Analysis of zz-www.sudokuoftheday.co.uk-20060611-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006
level: medium
position: .736......2....4735........25.1....8369.8.......264..9.1.....5....8.12......5.6.. initial
Autosolve
position: .736....5.26...4735.......62541..768369.8.142.8.264539.1...635.6.58.129.....5.681 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D3: 4,9 => CTR => D3: 3,7 * PRF # E3: 4,9 => SOL * DIS # B9: 3 => CTR => B9: 4,9 * DIS # F2: 5,9 => CTR => F2: 8 * DIS # E1: 1,9 => CTR => E1: 2,4 * PRF # E3: 1,9 => SOL * DIS # A2: 8 => CTR => A2: 1,9 * PRF # A1: 8,9 => SOL * DIS # E1: 1,2 => CTR => E1: 4,9 * DIS # F3: 8,9 => CTR => F3: 2,3,7 * DIS # E3: 1,2 => CTR => E3: 3,4,7,9 * DIS # B9: 3,4 => CTR => B9: 9 * DIS # C7: 2,7 => CTR => C7: 8 * DIS # E7: 4,7 => CTR => E7: 2,9 * DIS # E8: 3 => CTR => E8: 4,7 * CNT 15 HDP CHAINS / 45 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D3: 4,9 => CTR => D3: 3,7 * PRF D3: 3,7 # E3: 4,9 => SOL * STA D3: 3,7 + E3: 4,9 * CNT 2 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .736......2....4735........25.1....8369.8.......264..9.1.....5....8.12......5.6.. | initial |
| .736....5.26...4735.......62541..768369.8.142.8.264539.1...635.6.58.129.....5.681 | autosolve |
| 873642915926518473541397826254139768369785142187264539418926357635871294792453681 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) B3: 4,9 C3: 1,8 D2: 5,9 E2: 1,9 G1: 8,9 H1: 1,2 G3: 8,9 H3: 1,2 A6: 1,7 C6: 1,7 E4: 3,9 F4: 3,9 D5: 5,7 F5: 5,7 B8: 3,4 C9: 2,7 I7: 4,7 I8: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H1,H3: 1.. / H1 = 1 => 16 pairs (_) / H3 = 1 => 0 pairs (X) A6,C6: 1.. / A6 = 1 => 13 pairs (_) / C6 = 1 => 0 pairs (X) A2,E2: 1.. / A2 = 1 => 0 pairs (X) / E2 = 1 => 18 pairs (_) C3,C6: 1.. / C3 = 1 => 13 pairs (_) / C6 = 1 => 0 pairs (X) H1,H3: 2.. / H1 = 2 => 0 pairs (X) / H3 = 2 => 16 pairs (_) C7,C9: 2.. / C7 = 2 => 0 pairs (X) / C9 = 2 => 18 pairs (_) E7,F9: 2.. / E7 = 2 => 18 pairs (_) / F9 = 2 => 0 pairs (X) C7,E7: 2.. / C7 = 2 => 0 pairs (X) / E7 = 2 => 18 pairs (_) C9,F9: 2.. / C9 = 2 => 18 pairs (_) / F9 = 2 => 0 pairs (X) E4,F4: 3.. / E4 = 3 => 19 pairs (_) / F4 = 3 => 17 pairs (_) B8,B9: 3.. / B8 = 3 => 19 pairs (_) / B9 = 3 => 0 pairs (X) B8,E8: 3.. / B8 = 3 => 19 pairs (_) / E8 = 3 => 0 pairs (X) D3,D9: 3.. / D3 = 3 => 19 pairs (_) / D9 = 3 => 19 pairs (_) A1,B3: 4.. / A1 = 4 => 0 pairs (X) / B3 = 4 => 21 pairs (_) I7,I8: 4.. / I7 = 4 => 20 pairs (_) / I8 = 4 => 18 pairs (_) A1,E1: 4.. / A1 = 4 => 0 pairs (X) / E1 = 4 => 21 pairs (_) D2,F2: 5.. / D2 = 5 => 17 pairs (_) / F2 = 5 => 0 pairs (X) D5,F5: 5.. / D5 = 5 => 0 pairs (X) / F5 = 5 => 17 pairs (_) D2,D5: 5.. / D2 = 5 => 17 pairs (_) / D5 = 5 => 0 pairs (X) F2,F5: 5.. / F2 = 5 => 0 pairs (X) / F5 = 5 => 17 pairs (_) A6,C6: 7.. / A6 = 7 => 0 pairs (X) / C6 = 7 => 13 pairs (_) D5,F5: 7.. / D5 = 7 => 17 pairs (_) / F5 = 7 => 0 pairs (X) I7,I8: 7.. / I7 = 7 => 18 pairs (_) / I8 = 7 => 20 pairs (_) E8,I8: 7.. / E8 = 7 => 18 pairs (_) / I8 = 7 => 20 pairs (_) G1,G3: 8.. / G1 = 8 => 22 pairs (_) / G3 = 8 => 0 pairs (*) A7,C7: 8.. / A7 = 8 => 0 pairs (X) / C7 = 8 => 13 pairs (_) A2,F2: 8.. / A2 = 8 => 0 pairs (X) / F2 = 8 => 18 pairs (_) C3,C7: 8.. / C3 = 8 => 0 pairs (X) / C7 = 8 => 13 pairs (_) G1,G3: 9.. / G1 = 9 => 0 pairs (*) / G3 = 9 => 0 pairs (X) E4,F4: 9.. / E4 = 9 => 17 pairs (_) / F4 = 9 => 19 pairs (_) B3,B9: 9.. / B3 = 9 => 0 pairs (X) / B9 = 9 => 21 pairs (_) * DURATION: 0:00:33.956077 START: 23:45:52.440576 END: 23:46:26.396653 2019-04-30 * CP COUNT: (31) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B3,B8,C3,C6,C9,D2,D5,E2,E4,F4,F5,G1,G3,H1,H3,I7,I8) * .736....5.26...4735.......62541..768369.8.142.8.264539.1...635.6.58.129.....5.681 * PAIR B3: 4,9 BLK 1 A1: 4,9,1,8 # reduction candidate for 4,9 A1: 4,9 # 21 pairs A1: 1,8 # 20 pairs * PAIR B3: 4,9 ROW 3 D3: 4,9,3,7 # reduction candidate for 4,9 D3: 4,9 => CTR * 873642915926.184735.1...826254193768369.85142187264539.18.2635.6358.129...2359681 D3: 3,7 # 20 pairs E3: 4,9,1,2,3,7 # reduction candidate for 4,9 E3: 4,9 => SOLVED * 873642915926518473541397826254139768369785142187264539418926357635871294792453681 E3: 1,2,3,7 # 18 pairs * PAIR B3: 4,9 COL B B9: 4,9,3 # reduction candidate for 4,9 B9: 3 => CTR * .736....5.26...47359....8.62541..768369.8.142.8.264539.18.2635.645831297.3245.681 B9: 4,9 # 19 pairs * PAIR C3: 1,8 BLK 1 A1: 1,8,4,9 # reduction candidate for 1,8 A1: 1,8 # 20 pairs A2: 1,8,9 # reduction candidate for 1,8 A2: 1,8 # 21 pairs * PAIR D2: 5,9 BLK 2 F2: 5,9,8 # reduction candidate for 5,9 F2: 5,9 => CTR * 973642815826.1.473541..8926254193768369.8.142187264539.1892635.63587129..92.5.681 F2: 8 # 18 pairs * PAIR E2: 1,9 BLK 2 E1: 1,9,2,4 # reduction candidate for 1,9 E1: 1,9 => CTR * 4736.8925826.1.47359....8.62541..768369.8.142.8.264539.18.2635.6.58.129...2.5.681 E1: 2,4 # 19 pairs E3: 1,9,2,3,4,7 # reduction candidate for 1,9 E3: 1,9 => SOLVED * 873642915926518473541397826254139768369785142187264539418926357635871294792453681 E3: 2,3,4,7 # 18 pairs * PAIR E2: 1,9 ROW 2 A2: 1,9,8 # reduction candidate for 1,9 A2: 8 => CTR * 973642815826.1.473541..8926254193768369.8.142187264539.1892635.63587129..92.5.681 A2: 1,9 # 18 pairs * PAIR G1: 8,9 ROW 1 A1: 8,9,1,4 # reduction candidate for 8,9 A1: 8,9 => SOLVED * 873642915926518473541397826254139768369785142187264539418926357635871294792453681 A1: 1,4 # 19 pairs F1: 8,9,2 # reduction candidate for 8,9 F1: 8,9 # 21 pairs * PAIR H1: 1,2 ROW 1 E1: 1,2,4,9 # reduction candidate for 1,2 E1: 1,2 => CTR * 473618925.26...47359....8.62541..768369.8.142.8.264539.18.2635.6.58.129...2.5.681 E1: 4,9 # 19 pairs * PAIR G3: 8,9 ROW 3 F3: 8,9,2,3,7 # reduction candidate for 8,9 F3: 8,9 => CTR * .73642.15.26.1.473541....262541..768369.8.142187264539.18.2635.635871294792453681 F3: 2,3,7 # 18 pairs * PAIR H3: 1,2 ROW 3 E3: 1,2,3,4,7,9 # reduction candidate for 1,2 E3: 1,2 => CTR * .7364.825.26..84735487239.62541..768369.8.142.81264539812..635.635871294497352681 E3: 3,4,7,9 # 18 pairs * PAIR E4: 3,9 COL E E3: 3,9,1,2,4,7 # reduction candidate for 3,9 E3: 3,9 # 23 pairs E3: 1,2,4,7 # 18 pairs * PAIR F4: 3,9 COL F F3: 3,9,2,7,8 # reduction candidate for 3,9 F3: 3,9 # 25 pairs F9: 3,9,2,7 # reduction candidate for 3,9 F9: 3,9 # 21 pairs * PAIR B8: 3,4 BLK 7 B9: 3,4,9 # reduction candidate for 3,4 B9: 3,4 => CTR * 4736.8925826.1.47359....8.62541..768369.8.142.8.264539.18.2635.6.58.129...2.5.681 B9: 9 # 21 pairs * PAIR B8: 3,4 ROW 8 E8: 3,4,7 # reduction candidate for 3,4 E8: 3,4 # 20 pairs E8: 7 # 18 pairs * PAIR C9: 2,7 BLK 7 C7: 2,7,8 # reduction candidate for 2,7 C7: 2,7 => CTR * .7364.8.5.265.8473548...9.62541..76836978514278126453981...635.6358.129.49..5.681 C7: 8 # 13 pairs * PAIR C9: 2,7 ROW 9 F9: 2,7,3,9 # reduction candidate for 2,7 F9: 2,7 # 22 pairs F9: 3,9 # 21 pairs * PAIR I7: 4,7 ROW 7 A7: 4,7,8,9 # reduction candidate for 4,7 A7: 4,7 # 15 pairs D7: 4,7,9 # reduction candidate for 4,7 D7: 4,7 # 22 pairs E7: 4,7,2,9 # reduction candidate for 4,7 E7: 4,7 => CTR * .736..8.5.265.84735487..9.62541..768369.8.1427812645398129.635.6.58.129..97352681 E7: 2,9 # 19 pairs * PAIR I8: 4,7 ROW 8 E8: 4,7,3 # reduction candidate for 4,7 E8: 3 => CTR * .736....5.26...47359.347826254193768369785142.8.264539.18..635.6.5831297.3..5.681 E8: 4,7 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060611-absurd-base-pr-000.dot * REASONING * DIS # D3: 4,9 => CTR => D3: 3,7 * PRF # E3: 4,9 => SOL * DIS # B9: 3 => CTR => B9: 4,9 * DIS # F2: 5,9 => CTR => F2: 8 * DIS # E1: 1,9 => CTR => E1: 2,4 * PRF # E3: 1,9 => SOL * DIS # A2: 8 => CTR => A2: 1,9 * PRF # A1: 8,9 => SOL * DIS # E1: 1,2 => CTR => E1: 4,9 * DIS # F3: 8,9 => CTR => F3: 2,3,7 * DIS # E3: 1,2 => CTR => E3: 3,4,7,9 * DIS # B9: 3,4 => CTR => B9: 9 * DIS # C7: 2,7 => CTR => C7: 8 * DIS # E7: 4,7 => CTR => E7: 2,9 * DIS # E8: 3 => CTR => E8: 4,7 * CNT 15 HDP CHAINS / 45 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B3,B8,C3,C6,C9,D2,D5,E2,E4,F4,F5,G1,G3,H1,H3,I7,I8) * .736....5.26...4735.......62541..768369.8.142.8.264539.1...635.6.58.129.....5.681 * PAIR B3: 4,9 BLK 1 A1: 4,9,1,8 # reduction candidate for 4,9 A1: 4,9 # 21 pairs A1: 1,8 # 20 pairs * PAIR B3: 4,9 ROW 3 D3: 4,9,3,7 # reduction candidate for 4,9 D3: 4,9 => CTR * 873642915926.184735.1...826254193768369.85142187264539.18.2635.6358.129...2359681 E3: 4,9,1,2,3,7 # reduction candidate for 4,9 E3: 4,9 => SOLVED * 873642915926518473541397826254139768369785142187264539418926357635871294792453681 * DURATION: 0:00:03.919155 START: 23:46:54.250430 END: 23:46:58.169585 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060611-absurd-base-pr-001.dot * REASONING * DIS # D3: 4,9 => CTR => D3: 3,7 * PRF D3: 3,7 # E3: 4,9 => SOL * STA D3: 3,7 + E3: 4,9 * CNT 2 HDP CHAINS / 4 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060611, absurd
Solution
position: 873642915926518473541397826254139768369785142187264539418926357635871294792453681 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 # A1: 4,9 => UNS * INC # A1: 1,8 => UNS * DIS # D3: 4,9 => CTR => D3: 3,7 * INC # D3: 3,7 => UNS * PRF # E3: 4,9 => SOL * INC # E3: 1,2,3,7 => UNS * INC # B9: 4,9 => UNS * DIS # B9: 3 => CTR => B9: 4,9 * INC # A1: 1,8 => UNS * INC # A2: 1,8 => UNS * DIS # F2: 5,9 => CTR => F2: 8 * INC # F2: 8 => UNS * DIS # E1: 1,9 => CTR => E1: 2,4 * INC # E1: 2,4 => UNS * PRF # E3: 1,9 => SOL * INC # E3: 2,3,4,7 => UNS * INC # A2: 1,9 => UNS * DIS # A2: 8 => CTR => A2: 1,9 * PRF # A1: 8,9 => SOL * INC # A1: 1,4 => UNS * INC # F1: 8,9 => UNS * DIS # E1: 1,2 => CTR => E1: 4,9 * INC # E1: 4,9 => UNS * DIS # F3: 8,9 => CTR => F3: 2,3,7 * INC # F3: 2,3,7 => UNS * DIS # E3: 1,2 => CTR => E3: 3,4,7,9 * INC # E3: 3,4,7,9 => UNS * INC # E3: 3,9 => UNS * INC # E3: 1,2,4,7 => UNS * INC # F3: 3,9 => UNS * INC # F9: 3,9 => UNS * DIS # B9: 3,4 => CTR => B9: 9 * INC # B9: 9 => UNS * INC # E8: 3,4 => UNS * INC # E8: 7 => UNS * DIS # C7: 2,7 => CTR => C7: 8 * INC # C7: 8 => UNS * INC # F9: 2,7 => UNS * INC # F9: 3,9 => UNS * INC # A7: 4,7 => UNS * INC # D7: 4,7 => UNS * DIS # E7: 4,7 => CTR => E7: 2,9 * INC # E7: 2,9 => UNS * INC # E8: 4,7 => UNS * DIS # E8: 3 => CTR => E8: 4,7 * CNT 45 HDP CHAINS / 45 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 4,9 => UNS * INC # A1: 1,8 => UNS * DIS # D3: 4,9 => CTR => D3: 3,7 * PRF D3: 3,7 # E3: 4,9 => SOL * STA D3: 3,7 + E3: 4,9 * CNT 4 HDP CHAINS / 4 HYP OPENED