,9 * PRF # C6: 2,4 => SOL * DIS # C6: 6,7 => CTR => C6: 2,4 * DIS # C6: 4,7 => CTR => C6: 2,6 * DIS # D6: 6 => CTR => D6: 4,7 * PRF # B8: 4,7 => SOL * DIS # B8: 8 => CTR => B8: 4,7 * PRF # B8: 4,8 => SOL * DIS # B8: 7 => CTR => B8: 4,8 * PRF # F9: 4,8 => SOL * DIS # F9: 1 => CTR => F9: 4,8 * DIS # F9: 1,8 => CTR => F9: 4 * PRF # F9: 4 => SOL * DIS # G8: 1 => CTR => G8: 8,9 * DIS # H2: 1 => CTR => H2: 4,5 * CNT 19 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B6,B9,C3,C5,D5,E5,E9,G7,H7,H8,I1) * .1...239.263.9.....9..43.62.5..3.42183...56791....9583.213.....3..25....6.59..237 * PAIR A3: 5,7 BLK 1 A1: 5,7,4 # reduction candidate for 5,7 A1: 5,7 => CTR * .14..239.263.9.....98.43.62.5..3.42183241567914..295834213..95.37925....6859..237 * PAIR C3: 7,8 ROW 3 D3: 7,8,1 # reduction candidate for 7,8 D3: 7,8 # 20 pairs G3: 7,8,1 # reduction candidate for 7,8 G3: 7,8 => CTR * 41..7239.263.98714597143862.5.83642183241567917..29583.213.....38.257..6645981237 * RESTART * PAIR RESTART * PAIR I1: 5,8 BLK 3 I2: 5,8,4 # reduction candidate for 5,8 I2: 4 # 21 pairs I2: 5,8 # 20 pairs * PAIR I1: 5,8 ROW 1 D1: 5,8,6,7 # reduction candidate for 5,8 D1: 6,7 => SOLVED * 418672395263591748597843162956738421834125679172469583721386954349257816685914237 * DURATION: 0:00:06.619527 START: 00:36:18.404036 END: 00:36:25.023563 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060710-absurd-base-pr-001.dot * REASONING * DIS # A1: 5,7 => CTR => A1: 4 * DIS A1: 4 # G3: 7,8 => CTR => G3: 1 * PRF A1: 4 + G3: 1 # D1: 6,7 => SOL * STA A1: 4 + G3: 1 + D1: 6,7 * CNT 3 HDP CHAINS / 7 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060710, absurd
Solution
position: 418672395263591748597843162956738421834125679172469583721386954349257816685914237 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 # A1: 5,7 => CTR => A1: 4 * INC # A1: 4 => UNS * INC # D3: 5,7 => UNS * INC # D3: 1,8 => UNS * INC # C1: 7,8 => UNS * DIS # C1: 4 => CTR => C1: 7,8 * INC # D3: 7,8 => UNS * DIS # G3: 7,8 => CTR => G3: 1 * INC # G3: 1 => UNS * INC # I2: 5,8 => UNS * INC # I2: 4 => UNS * INC # D1: 5,8 => UNS * INC # D1: 6,7 => UNS * INC # I7: 5,8 => UNS * INC # I7: 4,6 => UNS * DIS # C4: 7,9 => CTR => C4: 6 * INC # C4: 6 => UNS * INC # A7: 7,9 => UNS * DIS # A7: 4 => CTR => A7: 7,9 * PRF # C6: 2,4 => SOL * DIS # C6: 6,7 => CTR => C6: 2,4 * DIS # C6: 4,7 => CTR => C6: 2,6 * INC # C6: 2,6 => UNS * INC # D6: 4,7 => UNS * DIS # D6: 6 => CTR => D6: 4,7 * PRF # B8: 4,7 => SOL * DIS # B8: 8 => CTR => B8: 4,7 * PRF # B8: 4,8 => SOL * DIS # B8: 7 => CTR => B8: 4,8 * PRF # F9: 4,8 => SOL * DIS # F9: 1 => CTR => F9: 4,8 * DIS # F9: 1,8 => CTR => F9: 4 * PRF # F9: 4 => SOL * INC # G8: 8,9 => UNS * DIS # G8: 1 => CTR => G8: 8,9 * INC # I7: 4,5 => UNS * INC # I7: 6,8 => UNS * INC # H2: 4,5 => UNS * DIS # H2: 1 => CTR => H2: 4,5 * INC # H2: 1,4 => UNS * INC # H2: 5 => UNS * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 5,7 => CTR => A1: 4 * INC A1: 4 # D3: 7,8 => UNS * DIS A1: 4 # G3: 7,8 => CTR => G3: 1 * INC A1: 4 + G3: 1 # I2: 5,8 => UNS * INC A1: 4 + G3: 1 # I2: 4 => UNS * INC A1: 4 + G3: 1 # D1: 5,8 => UNS * PRF A1: 4 + G3: 1 # D1: 6,7 => SOL * STA A1: 4 + G3: 1 + D1: 6,7 * CNT 7 HDP CHAINS / 7 HYP OPENED