Analysis of zz-www.sudokuoftheday.co.uk-20060325-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006
level: medium
position: ..5.............261...6.43.....7...3..952.681...1.....57..3...2...856.....6...9.. initial
Autosolve
position: ..5.............261...6.43....67...37.952.681...1.....57..3..62...8563....6...9.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A6: 3,4 => CTR => A6: 2,6,8 * DIS # B6: 3,4 => CTR => B6: 2,5,6,8 * PRF # F7: 1 => SOL * DIS # D1: 2,7 => CTR => D1: 3,4,9 * DIS # B9: 1,4 => CTR => B9: 3,8 * DIS # F3: 2,7 => CTR => F3: 5,8,9 * PRF # C7: 4 => SOL * DIS # H8: 1 => CTR => H8: 4,7 * CNT 8 HDP CHAINS / 39 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A6: 3,4 => CTR => A6: 2,6,8 * DIS A6: 2,6,8 # B6: 3,4 => CTR => B6: 2,5,6,8 * PRF A6: 2,6,8 + B6: 2,5,6,8 # F7: 1 => SOL * STA A6: 2,6,8 + B6: 2,5,6,8 + F7: 1 * CNT 3 HDP CHAINS / 16 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..5.............261...6.43.....7...3..952.681...1.....57..3...2...856.....6...9.. | initial |
| ..5.............261...6.43....67...37.952.681...1.....57..3..62...8563....6...9.. | autosolve |
| 635492178497318526128765439851674293749523681263189754574931862912856347386247915 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) B5: 3,4 F5: 3,4 G4: 2,5 D7: 4,9 D9: 2,7 E9: 1,4 F9: 2,7 G7: 1,8 I8: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B4,C4: 1.. / B4 = 1 => 10 pairs (_) / C4 = 1 => 11 pairs (_) F7,E9: 1.. / F7 = 1 => 0 pairs (*) / E9 = 1 => 0 pairs (X) G4,G6: 2.. / G4 = 2 => 10 pairs (_) / G6 = 2 => 12 pairs (_) D9,F9: 2.. / D9 = 2 => 8 pairs (_) / F9 = 2 => 0 pairs (X) D1,D2: 3.. / D1 = 3 => 9 pairs (_) / D2 = 3 => 15 pairs (_) F5,F6: 3.. / F5 = 3 => 11 pairs (_) / F6 = 3 => 11 pairs (_) A9,B9: 3.. / A9 = 3 => 9 pairs (_) / B9 = 3 => 13 pairs (_) B5,F5: 3.. / B5 = 3 => 11 pairs (_) / F5 = 3 => 11 pairs (_) C2,C6: 3.. / C2 = 3 => 10 pairs (_) / C6 = 3 => 11 pairs (_) B5,F5: 4.. / B5 = 4 => 11 pairs (_) / F5 = 4 => 11 pairs (_) F2,F3: 5.. / F2 = 5 => 14 pairs (_) / F3 = 5 => 10 pairs (_) G2,I3: 5.. / G2 = 5 => 10 pairs (_) / I3 = 5 => 14 pairs (_) B4,B6: 5.. / B4 = 5 => 13 pairs (_) / B6 = 5 => 10 pairs (_) H9,I9: 5.. / H9 = 5 => 11 pairs (_) / I9 = 5 => 14 pairs (_) F2,G2: 5.. / F2 = 5 => 14 pairs (_) / G2 = 5 => 10 pairs (_) F3,I3: 5.. / F3 = 5 => 10 pairs (_) / I3 = 5 => 14 pairs (_) A1,B1: 6.. / A1 = 6 => 13 pairs (_) / B1 = 6 => 9 pairs (_) A6,B6: 6.. / A6 = 6 => 9 pairs (_) / B6 = 6 => 13 pairs (_) A1,A6: 6.. / A1 = 6 => 13 pairs (_) / A6 = 6 => 9 pairs (_) B1,B6: 6.. / B1 = 6 => 9 pairs (_) / B6 = 6 => 13 pairs (_) C2,C3: 7.. / C2 = 7 => 14 pairs (_) / C3 = 7 => 10 pairs (_) D9,F9: 7.. / D9 = 7 => 0 pairs (X) / F9 = 7 => 8 pairs (_) H8,I8: 7.. / H8 = 7 => 14 pairs (_) / I8 = 7 => 10 pairs (_) G7,I9: 8.. / G7 = 8 => 14 pairs (_) / I9 = 8 => 0 pairs (X) C7,G7: 8.. / C7 = 8 => 0 pairs (X) / G7 = 8 => 14 pairs (_) A8,B8: 9.. / A8 = 9 => 9 pairs (_) / B8 = 9 => 11 pairs (_) D7,F7: 9.. / D7 = 9 => 15 pairs (_) / F7 = 9 => 16 pairs (_) F4,H4: 9.. / F4 = 9 => 18 pairs (_) / H4 = 9 => 13 pairs (_) * DURATION: 0:00:25.698332 START: 21:53:10.362378 END: 21:53:36.060710 2019-04-30 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,D7,D9,E9,F5,F9,G4,G7,I8) * ..5.............261...6.43....67...37.952.681...1.....57..3..62...8563....6...9.. * PAIR B5: 3,4 BLK 4 A6: 3,4,2,6,8 # reduction candidate for 3,4 A6: 3,4 => CTR * 6.5.............261...6.43..5167.2.37.952.681.621.....57..3..62294856317.16.4.958 A6: 2,6,8 # 9 pairs B6: 3,4,2,5,6,8 # reduction candidate for 3,4 B6: 3,4 => CTR * .65........3....261.7.6.43.85167.2.37.952.6816.21.....578.3.162..48563.7..6...9.. B6: 2,5,6,8 # 9 pairs C6: 3,4,2,8 # reduction candidate for 3,4 C6: 3,4 # 14 pairs * PAIR B5: 3,4 COL B B1: 3,4,2,6,8,9 # reduction candidate for 3,4 B1: 3,4 # 17 pairs B2: 3,4,8,9 # reduction candidate for 3,4 B2: 3,4 # 11 pairs B9: 3,4,1,8 # reduction candidate for 3,4 B9: 3,4 # 11 pairs * PAIR F5: 3,4 BLK 5 F6: 3,4,8,9 # reduction candidate for 3,4 F6: 3,4 # 13 pairs F6: 8,9 # 12 pairs * PAIR G4: 2,5 BLK 6 G6: 2,5,7 # reduction candidate for 2,5 G6: 2,5 # 14 pairs G6: 7 # 10 pairs * PAIR G4: 2,5 ROW 4 B4: 2,5,1,4,8 # reduction candidate for 2,5 B4: 2,5 # 14 pairs B4: 1,4,8 # 10 pairs * PAIR D7: 4,9 BLK 8 F7: 4,9,1 # reduction candidate for 4,9 F7: 1 => SOLVED * 635492178497318526128765439851674293749523681263189754574931862912856347386247915 F7: 4,9 # 14 pairs * PAIR D7: 4,9 COL D D1: 4,9,2,3,7 # reduction candidate for 4,9 D1: 4,9 # 18 pairs D2: 4,9,3,7 # reduction candidate for 4,9 D2: 4,9 # 11 pairs * PAIR D9: 2,7 COL D D1: 2,7,3,4,9 # reduction candidate for 2,7 D1: 2,7 => CTR * ..5.4.8.949738..261..96.43....674.93749523681..31987..5784391629.485637...6.1.9.. D1: 3,4,9 # 9 pairs D3: 2,7,9 # reduction candidate for 2,7 D3: 2,7 # 10 pairs * PAIR E9: 1,4 BLK 8 F7: 1,4,9 # reduction candidate for 1,4 F7: 9 # 16 pairs F7: 1,4 # 15 pairs * PAIR E9: 1,4 ROW 9 B9: 1,4,3,8 # reduction candidate for 1,4 B9: 1,4 => CTR * ..5...81.....8152618..6543..5167.2.3739524681...193745578439162912856374346.1.958 B9: 3,8 # 10 pairs H9: 1,4,5 # reduction candidate for 1,4 H9: 1,4 # 14 pairs * PAIR E9: 1,4 COL E E1: 1,4,8,9 # reduction candidate for 1,4 E1: 1,4 # 15 pairs E2: 1,4,8,9 # reduction candidate for 1,4 E2: 1,4 # 14 pairs * PAIR F9: 2,7 COL F F1: 2,7,1,4,8,9 # reduction candidate for 2,7 F1: 2,7 # 10 pairs F3: 2,7,5,8,9 # reduction candidate for 2,7 F3: 2,7 => CTR * ..5.4179......5.261...6.435...67...37.952.681...19....57..39.62...8563....6.1.95. F3: 5,8,9 # 9 pairs * PAIR G7: 1,8 ROW 7 C7: 1,8,4 # reduction candidate for 1,8 C7: 4 => SOLVED * 635492178497318526128765439851674293749523681263189754574931862912856347386247915 C7: 1,8 # 14 pairs * PAIR G7: 1,8 COL G G1: 1,8,7 # reduction candidate for 1,8 G1: 1,8 # 11 pairs G2: 1,8,5,7 # reduction candidate for 1,8 G2: 1,8 # 15 pairs * PAIR I8: 4,7 BLK 9 H8: 4,7,1 # reduction candidate for 4,7 H8: 1 => CTR * .65...798....8.1261...6.435.1.67954374952368165314....571.3.862...856317..6.1.9.. H8: 4,7 # 15 pairs * PAIR I8: 4,7 COL I I6: 4,7,5,9 # reduction candidate for 4,7 I6: 4,7 # 13 pairs I6: 5,9 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060325-absurd-base-pr-000.dot * REASONING * DIS # A6: 3,4 => CTR => A6: 2,6,8 * DIS # B6: 3,4 => CTR => B6: 2,5,6,8 * PRF # F7: 1 => SOL * DIS # D1: 2,7 => CTR => D1: 3,4,9 * DIS # B9: 1,4 => CTR => B9: 3,8 * DIS # F3: 2,7 => CTR => F3: 5,8,9 * PRF # C7: 4 => SOL * DIS # H8: 1 => CTR => H8: 4,7 * CNT 8 HDP CHAINS / 39 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,D7,D9,E9,F5,F9,G4,G7,I8) * ..5.............261...6.43....67...37.952.681...1.....57..3..62...8563....6...9.. * PAIR B5: 3,4 BLK 4 A6: 3,4,2,6,8 # reduction candidate for 3,4 A6: 3,4 => CTR * 6.5.............261...6.43..5167.2.37.952.681.621.....57..3..62294856317.16.4.958 B6: 3,4,2,5,6,8 # reduction candidate for 3,4 B6: 3,4 => CTR * .65........3....261.7.6.43.85167.2.37.952.6816.21.....578.3.162..48563.7..6...9.. C6: 3,4,2,8 # reduction candidate for 3,4 C6: 3,4 # 14 pairs * RESTART * PAIR B5: 3,4 BLK 4 C6: 3,4,2,8 # reduction candidate for 3,4 C6: 3,4 # 14 pairs C6: 2,8 # 13 pairs * PAIR B5: 3,4 COL B B1: 3,4,2,6,8,9 # reduction candidate for 3,4 B1: 3,4 # 18 pairs B2: 3,4,8,9 # reduction candidate for 3,4 B2: 3,4 # 11 pairs B9: 3,4,1,8 # reduction candidate for 3,4 B9: 3,4 # 11 pairs * PAIR F5: 3,4 BLK 5 F6: 3,4,8,9 # reduction candidate for 3,4 F6: 3,4 # 13 pairs F6: 8,9 # 12 pairs * PAIR G4: 2,5 BLK 6 G6: 2,5,7 # reduction candidate for 2,5 G6: 2,5 # 14 pairs G6: 7 # 10 pairs * PAIR G4: 2,5 ROW 4 B4: 2,5,1,4,8 # reduction candidate for 2,5 B4: 2,5 # 14 pairs B4: 1,4,8 # 10 pairs * PAIR D7: 4,9 BLK 8 F7: 4,9,1 # reduction candidate for 4,9 F7: 1 => SOLVED * 635492178497318526128765439851674293749523681263189754574931862912856347386247915 * DURATION: 0:00:09.634574 START: 21:53:57.258015 END: 21:54:06.892589 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060325-absurd-base-pr-001.dot * REASONING * DIS # A6: 3,4 => CTR => A6: 2,6,8 * DIS A6: 2,6,8 # B6: 3,4 => CTR => B6: 2,5,6,8 * PRF A6: 2,6,8 + B6: 2,5,6,8 # F7: 1 => SOL * STA A6: 2,6,8 + B6: 2,5,6,8 + F7: 1 * CNT 3 HDP CHAINS / 16 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006, 20060325, absurd
Solution
position: 635492178497318526128765439851674293749523681263189754574931862912856347386247915 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 # A6: 3,4 => CTR => A6: 2,6,8 * INC # A6: 2,6,8 => UNS * DIS # B6: 3,4 => CTR => B6: 2,5,6,8 * INC # B6: 2,5,6,8 => UNS * INC # C6: 3,4 => UNS * INC # B1: 3,4 => UNS * INC # B2: 3,4 => UNS * INC # B9: 3,4 => UNS * INC # F6: 3,4 => UNS * INC # F6: 8,9 => UNS * INC # G6: 2,5 => UNS * INC # G6: 7 => UNS * INC # B4: 2,5 => UNS * INC # B4: 1,4,8 => UNS * INC # F7: 4,9 => UNS * PRF # F7: 1 => SOL * INC # D1: 4,9 => UNS * INC # D2: 4,9 => UNS * DIS # D1: 2,7 => CTR => D1: 3,4,9 * INC # D1: 3,4,9 => UNS * INC # D3: 2,7 => UNS * INC # F7: 1,4 => UNS * INC # F7: 9 => UNS * DIS # B9: 1,4 => CTR => B9: 3,8 * INC # B9: 3,8 => UNS * INC # H9: 1,4 => UNS * INC # E1: 1,4 => UNS * INC # E2: 1,4 => UNS * INC # F1: 2,7 => UNS * DIS # F3: 2,7 => CTR => F3: 5,8,9 * INC # F3: 5,8,9 => UNS * INC # C7: 1,8 => UNS * PRF # C7: 4 => SOL * INC # G1: 1,8 => UNS * INC # G2: 1,8 => UNS * INC # H8: 4,7 => UNS * DIS # H8: 1 => CTR => H8: 4,7 * INC # I6: 4,7 => UNS * INC # I6: 5,9 => UNS * CNT 39 HDP CHAINS / 39 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A6: 3,4 => CTR => A6: 2,6,8 * DIS A6: 2,6,8 # B6: 3,4 => CTR => B6: 2,5,6,8 * INC A6: 2,6,8 + B6: 2,5,6,8 # C6: 3,4 => UNS * INC A6: 2,6,8 + B6: 2,5,6,8 # C6: 3,4 => UNS * INC A6: 2,6,8 + B6: 2,5,6,8 # C6: 2,8 => UNS * INC A6: 2,6,8 + B6: 2,5,6,8 # B1: 3,4 => UNS * INC A6: 2,6,8 + B6: 2,5,6,8 # B2: 3,4 => UNS * INC A6: 2,6,8 + B6: 2,5,6,8 # B9: 3,4 => UNS * INC A6: 2,6,8 + B6: 2,5,6,8 # F6: 3,4 => UNS * INC A6: 2,6,8 + B6: 2,5,6,8 # F6: 8,9 => UNS * INC A6: 2,6,8 + B6: 2,5,6,8 # G6: 2,5 => UNS * INC A6: 2,6,8 + B6: 2,5,6,8 # G6: 7 => UNS * INC A6: 2,6,8 + B6: 2,5,6,8 # B4: 2,5 => UNS * INC A6: 2,6,8 + B6: 2,5,6,8 # B4: 1,4,8 => UNS * INC A6: 2,6,8 + B6: 2,5,6,8 # F7: 4,9 => UNS * PRF A6: 2,6,8 + B6: 2,5,6,8 # F7: 1 => SOL * STA A6: 2,6,8 + B6: 2,5,6,8 + F7: 1 * CNT 16 HDP CHAINS / 16 HYP OPENED