Analysis of zz-www.sudokuoftheday.co.uk-20060810-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006
level: medium
position: .1..3..89.27...........2......34.1.64...2.89..8..6....8..65.73.6.1..........8.4.. initial
Autosolve
position: 51..3.289.278.......8..2......3481.64...2.89.18..6....8..65.73.6.1.7.9.8....8.46. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # F1: 7 => SOL * PRF # F1: 4,7 => SOL * PRF # F2: 6 => SOL * DIS # I3: 4,5 => CTR => I3: 3,7 * DIS # H4: 5 => CTR => H4: 2,7 * PRF # I6: 3,5 => SOL * PRF # C6: 2 => SOL * PRF # G2: 3,5 => SOL * DIS # B8: 5 => CTR => B8: 3,4 * DIS # I9: 5 => CTR => I9: 1,2 * DIS # H6: 2,5 => CTR => H6: 4,7 * CNT 11 HDP CHAINS / 32 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # F1: 7 => SOL * STA F1: 7 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .1..3..89.27...........2......34.1.64...2.89..8..6....8..65.73.6.1..........8.4.. | initial |
| 51..3.289.278.......8..2......3481.64...2.89.18..6....8..65.73.6.1.7.9.8....8.46. | autosolve |
| 516437289327896514948512673759348126463125897182769345894651732631274958275983461 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) C1: 4,6 A2: 3,9 A3: 3,9 B3: 4,6 D1: 4,7 E2: 1,9 D3: 4,5 E3: 1,9 A4: 2,7 G6: 3,5 B7: 4,9 A9: 2,7 D8: 2,4 F8: 3,4 I7: 1,2 H8: 2,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,E3: 1.. / E2 = 1 => 22 pairs (_) / E3 = 1 => 14 pairs (_) H2,H3: 1.. / H2 = 1 => 14 pairs (_) / H3 = 1 => 22 pairs (_) D5,F5: 1.. / D5 = 1 => 18 pairs (_) / F5 = 1 => 0 pairs (X) I7,I9: 1.. / I7 = 1 => 24 pairs (_) / I9 = 1 => 27 pairs (_) E2,H2: 1.. / E2 = 1 => 22 pairs (_) / H2 = 1 => 14 pairs (_) E3,H3: 1.. / E3 = 1 => 14 pairs (_) / H3 = 1 => 22 pairs (_) F7,I7: 1.. / F7 = 1 => 27 pairs (_) / I7 = 1 => 24 pairs (_) D5,D9: 1.. / D5 = 1 => 18 pairs (_) / D9 = 1 => 0 pairs (X) D8,D9: 2.. / D8 = 2 => 26 pairs (_) / D9 = 2 => 0 pairs (X) C7,I7: 2.. / C7 = 2 => 24 pairs (_) / I7 = 2 => 27 pairs (_) D8,H8: 2.. / D8 = 2 => 26 pairs (_) / H8 = 2 => 0 pairs (X) A4,A9: 2.. / A4 = 2 => 25 pairs (_) / A9 = 2 => 0 pairs (*) A2,A3: 3.. / A2 = 3 => 14 pairs (_) / A3 = 3 => 22 pairs (_) F8,F9: 3.. / F8 = 3 => 17 pairs (_) / F9 = 3 => 26 pairs (_) B8,F8: 3.. / B8 = 3 => 26 pairs (_) / F8 = 3 => 17 pairs (_) C1,B3: 4.. / C1 = 4 => 18 pairs (_) / B3 = 4 => 0 pairs (*) H6,I6: 4.. / H6 = 4 => 17 pairs (_) / I6 = 4 => 24 pairs (_) C1,C7: 4.. / C1 = 4 => 18 pairs (_) / C7 = 4 => 0 pairs (*) F2,D3: 5.. / F2 = 5 => 27 pairs (_) / D3 = 5 => 19 pairs (_) H8,I9: 5.. / H8 = 5 => 26 pairs (_) / I9 = 5 => 0 pairs (X) B8,H8: 5.. / B8 = 5 => 0 pairs (X) / H8 = 5 => 26 pairs (_) C1,B3: 6.. / C1 = 6 => 0 pairs (*) / B3 = 6 => 0 pairs (X) F1,F2: 6.. / F1 = 6 => 18 pairs (_) / F2 = 6 => 0 pairs (*) G2,G3: 6.. / G2 = 6 => 18 pairs (_) / G3 = 6 => 0 pairs (*) B5,C5: 6.. / B5 = 6 => 0 pairs (*) / C5 = 6 => 0 pairs (X) C1,F1: 6.. / C1 = 6 => 0 pairs (*) / F1 = 6 => 0 pairs (X) F2,G2: 6.. / F2 = 6 => 0 pairs (*) / G2 = 6 => 0 pairs (X) B3,G3: 6.. / B3 = 6 => 18 pairs (_) / G3 = 6 => 0 pairs (*) B3,B5: 6.. / B3 = 6 => 18 pairs (_) / B5 = 6 => 0 pairs (*) C1,C5: 6.. / C1 = 6 => 0 pairs (*) / C5 = 6 => 0 pairs (X) D1,F1: 7.. / D1 = 7 => 18 pairs (_) / F1 = 7 => 0 pairs (*) H3,I3: 7.. / H3 = 7 => 15 pairs (_) / I3 = 7 => 23 pairs (_) A9,B9: 7.. / A9 = 7 => 25 pairs (_) / B9 = 7 => 0 pairs (*) A4,A9: 7.. / A4 = 7 => 0 pairs (*) / A9 = 7 => 0 pairs (X) A2,A3: 9.. / A2 = 9 => 22 pairs (_) / A3 = 9 => 14 pairs (_) E2,E3: 9.. / E2 = 9 => 14 pairs (_) / E3 = 9 => 22 pairs (_) B4,C4: 9.. / B4 = 9 => 20 pairs (_) / C4 = 9 => 18 pairs (_) D6,F6: 9.. / D6 = 9 => 18 pairs (_) / F6 = 9 => 29 pairs (_) A2,E2: 9.. / A2 = 9 => 22 pairs (_) / E2 = 9 => 14 pairs (_) A3,E3: 9.. / A3 = 9 => 14 pairs (_) / E3 = 9 => 22 pairs (_) D6,D9: 9.. / D6 = 9 => 18 pairs (_) / D9 = 9 => 29 pairs (_) * DURATION: 0:00:50.688021 START: 01:41:28.984809 END: 01:42:19.672830 2019-05-01 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A4,A9,B3,B7,C1,D1,D3,D8,E2,E3,F8,G6,H8,I7) * 51..3.289.278.......8..2......3481.64...2.89.18..6....8..65.73.6.1.7.9.8....8.46. * PAIR C1: 4,6 ROW 1 F1: 4,6,7 # reduction candidate for 4,6 F1: 7 => SOLVED * 516437289327896514948512673759348126463125897182769345894651732631274958275983461 F1: 4,6 # 18 pairs * PAIR D1: 4,7 BLK 2 F1: 4,7,6 # reduction candidate for 4,7 F1: 4,7 => SOLVED * 516437289327896514948512673759348126463125897182769345894651732631274958275983461 F1: 6 # 18 pairs * PAIR D3: 4,5 BLK 2 F2: 4,5,6 # reduction candidate for 4,5 F2: 6 => SOLVED * 516437289327896514948512673759348126463125897182769345894651732631274958275983461 F2: 4,5 # 18 pairs * PAIR D3: 4,5 ROW 3 H3: 4,5,1,7 # reduction candidate for 4,5 H3: 4,5 # 17 pairs I3: 4,5,3,7 # reduction candidate for 4,5 I3: 4,5 => CTR * 51..3.28932789.61.968.1237....3481264.6.2.89.182.6.5438..65.7326.127.95827..8.46. I3: 3,7 # 17 pairs * PAIR A4: 2,7 ROW 4 H4: 2,7,5 # reduction candidate for 2,7 H4: 5 => CTR * 514736289.278.4.....8..2...2793481564..12.8971859673428.265.7316514739287.3281465 H4: 2,7 # 21 pairs * PAIR G6: 3,5 BLK 6 I5: 3,5,7 # reduction candidate for 3,5 I5: 3,5 # 22 pairs I6: 3,5,2,4,7 # reduction candidate for 3,5 I6: 3,5 => SOLVED * 516437289327896514948512673759348126463125897182769345894651732631274958275983461 I6: 2,4,7 # 16 pairs * PAIR G6: 3,5 ROW 6 C6: 3,5,2 # reduction candidate for 3,5 C6: 2 => SOLVED * 516437289327896514948512673759348126463125897182769345894651732631274958275983461 C6: 3,5 # 26 pairs * PAIR G6: 3,5 COL G G2: 3,5,6 # reduction candidate for 3,5 G2: 3,5 => SOLVED * 516437289327896514948512673759348126463125897182769345894651732631274958275983461 G2: 6 # 18 pairs G3: 3,5,6 # reduction candidate for 3,5 G3: 3,5 # 18 pairs * PAIR B7: 4,9 BLK 7 C7: 4,9,2 # reduction candidate for 4,9 C7: 4,9 # 27 pairs C7: 2 # 24 pairs * PAIR B7: 4,9 ROW 7 F7: 4,9,1 # reduction candidate for 4,9 F7: 1 # 27 pairs F7: 4,9 # 24 pairs * PAIR F8: 3,4 ROW 8 B8: 3,4,5 # reduction candidate for 3,4 B8: 5 => CTR * 514736289.278.4653..8..2...2..3481.64..12.89.18.96...28.265.7316514739287..281465 B8: 3,4 # 26 pairs * PAIR I7: 1,2 BLK 9 I9: 1,2,5 # reduction candidate for 1,2 I9: 5 => CTR * 514736289.278.4653..8..2...2..3481.64..12.89.18.96...28.26597316514739287..281465 I9: 1,2 # 26 pairs * PAIR H8: 2,5 BLK 9 I9: 2,5,1 # reduction candidate for 2,5 I9: 1 # 27 pairs I9: 2,5 # 24 pairs * PAIR H8: 2,5 COL H H4: 2,5,7 # reduction candidate for 2,5 H4: 2,5 # 19 pairs H6: 2,5,4,7 # reduction candidate for 2,5 H6: 2,5 => CTR * 514736289.278..6.5.68..2......348176476.2.893183.6.5248..65.73.6.127.9587...8.46. H6: 4,7 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060810-absurd-base-pr-000.dot * REASONING * PRF # F1: 7 => SOL * PRF # F1: 4,7 => SOL * PRF # F2: 6 => SOL * DIS # I3: 4,5 => CTR => I3: 3,7 * DIS # H4: 5 => CTR => H4: 2,7 * PRF # I6: 3,5 => SOL * PRF # C6: 2 => SOL * PRF # G2: 3,5 => SOL * DIS # B8: 5 => CTR => B8: 3,4 * DIS # I9: 5 => CTR => I9: 1,2 * DIS # H6: 2,5 => CTR => H6: 4,7 * CNT 11 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A4,A9,B3,B7,C1,D1,D3,D8,E2,E3,F8,G6,H8,I7) * 51..3.289.278.......8..2......3481.64...2.89.18..6....8..65.73.6.1.7.9.8....8.46. * PAIR C1: 4,6 ROW 1 F1: 4,6,7 # reduction candidate for 4,6 F1: 7 => SOLVED * 516437289327896514948512673759348126463125897182769345894651732631274958275983461 * DURATION: 0:00:02.303733 START: 01:42:43.724169 END: 01:42:46.027902 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060810-absurd-base-pr-001.dot * REASONING * PRF # F1: 7 => SOL * STA F1: 7 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060810, absurd
Solution
position: 516437289327896514948512673759348126463125897182769345894651732631274958275983461 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 # F1: 4,6 => UNS * PRF # F1: 7 => SOL * PRF # F1: 4,7 => SOL * INC # F1: 6 => UNS * INC # F2: 4,5 => UNS * PRF # F2: 6 => SOL * INC # H3: 4,5 => UNS * DIS # I3: 4,5 => CTR => I3: 3,7 * INC # I3: 3,7 => UNS * INC # H4: 2,7 => UNS * DIS # H4: 5 => CTR => H4: 2,7 * INC # I5: 3,5 => UNS * PRF # I6: 3,5 => SOL * INC # I6: 2,4,7 => UNS * INC # C6: 3,5 => UNS * PRF # C6: 2 => SOL * PRF # G2: 3,5 => SOL * INC # G2: 6 => UNS * INC # G3: 3,5 => UNS * INC # C7: 4,9 => UNS * INC # C7: 2 => UNS * INC # F7: 4,9 => UNS * INC # F7: 1 => UNS * INC # B8: 3,4 => UNS * DIS # B8: 5 => CTR => B8: 3,4 * INC # I9: 1,2 => UNS * DIS # I9: 5 => CTR => I9: 1,2 * INC # I9: 2,5 => UNS * INC # I9: 1 => UNS * INC # H4: 2,5 => UNS * DIS # H6: 2,5 => CTR => H6: 4,7 * INC # H6: 4,7 => UNS * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F1: 4,6 => UNS * PRF # F1: 7 => SOL * STA F1: 7 * CNT 2 HDP CHAINS / 2 HYP OPENED