Analysis of zz-www.sudokuoftheday.co.uk-20060904-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Sep&YEAR=2006
level: medium
position: .81.6.49..........6..85.37.2.6....4...7..6.89.....7.....91...3.3......52....4.... initial
Autosolve
position: 781.6.495.........6..85.3712.6....4...7..6.89.....7.....91...343......52....4.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B3: 2,4 => SOL * DIS # B3: 9 => CTR => B3: 2,4 * PRF # F9: 5,8,9 => SOL * DIS # E2: 7,9 => CTR => E2: 1 * PRF # E2: 1 => SOL * DIS # D8: 7,9 => CTR => D8: 6 * DIS # D9: 7,9 => CTR => D9: 2,3,5,6 * PRF # F2: 4,9 => SOL * DIS # F2: 1 => CTR => F2: 4,9 * DIS # B3: 2 => CTR => B3: 4,9 * DIS # H6: 2,6 => CTR => H6: 1 * DIS # G2: 2 => CTR => G2: 6,8 * DIS # F4: 5,9 => CTR => F4: 1,8 * DIS # D6: 5,9 => CTR => D6: 2,4 * DIS # D9: 5,9 => CTR => D9: 2,3,6,7 * DIS # A9: 5,8 => CTR => A9: 1 * PRF # F7: 2 => SOL * PRF # A6: 5,8 => SOL * DIS # A6: 1,4,9 => CTR => A6: 5,8 * DIS # C6: 4,8 => CTR => C6: 3,5 * PRF # C6: 3,5 => SOL * DIS # F9: 8,9 => CTR => F9: 2,3,5 * DIS # G8: 8,9 => CTR => G8: 1,6,7 * DIS # F4: 8,9 => CTR => F4: 1,5 * DIS # G9: 1,6 => CTR => G9: 7,8,9 * DIS # B9: 1,6 => CTR => B9: 2,5,7 * DIS # H6: 2 => CTR => H6: 1,6 * CNT 27 HDP CHAINS / 55 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B3: 2,4 => SOL * STA B3: 2,4 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .81.6.49..........6..85.37.2.6....4...7..6.89.....7.....91...3.3......52....4.... | initial |
| 781.6.495.........6..85.3712.6....4...7..6.89.....7.....91...343......52....4.... | autosolve |
| 781263495935714628642859371256981743417536289893427516569172834374698152128345967 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) C3: 2,4 D1: 2,3 F1: 2,3 D2: 7,9 F3: 4,9 H2: 2,6 I2: 6,8 D4: 5,9 I4: 3,7 I6: 3,6 A7: 5,8 C8: 4,8 F8: 8,9 H9: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,F2: 1.. / E2 = 1 => 0 pairs (*) / F2 = 1 => 0 pairs (X) B8,G8: 1.. / B8 = 1 => 0 pairs (X) / G8 = 1 => 18 pairs (_) F2,F4: 1.. / F2 = 1 => 0 pairs (X) / F4 = 1 => 0 pairs (_) H6,H9: 1.. / H6 = 1 => 19 pairs (_) / H9 = 1 => 0 pairs (X) B3,C3: 2.. / B3 = 2 => 0 pairs (X) / C3 = 2 => 25 pairs (_) D1,F1: 2.. / D1 = 2 => 17 pairs (_) / F1 = 2 => 15 pairs (_) G2,H2: 2.. / G2 = 2 => 0 pairs (X) / H2 = 2 => 15 pairs (_) C3,C9: 2.. / C3 = 2 => 25 pairs (_) / C9 = 2 => 0 pairs (X) H2,H6: 2.. / H2 = 2 => 15 pairs (_) / H6 = 2 => 0 pairs (X) B2,C2: 3.. / B2 = 3 => 0 pairs (*) / C2 = 3 => 0 pairs (X) D1,F1: 3.. / D1 = 3 => 15 pairs (_) / F1 = 3 => 17 pairs (_) I4,I6: 3.. / I4 = 3 => 14 pairs (_) / I6 = 3 => 14 pairs (_) D9,F9: 3.. / D9 = 3 => 17 pairs (_) / F9 = 3 => 15 pairs (_) B5,E5: 3.. / B5 = 3 => 15 pairs (_) / E5 = 3 => 14 pairs (_) C2,C6: 3.. / C2 = 3 => 14 pairs (_) / C6 = 3 => 0 pairs (*) D1,D9: 3.. / D1 = 3 => 15 pairs (_) / D9 = 3 => 17 pairs (_) F1,F9: 3.. / F1 = 3 => 17 pairs (_) / F9 = 3 => 15 pairs (_) F2,F3: 4.. / F2 = 4 => 0 pairs (*) / F3 = 4 => 0 pairs (X) D5,D6: 4.. / D5 = 4 => 0 pairs (X) / D6 = 4 => 15 pairs (_) B8,C8: 4.. / B8 = 4 => 0 pairs (X) / C8 = 4 => 25 pairs (_) D8,D9: 6.. / D8 = 6 => 14 pairs (_) / D9 = 6 => 0 pairs (X) B7,G7: 6.. / B7 = 6 => 15 pairs (_) / G7 = 6 => 0 pairs (X) D2,E2: 7.. / D2 = 7 => 15 pairs (_) / E2 = 7 => 0 pairs (X) G4,I4: 7.. / G4 = 7 => 14 pairs (_) / I4 = 7 => 14 pairs (_) I4,I9: 7.. / I4 = 7 => 14 pairs (_) / I9 = 7 => 14 pairs (_) G2,I2: 8.. / G2 = 8 => 15 pairs (_) / I2 = 8 => 15 pairs (_) A6,C6: 8.. / A6 = 8 => 0 pairs (*) / C6 = 8 => 0 pairs (X) E4,F4: 8.. / E4 = 8 => 16 pairs (_) / F4 = 8 => 0 pairs (X) I2,I9: 8.. / I2 = 8 => 15 pairs (_) / I9 = 8 => 15 pairs (_) G8,G9: 9.. / G8 = 9 => 0 pairs (X) / G9 = 9 => 14 pairs (_) B3,F3: 9.. / B3 = 9 => 0 pairs (X) / F3 = 9 => 0 pairs (_) A2,A6: 9.. / A2 = 9 => 0 pairs (*) / A6 = 9 => 0 pairs (X) * DURATION: 0:00:33.495098 START: 02:21:25.241320 END: 02:21:58.736418 2019-05-01 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,C3,C8,D1,D2,D4,F1,F3,F8,H2,H9,I2,I4,I6) * 781.6.495.........6..85.3712.6....4...7..6.89.....7.....91...343......52....4.... * PAIR C3: 2,4 BLK 1 B3: 2,4,9 # reduction candidate for 2,4 B3: 2,4 => SOLVED * 781263495935714628642859371256981743417536289893427516569172834374698152128345967 B3: 9 => CTR * 781362495..39718266928543712.65...4...7..6.899.8..7.1.8691257343746..152125743968 * PAIR D1: 2,3 COL D D9: 2,3,5,6,7,9 # reduction candidate for 2,3 D9: 5,6,7,9 # 19 pairs D9: 2,3 # 19 pairs * PAIR F1: 2,3 COL F F9: 2,3,5,8,9 # reduction candidate for 2,3 F9: 5,8,9 => SOLVED * 781263495935714628642859371256981743417536289893427516569172834374698152128345967 F9: 2,3 # 18 pairs * PAIR D2: 7,9 BLK 2 E2: 7,9,1 # reduction candidate for 7,9 E2: 7,9 => CTR * 781362495..39718266928543712.65...4...7..6.899.8..7.1.8691257343746..152125743968 E2: 1 => SOLVED * 781263495935714628642859371256981743417536289893427516569172834374698152128345967 * PAIR D2: 7,9 COL D D8: 7,9,6 # reduction candidate for 7,9 D8: 7,9 => CTR * 781362495.........6.285.3712.6....4...7..6.89.....7...869125734314...6525..64391. D8: 6 # 14 pairs D9: 7,9,2,3,5,6 # reduction candidate for 7,9 D9: 7,9 => CTR * 781362495..39718266928543712.65...4...7..6.89..8..7...8691257343746..152125743968 D9: 2,3,5,6 # 14 pairs * PAIR F3: 4,9 BLK 2 F2: 4,9,1 # reduction candidate for 4,9 F2: 4,9 => SOLVED * 781263495935714628642859371256981743417536289893427516569172834374698152128345967 F2: 1 => CTR * 781362495..39718266928543712.65...4...7..6.899.8..7.1.8691257343746..152125743968 * PAIR F3: 4,9 ROW 3 B3: 4,9,2 # reduction candidate for 4,9 B3: 2 => CTR * 781.6.495.........6248593712.6....4...7..6.89.....7.....91...34348....52....4.... B3: 4,9 # 25 pairs * PAIR H2: 2,6 BLK 3 G2: 2,6,8 # reduction candidate for 2,6 G2: 8 # 15 pairs G2: 2,6 # 15 pairs * PAIR H2: 2,6 COL H H6: 2,6,1 # reduction candidate for 2,6 H6: 2,6 => CTR * 781.6.495.........6.285.3712.6....4...7..6.89.....7.....91...34314....52....4..1. H6: 1 # 19 pairs * PAIR I2: 6,8 BLK 3 G2: 6,8,2 # reduction candidate for 6,8 G2: 2 => CTR * 781.6.495......2686.285.3712.6....4...7..6.89.....7.2...91...34314....52....4..1. G2: 6,8 # 15 pairs * PAIR I2: 6,8 COL I I9: 6,8,7 # reduction candidate for 6,8 I9: 7 # 14 pairs I9: 6,8 # 14 pairs * PAIR D4: 5,9 BLK 5 F4: 5,9,1,8 # reduction candidate for 5,9 F4: 5,9 => CTR * 781.6.495..3..1.2.6928543712.6.89.4...7..6.899.8..7.1.869125734374698152125743968 F4: 1,8 # 16 pairs D6: 5,9,2,4 # reduction candidate for 5,9 D6: 5,9 => CTR * 781.6.495.537.....6.285.3712.6....4.5.74.6.89..8..7...8.91756343.46...521.5.4.9.. D6: 2,4 # 15 pairs * PAIR D4: 5,9 ROW 4 B4: 5,9,1,3 # reduction candidate for 5,9 B4: 5,9 # 18 pairs B4: 1,3 # 15 pairs * PAIR D4: 5,9 COL D D9: 5,9,2,3,6,7 # reduction candidate for 5,9 D9: 5,9 => CTR * 781362495...7.....6248593712.6.8..4...7..6.898...97...5.9128.343..67..52....43... D9: 2,3,6,7 # 15 pairs * PAIR A7: 5,8 BLK 7 A9: 5,8,1 # reduction candidate for 5,8 A9: 5,8 => CTR * 781.6.495.........6..85.3712.6....4...7..6.89.....7.....91...343......52....4.... A9: 1 # 21 pairs C9: 5,8,2 # reduction candidate for 5,8 C9: 5,8 # 25 pairs * PAIR A7: 5,8 ROW 7 F7: 5,8,2 # reduction candidate for 5,8 F7: 2 => SOLVED * 781263495935714628642859371256981743417536289893427516569172834374698152128345967 F7: 5,8 # 18 pairs * PAIR A7: 5,8 COL A A6: 5,8,1,4,9 # reduction candidate for 5,8 A6: 5,8 => SOLVED * 781263495935714628642859371256981743417536289893427516569172834374698152128345967 A6: 1,4,9 => CTR * 781362495..39718266928543712.65...4...7..6.89..8..7.1.8691257343746..152125743968 * PAIR C8: 4,8 COL C C6: 4,8,3,5 # reduction candidate for 4,8 C6: 4,8 => CTR * 781362495..39718266928543712.65...4...7..6.89..8..7.1.8691257343746..152125743968 C6: 3,5 => SOLVED * 781263495935714628642859371256981743417536289893427516569172834374698152128345967 * PAIR F8: 8,9 BLK 8 E8: 8,9,7 # reduction candidate for 8,9 E8: 8,9 # 25 pairs F9: 8,9,2,3,5 # reduction candidate for 8,9 F9: 8,9 => CTR * 781.63495.........6..85.3712.6....4...7..6.89.....7.....91.2.343......52....4.... F9: 2,3,5 # 14 pairs * PAIR F8: 8,9 ROW 8 G8: 8,9,1,6,7 # reduction candidate for 8,9 G8: 8,9 => CTR * 781.6.495...7.....6.285.3712.6....4...7..6.89.....7.....91...3431467..52....4.... G8: 1,6,7 # 14 pairs * PAIR F8: 8,9 COL F F4: 8,9,1,5 # reduction candidate for 8,9 F4: 8,9 => CTR * 781362495..39718266928543712.65...4...7..6.899.8..7.1.8691257343746..152125743968 F4: 1,5 # 17 pairs * PAIR H9: 1,6 BLK 9 G8: 1,6,7,8,9 # reduction candidate for 1,6 G8: 1,6 # 17 pairs G9: 1,6,7,8,9 # reduction candidate for 1,6 G9: 1,6 => CTR * 781.6.495...7.....6.285.3712.6.8..4...7..6.89.....7.....9125.34314678952.2..4...7 G9: 7,8,9 # 14 pairs * PAIR H9: 1,6 ROW 9 B9: 1,6,2,5,7 # reduction candidate for 1,6 B9: 1,6 => CTR * 781.6.495..3......6.285.3712.6....4...7..6.89..8..7....291..6343746..152....4.... B9: 2,5,7 # 14 pairs * PAIR H9: 1,6 COL H H6: 1,6,2 # reduction candidate for 1,6 H6: 2 => CTR * 781.6.495......2686.285.3712.6....4...7..6.89.....7.2...91...34314....52....4..1. H6: 1,6 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060904-absurd-base-pr-000.dot * REASONING * PRF # B3: 2,4 => SOL * DIS # B3: 9 => CTR => B3: 2,4 * PRF # F9: 5,8,9 => SOL * DIS # E2: 7,9 => CTR => E2: 1 * PRF # E2: 1 => SOL * DIS # D8: 7,9 => CTR => D8: 6 * DIS # D9: 7,9 => CTR => D9: 2,3,5,6 * PRF # F2: 4,9 => SOL * DIS # F2: 1 => CTR => F2: 4,9 * DIS # B3: 2 => CTR => B3: 4,9 * DIS # H6: 2,6 => CTR => H6: 1 * DIS # G2: 2 => CTR => G2: 6,8 * DIS # F4: 5,9 => CTR => F4: 1,8 * DIS # D6: 5,9 => CTR => D6: 2,4 * DIS # D9: 5,9 => CTR => D9: 2,3,6,7 * DIS # A9: 5,8 => CTR => A9: 1 * PRF # F7: 2 => SOL * PRF # A6: 5,8 => SOL * DIS # A6: 1,4,9 => CTR => A6: 5,8 * DIS # C6: 4,8 => CTR => C6: 3,5 * PRF # C6: 3,5 => SOL * DIS # F9: 8,9 => CTR => F9: 2,3,5 * DIS # G8: 8,9 => CTR => G8: 1,6,7 * DIS # F4: 8,9 => CTR => F4: 1,5 * DIS # G9: 1,6 => CTR => G9: 7,8,9 * DIS # B9: 1,6 => CTR => B9: 2,5,7 * DIS # H6: 2 => CTR => H6: 1,6 * CNT 27 HDP CHAINS / 55 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,C3,C8,D1,D2,D4,F1,F3,F8,H2,H9,I2,I4,I6) * 781.6.495.........6..85.3712.6....4...7..6.89.....7.....91...343......52....4.... * PAIR C3: 2,4 BLK 1 B3: 2,4,9 # reduction candidate for 2,4 B3: 2,4 => SOLVED * 781263495935714628642859371256981743417536289893427516569172834374698152128345967 * DURATION: 0:00:01.906012 START: 02:22:33.782796 END: 02:22:35.688808 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060904-absurd-base-pr-001.dot * REASONING * PRF # B3: 2,4 => SOL * STA B3: 2,4 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Sep&YEAR=2006, 20060904, absurd
Solution
position: 781263495935714628642859371256981743417536289893427516569172834374698152128345967 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:
* PRF # B3: 2,4 => SOL * DIS # B3: 9 => CTR => B3: 2,4 * INC # D9: 2,3 => UNS * INC # D9: 5,6,7,9 => UNS * INC # F9: 2,3 => UNS * PRF # F9: 5,8,9 => SOL * DIS # E2: 7,9 => CTR => E2: 1 * PRF # E2: 1 => SOL * DIS # D8: 7,9 => CTR => D8: 6 * INC # D8: 6 => UNS * DIS # D9: 7,9 => CTR => D9: 2,3,5,6 * INC # D9: 2,3,5,6 => UNS * PRF # F2: 4,9 => SOL * DIS # F2: 1 => CTR => F2: 4,9 * INC # B3: 4,9 => UNS * DIS # B3: 2 => CTR => B3: 4,9 * INC # G2: 2,6 => UNS * INC # G2: 8 => UNS * DIS # H6: 2,6 => CTR => H6: 1 * INC # H6: 1 => UNS * INC # G2: 6,8 => UNS * DIS # G2: 2 => CTR => G2: 6,8 * INC # I9: 6,8 => UNS * INC # I9: 7 => UNS * DIS # F4: 5,9 => CTR => F4: 1,8 * INC # F4: 1,8 => UNS * DIS # D6: 5,9 => CTR => D6: 2,4 * INC # D6: 2,4 => UNS * INC # B4: 5,9 => UNS * INC # B4: 1,3 => UNS * DIS # D9: 5,9 => CTR => D9: 2,3,6,7 * INC # D9: 2,3,6,7 => UNS * DIS # A9: 5,8 => CTR => A9: 1 * INC # A9: 1 => UNS * INC # C9: 5,8 => UNS * INC # F7: 5,8 => UNS * PRF # F7: 2 => SOL * PRF # A6: 5,8 => SOL * DIS # A6: 1,4,9 => CTR => A6: 5,8 * DIS # C6: 4,8 => CTR => C6: 3,5 * PRF # C6: 3,5 => SOL * INC # E8: 8,9 => UNS * DIS # F9: 8,9 => CTR => F9: 2,3,5 * INC # F9: 2,3,5 => UNS * DIS # G8: 8,9 => CTR => G8: 1,6,7 * INC # G8: 1,6,7 => UNS * DIS # F4: 8,9 => CTR => F4: 1,5 * INC # F4: 1,5 => UNS * INC # G8: 1,6 => UNS * DIS # G9: 1,6 => CTR => G9: 7,8,9 * INC # G9: 7,8,9 => UNS * DIS # B9: 1,6 => CTR => B9: 2,5,7 * INC # B9: 2,5,7 => UNS * INC # H6: 1,6 => UNS * DIS # H6: 2 => CTR => H6: 1,6 * CNT 55 HDP CHAINS / 55 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # B3: 2,4 => SOL * STA B3: 2,4 * CNT 1 HDP CHAINS / 1 HYP OPENED