Analysis of zz-www.sudokuoftheday.co.uk-20060404-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006
level: medium
position: ...5.4......86.9.5.......813..12..5......9826..........17.4.....9...12....893.... initial
Autosolve
position: ...514..2...86.9.5....9..813..12..5....3.9826...4......17.4.....93..12....893.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # E6: 5,7 => SOL * DIS # E6: 8 => CTR => E6: 5,7 * DIS # F6: 5,7 => CTR => F6: 6,8 * DIS # E8: 5,7 => CTR => E8: 8 * PRF # E8: 8 => SOL * DIS # I4: 4,7 => CTR => I4: 9 * PRF # I4: 9 => SOL * DIS # G3: 4,7 => CTR => G3: 3,6 * DIS # G9: 4,7 => CTR => G9: 1,5,6 * DIS # A7: 5 => CTR => A7: 2,6 * DIS # H8: 4 => CTR => H8: 6,7 * DIS # H8: 4,7 => CTR => H8: 6 * PRF # I8: 4,7 => SOL * DIS # I8: 8 => CTR => I8: 4,7 * DIS # G9: 4,7 => CTR => G9: 1,5,6 * DIS # H9: 4,7 => CTR => H9: 1,6 * DIS # I4: 4,7 => CTR => I4: 9 * PRF # I4: 9 => SOL * CNT 18 HDP CHAINS / 36 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # E6: 5,7 => SOL * STA E6: 5,7 * CNT 1 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...5.4......86.9.5.......813..12..5......9826..........17.4.....9...12....893.... | initial |
| ...514..2...86.9.5....9..813..12..5....3.9826...4......17.4.....93..12....893.... | autosolve |
| 869514732721863945435297681376128459154379826982456173217645398593781264648932517 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) A1: 8,9 C1: 6,9 D3: 2,7 C4: 6,9 A6: 8,9 C6: 2,5 E5: 5,7 G4: 4,7 D7: 2,6 D8: 6,7 I9: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,C2: 1.. / A2 = 1 => 12 pairs (_) / C2 = 1 => 13 pairs (_) A5,C5: 1.. / A5 = 1 => 13 pairs (_) / C5 = 1 => 12 pairs (_) G6,H6: 1.. / G6 = 1 => 11 pairs (_) / H6 = 1 => 0 pairs (X) G9,H9: 1.. / G9 = 1 => 0 pairs (X) / H9 = 1 => 11 pairs (_) A2,A5: 1.. / A2 = 1 => 12 pairs (_) / A5 = 1 => 13 pairs (_) C2,C5: 1.. / C2 = 1 => 13 pairs (_) / C5 = 1 => 12 pairs (_) G6,G9: 1.. / G6 = 1 => 11 pairs (_) / G9 = 1 => 0 pairs (X) H6,H9: 1.. / H6 = 1 => 0 pairs (X) / H9 = 1 => 11 pairs (_) B6,C6: 2.. / B6 = 2 => 26 pairs (_) / C6 = 2 => 12 pairs (_) D3,D7: 2.. / D3 = 2 => 19 pairs (_) / D7 = 2 => 0 pairs (X) F2,F3: 3.. / F2 = 3 => 16 pairs (_) / F3 = 3 => 12 pairs (_) I6,I7: 3.. / I6 = 3 => 13 pairs (_) / I7 = 3 => 0 pairs (X) H2,G3: 4.. / H2 = 4 => 17 pairs (_) / G3 = 4 => 0 pairs (X) G4,I4: 4.. / G4 = 4 => 17 pairs (_) / I4 = 4 => 0 pairs (X) G7,G9: 5.. / G7 = 5 => 0 pairs (X) / G9 = 5 => 18 pairs (_) A8,E8: 5.. / A8 = 5 => 21 pairs (_) / E8 = 5 => 0 pairs (X) F4,F6: 6.. / F4 = 6 => 0 pairs (X) / F6 = 6 => 22 pairs (_) D7,D8: 6.. / D7 = 6 => 19 pairs (_) / D8 = 6 => 0 pairs (X) B6,F6: 6.. / B6 = 6 => 0 pairs (X) / F6 = 6 => 22 pairs (_) C1,C4: 6.. / C1 = 6 => 0 pairs (X) / C4 = 6 => 0 pairs (_) D3,D8: 7.. / D3 = 7 => 0 pairs (X) / D8 = 7 => 19 pairs (_) A1,B1: 8.. / A1 = 8 => 0 pairs (*) / B1 = 8 => 0 pairs (X) F7,E8: 8.. / F7 = 8 => 0 pairs (X) / E8 = 8 => 0 pairs (_) I7,I8: 8.. / I7 = 8 => 0 pairs (*) / I8 = 8 => 0 pairs (X) B4,F4: 8.. / B4 = 8 => 0 pairs (X) / F4 = 8 => 0 pairs (_) F7,I7: 8.. / F7 = 8 => 0 pairs (X) / I7 = 8 => 0 pairs (_) E8,I8: 8.. / E8 = 8 => 0 pairs (*) / I8 = 8 => 0 pairs (X) A1,A6: 8.. / A1 = 8 => 0 pairs (*) / A6 = 8 => 0 pairs (X) E6,E8: 8.. / E6 = 8 => 0 pairs (X) / E8 = 8 => 0 pairs (_) A1,C1: 9.. / A1 = 9 => 0 pairs (X) / C1 = 9 => 0 pairs (_) C4,A6: 9.. / C4 = 9 => 0 pairs (X) / A6 = 9 => 0 pairs (_) H7,I7: 9.. / H7 = 9 => 12 pairs (_) / I7 = 9 => 0 pairs (X) C4,I4: 9.. / C4 = 9 => 0 pairs (X) / I4 = 9 => 0 pairs (_) A1,A6: 9.. / A1 = 9 => 0 pairs (X) / A6 = 9 => 0 pairs (_) C1,C4: 9.. / C1 = 9 => 0 pairs (*) / C4 = 9 => 0 pairs (X) H6,H7: 9.. / H6 = 9 => 0 pairs (X) / H7 = 9 => 12 pairs (_) * DURATION: 0:00:40.945539 START: 22:08:29.830946 END: 22:09:10.776485 2019-04-30 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,C1,C4,C6,D3,D7,D8,E5,G4,I9) * ...514..2...86.9.5....9..813..12..5....3.9826...4......17.4.....93..12....893.... * PAIR D3: 2,7 BLK 2 F2: 2,7,3 # reduction candidate for 2,7 F2: 2,7 # 12 pairs F3: 2,7,3 # reduction candidate for 2,7 F3: 2,7 # 16 pairs * PAIR D3: 2,7 ROW 3 A3: 2,7,4,5,6 # reduction candidate for 2,7 A3: 2,7 # 15 pairs B3: 2,7,3,4,5,6 # reduction candidate for 2,7 B3: 2,7 # 17 pairs * PAIR C6: 2,5 BLK 4 B6: 2,5,6,7,8 # reduction candidate for 2,5 B6: 2,5 # 26 pairs B6: 6,7,8 # 16 pairs * PAIR C6: 2,5 COL C C3: 2,5,4 # reduction candidate for 2,5 C3: 4 # 19 pairs C3: 2,5 # 14 pairs * PAIR E5: 5,7 BLK 5 E6: 5,7,8 # reduction candidate for 5,7 E6: 5,7 => SOLVED * 869514732721863945435297681376128459154379826982456173217645398593781264648932517 E6: 8 => CTR * 8.9514..2...86.9.5....9..81386127459...3598269..486....17.48.93593.71248..8935..7 F6: 5,7,6,8 # reduction candidate for 5,7 F6: 5,7 => CTR * ...514..2...86.9.5....9..813..126.5....3.9826.62485....17.48....93.512.8..893.... F6: 6,8 # 22 pairs * PAIR E5: 5,7 ROW 5 A5: 5,7,1,4 # reduction candidate for 5,7 A5: 5,7 # 13 pairs B5: 5,7,4 # reduction candidate for 5,7 B5: 5,7 # 15 pairs * PAIR E5: 5,7 COL E E8: 5,7,8 # reduction candidate for 5,7 E8: 5,7 => CTR * 8.9514..2...86.9.5....9..81386127459...3598269..486....17.48.93593.71248..8935..7 E8: 8 => SOLVED * 869514732721863945435297681376128459154379826982456173217645398593781264648932517 * PAIR G4: 4,7 BLK 6 I4: 4,7,9 # reduction candidate for 4,7 I4: 4,7 => CTR * 986514..2...86.9.5....9.6813.9128.5....3.98268..4.6....17.4...8593.812....893.... I4: 9 => SOLVED * 869514732721863945435297681376128459154379826982456173217645398593781264648932517 * PAIR G4: 4,7 COL G G3: 4,7,3,6 # reduction candidate for 4,7 G3: 4,7 => CTR * 879514632...867945...29378138612.459...3.98269..4.6....17.4..9..937.126...893.... G3: 3,6 # 18 pairs G9: 4,7,1,5,6 # reduction candidate for 4,7 G9: 4,7 => CTR * ...514.72...86.945...29..8138.12..5....3798269724..1..2176485...93751268..8932.1. G9: 1,5,6 # 11 pairs * PAIR D7: 2,6 ROW 7 A7: 2,6,5 # reduction candidate for 2,6 A7: 5 => CTR * 8.9514..2...86.9.5....9..8138612..5....379826...4851..517.48....93.512.8..893.51. A7: 2,6 # 15 pairs * PAIR D8: 6,7 ROW 8 H8: 6,7,4 # reduction candidate for 6,7 H8: 4 => CTR * ...514..2...86.9.5....9.4813.912.754...3.98268..4......17.48....93..1248..893...7 H8: 6,7 # 16 pairs * PAIR I9: 4,7 BLK 9 H8: 4,7,6 # reduction candidate for 4,7 H8: 4,7 => CTR * 8.9514..2...86.9.5....9..81386127459...3.9826...48.....17.48....93..12.8..893.... H8: 6 # 20 pairs I8: 4,7,8 # reduction candidate for 4,7 I8: 4,7 => SOLVED * 869514732721863945435297681376128459154379826982456173217645398593781264648932517 I8: 8 => CTR * 8.9514..2...86.9.5....9..81386127459...3598269..486....17.48.93593.71248..8935..7 G9: 4,7,1,5,6 # reduction candidate for 4,7 G9: 4,7 => CTR * ...514.72...86.945...29..8138.12..5....3798269724..1..2176485...93751268..8932.1. G9: 1,5,6 # 11 pairs H9: 4,7,1,6 # reduction candidate for 4,7 H9: 4,7 => CTR * 8.9514..2...86.9.5...29..81386127.5....3.9826...48.31..17648593493751268..89321.. H9: 1,6 # 12 pairs * PAIR I9: 4,7 COL I I4: 4,7,9 # reduction candidate for 4,7 I4: 4,7 => CTR * 986514..2...86.9.5....9.6813.9128.5....3.98268..4.6....17.4...8593.812....893.... I4: 9 => SOLVED * 869514732721863945435297681376128459154379826982456173217645398593781264648932517 * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060404-absurd-base-pr-000.dot * REASONING * PRF # E6: 5,7 => SOL * DIS # E6: 8 => CTR => E6: 5,7 * DIS # F6: 5,7 => CTR => F6: 6,8 * DIS # E8: 5,7 => CTR => E8: 8 * PRF # E8: 8 => SOL * DIS # I4: 4,7 => CTR => I4: 9 * PRF # I4: 9 => SOL * DIS # G3: 4,7 => CTR => G3: 3,6 * DIS # G9: 4,7 => CTR => G9: 1,5,6 * DIS # A7: 5 => CTR => A7: 2,6 * DIS # H8: 4 => CTR => H8: 6,7 * DIS # H8: 4,7 => CTR => H8: 6 * PRF # I8: 4,7 => SOL * DIS # I8: 8 => CTR => I8: 4,7 * DIS # G9: 4,7 => CTR => G9: 1,5,6 * DIS # H9: 4,7 => CTR => H9: 1,6 * DIS # I4: 4,7 => CTR => I4: 9 * PRF # I4: 9 => SOL * CNT 18 HDP CHAINS / 36 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,C1,C4,C6,D3,D7,D8,E5,G4,I9) * ...514..2...86.9.5....9..813..12..5....3.9826...4......17.4.....93..12....893.... * PAIR D3: 2,7 BLK 2 F2: 2,7,3 # reduction candidate for 2,7 F2: 2,7 # 12 pairs F3: 2,7,3 # reduction candidate for 2,7 F3: 2,7 # 16 pairs * PAIR D3: 2,7 ROW 3 A3: 2,7,4,5,6 # reduction candidate for 2,7 A3: 2,7 # 15 pairs B3: 2,7,3,4,5,6 # reduction candidate for 2,7 B3: 2,7 # 17 pairs * PAIR C6: 2,5 BLK 4 B6: 2,5,6,7,8 # reduction candidate for 2,5 B6: 2,5 # 26 pairs B6: 6,7,8 # 16 pairs * PAIR C6: 2,5 COL C C3: 2,5,4 # reduction candidate for 2,5 C3: 4 # 19 pairs C3: 2,5 # 14 pairs * PAIR E5: 5,7 BLK 5 E6: 5,7,8 # reduction candidate for 5,7 E6: 5,7 => SOLVED * 869514732721863945435297681376128459154379826982456173217645398593781264648932517 * DURATION: 0:00:06.348427 START: 22:09:33.563648 END: 22:09:39.912075 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060404-absurd-base-pr-001.dot * REASONING * PRF # E6: 5,7 => SOL * STA E6: 5,7 * CNT 1 HDP CHAINS / 9 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060404, absurd
Solution
position: 869514732721863945435297681376128459154379826982456173217645398593781264648932517 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 # F2: 2,7 => UNS * INC # F3: 2,7 => UNS * INC # A3: 2,7 => UNS * INC # B3: 2,7 => UNS * INC # B6: 2,5 => UNS * INC # B6: 6,7,8 => UNS * INC # C3: 2,5 => UNS * INC # C3: 4 => UNS * PRF # E6: 5,7 => SOL * DIS # E6: 8 => CTR => E6: 5,7 * DIS # F6: 5,7 => CTR => F6: 6,8 * INC # F6: 6,8 => UNS * INC # A5: 5,7 => UNS * INC # B5: 5,7 => UNS * DIS # E8: 5,7 => CTR => E8: 8 * PRF # E8: 8 => SOL * DIS # I4: 4,7 => CTR => I4: 9 * PRF # I4: 9 => SOL * DIS # G3: 4,7 => CTR => G3: 3,6 * INC # G3: 3,6 => UNS * DIS # G9: 4,7 => CTR => G9: 1,5,6 * INC # G9: 1,5,6 => UNS * INC # A7: 2,6 => UNS * DIS # A7: 5 => CTR => A7: 2,6 * INC # H8: 6,7 => UNS * DIS # H8: 4 => CTR => H8: 6,7 * DIS # H8: 4,7 => CTR => H8: 6 * INC # H8: 6 => UNS * PRF # I8: 4,7 => SOL * DIS # I8: 8 => CTR => I8: 4,7 * DIS # G9: 4,7 => CTR => G9: 1,5,6 * INC # G9: 1,5,6 => UNS * DIS # H9: 4,7 => CTR => H9: 1,6 * INC # H9: 1,6 => UNS * DIS # I4: 4,7 => CTR => I4: 9 * PRF # I4: 9 => SOL * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F2: 2,7 => UNS * INC # F3: 2,7 => UNS * INC # A3: 2,7 => UNS * INC # B3: 2,7 => UNS * INC # B6: 2,5 => UNS * INC # B6: 6,7,8 => UNS * INC # C3: 2,5 => UNS * INC # C3: 4 => UNS * PRF # E6: 5,7 => SOL * STA E6: 5,7 * CNT 9 HDP CHAINS / 9 HYP OPENED