Analysis of xx-top500-166-base.sdk
Contents
Original Sudoku
level: medium
position: ......1.27..4...........8..3.....64.4....9.......1.....126........5...3..9....... initial
Autosolve
position: 9.....1.27.64.13951.59..8.43.12..64945..6921.269.1475.5126934876..5..931893147526 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 4,8 => CTR => B1: 3 * PRF # B1: 3 => SOL * DIS # D5: 3 => CTR => D5: 7,8 * PRF # E1: 3,7 => SOL * DIS # E1: 5 => CTR => E1: 3,7 * DIS # D5: 3 => CTR => D5: 7,8 * PRF # E1: 5,7 => SOL * DIS # E1: 3 => CTR => E1: 5,7 * PRF # F1: 5,8 => SOL * DIS # F1: 6 => CTR => F1: 5,8 * DIS # D5: 3,8 => CTR => D5: 7 * PRF # D5: 7 => SOL * DIS # D5: 3,8 => CTR => D5: 7 * PRF # D5: 7 => SOL * CNT 14 HDP CHAINS / 16 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B1: 4,8 => CTR => B1: 3 * PRF B1: 3 => SOL * STA B1: 3 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ......1.27..4...........8..3.....64.4....9.......1.....126........5...3..9....... | initial |
| 9.....1.27.64.13951.59..8.43.12..64945..6921.269.1475.5126934876..5..931893147526 | autosolve |
| 934875162786421395125936874371258649458769213269314758512693487647582931893147526 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) C1: 4,8 B2: 2,8 B3: 2,3 D1: 7,8 E2: 2,8 E3: 3,7 F3: 2,6 H1: 6,7 H3: 6,7 B4: 7,8 C5: 7,8 E4: 5,7 F4: 5,8 D6: 3,8 I5: 3,8 I6: 3,8 B8: 4,7 C8: 4,7 E8: 2,8 F8: 2,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,B3: 2.. / B2 = 2 => 0 pairs (X) / B3 = 2 => 0 pairs (_) E2,F3: 2.. / E2 = 2 => 0 pairs (*) / F3 = 2 => 0 pairs (X) E8,F8: 2.. / E8 = 2 => 0 pairs (X) / F8 = 2 => 0 pairs (_) B2,E2: 2.. / B2 = 2 => 0 pairs (X) / E2 = 2 => 0 pairs (_) B3,F3: 2.. / B3 = 2 => 0 pairs (*) / F3 = 2 => 0 pairs (X) E2,E8: 2.. / E2 = 2 => 0 pairs (*) / E8 = 2 => 0 pairs (X) F3,F8: 2.. / F3 = 2 => 0 pairs (X) / F8 = 2 => 0 pairs (_) B1,B3: 3.. / B1 = 3 => 0 pairs (*) / B3 = 3 => 0 pairs (X) E1,E3: 3.. / E1 = 3 => 0 pairs (X) / E3 = 3 => 0 pairs (_) D5,D6: 3.. / D5 = 3 => 0 pairs (X) / D6 = 3 => 18 pairs (_) I5,I6: 3.. / I5 = 3 => 18 pairs (_) / I6 = 3 => 0 pairs (X) B1,E1: 3.. / B1 = 3 => 0 pairs (*) / E1 = 3 => 0 pairs (X) B3,E3: 3.. / B3 = 3 => 0 pairs (X) / E3 = 3 => 0 pairs (_) D5,I5: 3.. / D5 = 3 => 0 pairs (X) / I5 = 3 => 18 pairs (_) D6,I6: 3.. / D6 = 3 => 18 pairs (_) / I6 = 3 => 0 pairs (X) B1,C1: 4.. / B1 = 4 => 0 pairs (X) / C1 = 4 => 0 pairs (_) B8,C8: 4.. / B8 = 4 => 0 pairs (*) / C8 = 4 => 0 pairs (X) B1,B8: 4.. / B1 = 4 => 0 pairs (X) / B8 = 4 => 0 pairs (_) C1,C8: 4.. / C1 = 4 => 0 pairs (*) / C8 = 4 => 0 pairs (X) E1,F1: 5.. / E1 = 5 => 0 pairs (X) / F1 = 5 => 0 pairs (_) E4,F4: 5.. / E4 = 5 => 0 pairs (*) / F4 = 5 => 0 pairs (X) E1,E4: 5.. / E1 = 5 => 0 pairs (X) / E4 = 5 => 0 pairs (_) F1,F4: 5.. / F1 = 5 => 0 pairs (*) / F4 = 5 => 0 pairs (X) F1,F3: 6.. / F1 = 6 => 0 pairs (X) / F3 = 6 => 0 pairs (_) H1,H3: 6.. / H1 = 6 => 0 pairs (*) / H3 = 6 => 0 pairs (X) F1,H1: 6.. / F1 = 6 => 0 pairs (X) / H1 = 6 => 0 pairs (_) F3,H3: 6.. / F3 = 6 => 0 pairs (*) / H3 = 6 => 0 pairs (X) H1,H3: 7.. / H1 = 7 => 0 pairs (X) / H3 = 7 => 0 pairs (_) B4,C5: 7.. / B4 = 7 => 0 pairs (*) / C5 = 7 => 0 pairs (X) E4,D5: 7.. / E4 = 7 => 0 pairs (X) / D5 = 7 => 0 pairs (_) B8,C8: 7.. / B8 = 7 => 0 pairs (X) / C8 = 7 => 0 pairs (_) E3,H3: 7.. / E3 = 7 => 0 pairs (X) / H3 = 7 => 0 pairs (_) B4,E4: 7.. / B4 = 7 => 0 pairs (*) / E4 = 7 => 0 pairs (X) C5,D5: 7.. / C5 = 7 => 0 pairs (X) / D5 = 7 => 0 pairs (_) B4,B8: 7.. / B4 = 7 => 0 pairs (*) / B8 = 7 => 0 pairs (X) C5,C8: 7.. / C5 = 7 => 0 pairs (X) / C8 = 7 => 0 pairs (_) D1,D5: 7.. / D1 = 7 => 0 pairs (X) / D5 = 7 => 0 pairs (_) B4,C5: 8.. / B4 = 8 => 0 pairs (X) / C5 = 8 => 0 pairs (_) I5,I6: 8.. / I5 = 8 => 0 pairs (X) / I6 = 8 => 18 pairs (_) E8,F8: 8.. / E8 = 8 => 0 pairs (*) / F8 = 8 => 0 pairs (X) B2,E2: 8.. / B2 = 8 => 0 pairs (*) / E2 = 8 => 0 pairs (X) B4,F4: 8.. / B4 = 8 => 0 pairs (X) / F4 = 8 => 0 pairs (_) D6,I6: 8.. / D6 = 8 => 0 pairs (X) / I6 = 8 => 18 pairs (_) C1,C5: 8.. / C1 = 8 => 0 pairs (X) / C5 = 8 => 0 pairs (_) E2,E8: 8.. / E2 = 8 => 0 pairs (X) / E8 = 8 => 0 pairs (_) * DURATION: 0:01:31.674275 START: 08:25:14.034728 END: 08:26:45.709003 2017-05-04 * CP COUNT: (45) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B3,B4,B8,C1,C5,C8,D1,D6,E2,E3,E4,E8,F3,F4,F8,H1,H3,I5,I6) * 9.....1.27.64.13951.59..8.43.12..64945..6921.269.1475.5126934876..5..931893147526 * PAIR C1: 4,8 BLK 1 B1: 4,8,3 # reduction candidate for 4,8 B1: 4,8 => CTR * 9...351627.64.139513597.8.43.12..64945..6921.269.1475.5126934876..5..931893147526 B1: 3 => SOLVED * 934875162786421395125936874371258649458769213269314758512693487647582931893147526 * PAIR D1: 7,8 COL D D5: 7,8,3 # reduction candidate for 7,8 D5: 3 => CTR * 9..7..1627.64.13951.59368743.12756494573692182698147535126934876745.2931893147526 D5: 7,8 # 18 pairs * PAIR E3: 3,7 BLK 2 E1: 3,7,5 # reduction candidate for 3,7 E1: 3,7 => SOLVED * 934875162786421395125936874371258649458769213269314758512693487647582931893147526 E1: 5 => CTR * 934.5.1.27864213951259368.43.12..64945..6921.269.1475.5126934876..5..931893147526 * PAIR C5: 7,8 ROW 5 D5: 7,8,3 # reduction candidate for 7,8 D5: 3 => CTR * 9..7..1627.64.13951.59368743.12756494573692182698147535126934876745.2931893147526 D5: 7,8 # 18 pairs * PAIR E4: 5,7 COL E E1: 5,7,3 # reduction candidate for 5,7 E1: 5,7 => SOLVED * 934875162786421395125936874371258649458769213269314758512693487647582931893147526 E1: 3 => CTR * 9...351627.64.139513597.8.43.12..64945..6921.269.1475.5126934876..5..931893147526 * PAIR F4: 5,8 COL F F1: 5,8,6 # reduction candidate for 5,8 F1: 5,8 => SOLVED * 934875162786421395125936874371258649458769213269314758512693487647582931893147526 F1: 6 => CTR * 9...561727.64.13951.59..8.43.12..64945..6921.269.1475.5126934876..5..931893147526 * PAIR D6: 3,8 BLK 5 D5: 3,8,7 # reduction candidate for 3,8 D5: 3,8 => CTR * 9..7..1627.64.13951.59368743.1275649457.6921.269.1475.5126934876745.2931893147526 D5: 7 => SOLVED * 934875162786421395125936874371258649458769213269314758512693487647582931893147526 * PAIR I5: 3,8 ROW 5 D5: 3,8,7 # reduction candidate for 3,8 D5: 3,8 => CTR * 9..7..1627.64.13951.59368743.1275649457.6921.269.1475.5126934876745.2931893147526 D5: 7 => SOLVED * 934875162786421395125936874371258649458769213269314758512693487647582931893147526 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-166-base-pr-000.dot * REASONING * DIS # B1: 4,8 => CTR => B1: 3 * PRF # B1: 3 => SOL * DIS # D5: 3 => CTR => D5: 7,8 * PRF # E1: 3,7 => SOL * DIS # E1: 5 => CTR => E1: 3,7 * DIS # D5: 3 => CTR => D5: 7,8 * PRF # E1: 5,7 => SOL * DIS # E1: 3 => CTR => E1: 5,7 * PRF # F1: 5,8 => SOL * DIS # F1: 6 => CTR => F1: 5,8 * DIS # D5: 3,8 => CTR => D5: 7 * PRF # D5: 7 => SOL * DIS # D5: 3,8 => CTR => D5: 7 * PRF # D5: 7 => SOL * CNT 14 HDP CHAINS / 16 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B3,B4,B8,C1,C5,C8,D1,D6,E2,E3,E4,E8,F3,F4,F8,H1,H3,I5,I6) * 9.....1.27.64.13951.59..8.43.12..64945..6921.269.1475.5126934876..5..931893147526 * PAIR C1: 4,8 BLK 1 B1: 4,8,3 # reduction candidate for 4,8 B1: 4,8 => CTR * 9...351627.64.139513597.8.43.12..64945..6921.269.1475.5126934876..5..931893147526 B1: 3 => SOLVED * 934875162786421395125936874371258649458769213269314758512693487647582931893147526 * DURATION: 0:00:03.172992 START: 08:27:07.362236 END: 08:27:10.535228 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-166-base-pr-001.dot * REASONING * DIS # B1: 4,8 => CTR => B1: 3 * PRF B1: 3 => SOL * STA B1: 3 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 166 solution: 934875162786421395125936874371258649458769213269314758512693487647582931893147526 info: 1824 FNBTWY S8.f 836 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 934875162786421395125936874371258649458769213269314758512693487647582931893147526 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 # B1: 4,8 => CTR => B1: 3 * PRF # B1: 3 => SOL * INC # D5: 7,8 => UNS * DIS # D5: 3 => CTR => D5: 7,8 * PRF # E1: 3,7 => SOL * DIS # E1: 5 => CTR => E1: 3,7 * INC # D5: 7,8 => UNS * DIS # D5: 3 => CTR => D5: 7,8 * PRF # E1: 5,7 => SOL * DIS # E1: 3 => CTR => E1: 5,7 * PRF # F1: 5,8 => SOL * DIS # F1: 6 => CTR => F1: 5,8 * DIS # D5: 3,8 => CTR => D5: 7 * PRF # D5: 7 => SOL * DIS # D5: 3,8 => CTR => D5: 7 * PRF # D5: 7 => SOL * CNT 16 HDP CHAINS / 16 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B1: 4,8 => CTR => B1: 3 * PRF B1: 3 => SOL * STA B1: 3 * CNT 2 HDP CHAINS / 1 HYP OPENED