Analysis of xx-top500-313-base.sdk
Contents
Original Sudoku
level: medium
position: 2.......6...7..3.......1...5...2..4..7.3..8............376.........4..25......... initial
Autosolve
position: 2..4.5.76.547.63.27..2.15.45...27.43.7236485.34.51.267.376524..6...43725425.7.63. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # E3: 8,9 => SOL * PRF # A2: 8,9 => SOL * DIS # A2: 1 => CTR => A2: 8,9 * DIS # H2: 8,9 => CTR => H2: 1 * PRF # H2: 1 => SOL * DIS # H2: 8 => CTR => H2: 1,9 * DIS # C1: 1,9 => CTR => C1: 3,8 * DIS # H2: 8,9 => CTR => H2: 1 * PRF # H2: 1 => SOL * PRF # E3: 8,9 => SOL * DIS # B4: 1,9 => CTR => B4: 6,8 * DIS # C4: 1,9 => CTR => C4: 6,8 * PRF # A2: 1,9 => SOL * DIS # A2: 8 => CTR => A2: 1,9 * DIS # A7: 1,9 => CTR => A7: 8 * PRF # A7: 8 => SOL * PRF # B4: 8,9 => SOL * DIS # C4: 8,9 => CTR => C4: 1,6 * PRF # C1: 8,9 => SOL * PRF # B4: 8,9 => SOL * DIS # C4: 8,9 => CTR => C4: 1,6 * DIS # D9: 8,9 => CTR => D9: 1 * DIS # B4: 1,9 => CTR => B4: 6,8 * DIS # C4: 1,9 => CTR => C4: 6,8 * PRF # I7: 1,9 => SOL * DIS # I7: 8 => CTR => I7: 1,9 * DIS # I9: 1,9 => CTR => I9: 8 * PRF # I9: 8 => SOL * DIS # D9: 8,9 => CTR => D9: 1 * DIS # I9: 1 => CTR => I9: 8,9 * PRF # I7: 1,9 => SOL * DIS # I7: 8 => CTR => I7: 1,9 * DIS # I9: 1,9 => CTR => I9: 8 * PRF # I9: 8 => SOL * DIS # A7: 1,9 => CTR => A7: 8 * PRF # A7: 8 => SOL * DIS # H2: 8 => CTR => H2: 1,9 * CNT 37 HDP CHAINS / 62 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # E3: 8,9 => SOL * STA E3: 8,9 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 2.......6...7..3.......1...5...2..4..7.3..8............376.........4..25......... | initial |
| 2..4.5.76.547.63.27..2.15.45...27.43.7236485.34.51.267.376524..6...43725425.7.63. | autosolve |
| 218435976954786312763291584586927143172364859349518267837652491691843725425179638 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) E2: 8,9 G1: 1,9 H3: 8,9 A5: 1,9 C6: 8,9 D4: 8,9 F6: 8,9 G4: 1,9 I5: 1,9 F9: 8,9 H7: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G1,H2: 1.. / G1 = 1 => 0 pairs (X) / H2 = 1 => 0 pairs (_) G4,I5: 1.. / G4 = 1 => 0 pairs (*) / I5 = 1 => 0 pairs (X) D8,D9: 1.. / D8 = 1 => 0 pairs (X) / D9 = 1 => 14 pairs (_) A2,H2: 1.. / A2 = 1 => 0 pairs (X) / H2 = 1 => 0 pairs (_) A5,I5: 1.. / A5 = 1 => 0 pairs (*) / I5 = 1 => 0 pairs (X) D9,I9: 1.. / D9 = 1 => 14 pairs (_) / I9 = 1 => 0 pairs (X) G1,G4: 1.. / G1 = 1 => 0 pairs (X) / G4 = 1 => 0 pairs (_) H2,H7: 1.. / H2 = 1 => 0 pairs (*) / H7 = 1 => 0 pairs (X) C1,C3: 3.. / C1 = 3 => 12 pairs (_) / C3 = 3 => 0 pairs (*) E1,E3: 3.. / E1 = 3 => 0 pairs (*) / E3 = 3 => 0 pairs (X) C1,E1: 3.. / C1 = 3 => 12 pairs (_) / E1 = 3 => 0 pairs (*) C3,E3: 3.. / C3 = 3 => 0 pairs (*) / E3 = 3 => 0 pairs (X) B3,C3: 6.. / B3 = 6 => 11 pairs (_) / C3 = 6 => 14 pairs (_) B4,C4: 6.. / B4 = 6 => 14 pairs (_) / C4 = 6 => 11 pairs (_) B3,B4: 6.. / B3 = 6 => 11 pairs (_) / B4 = 6 => 14 pairs (_) C3,C4: 6.. / C3 = 6 => 14 pairs (_) / C4 = 6 => 11 pairs (_) H2,H3: 8.. / H2 = 8 => 0 pairs (X) / H3 = 8 => 13 pairs (_) D4,F6: 8.. / D4 = 8 => 0 pairs (X) / F6 = 8 => 0 pairs (_) I7,I9: 8.. / I7 = 8 => 0 pairs (X) / I9 = 8 => 0 pairs (_) C6,F6: 8.. / C6 = 8 => 0 pairs (X) / F6 = 8 => 0 pairs (_) A7,I7: 8.. / A7 = 8 => 0 pairs (*) / I7 = 8 => 0 pairs (X) A2,A7: 8.. / A2 = 8 => 0 pairs (X) / A7 = 8 => 0 pairs (_) F6,F9: 8.. / F6 = 8 => 0 pairs (*) / F9 = 8 => 0 pairs (X) D4,F6: 9.. / D4 = 9 => 0 pairs (*) / F6 = 9 => 0 pairs (X) G4,I5: 9.. / G4 = 9 => 0 pairs (X) / I5 = 9 => 0 pairs (_) A5,I5: 9.. / A5 = 9 => 0 pairs (X) / I5 = 9 => 0 pairs (_) C6,F6: 9.. / C6 = 9 => 0 pairs (*) / F6 = 9 => 0 pairs (X) F6,F9: 9.. / F6 = 9 => 0 pairs (X) / F9 = 9 => 0 pairs (_) G1,G4: 9.. / G1 = 9 => 0 pairs (*) / G4 = 9 => 0 pairs (X) * DURATION: 0:00:53.601741 START: 13:40:48.532454 END: 13:41:42.134195 2017-05-04 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,C6,D4,E2,F6,F9,G1,G4,H3,H7,I5) * 2..4.5.76.547.63.27..2.15.45...27.43.7236485.34.51.267.376524..6...43725425.7.63. * PAIR E2: 8,9 BLK 2 E1: 8,9,3 # reduction candidate for 8,9 E1: 8,9 # 12 pairs E3: 8,9,3 # reduction candidate for 8,9 E3: 8,9 => SOLVED * 218435976954786312763291584586927143172364859349518267837652491691843725425179638 E3: 3 # 12 pairs * PAIR E2: 8,9 ROW 2 A2: 8,9,1 # reduction candidate for 8,9 A2: 8,9 => SOLVED * 218435976954786312763291584586927143172364859349518267837652491691843725425179638 A2: 1 => CTR * 2..4.5.761547.63.27..2.15.45...27.439723648513485192678376524196..843725425.7.63. H2: 8,9,1 # reduction candidate for 8,9 H2: 8,9 => CTR * 2..4.51761547.63.27..2.15.45...279439723648513485192678376524196..843725425.7.63. H2: 1 => SOLVED * 218435976954786312763291584586927143172364859349518267837652491691843725425179638 * PAIR G1: 1,9 BLK 3 H2: 1,9,8 # reduction candidate for 1,9 H2: 8 => CTR * 2..4.51761547963827..2.15945...279439723648513485192678376524196..843725425.7.63. H2: 1,9 # 13 pairs * PAIR G1: 1,9 ROW 1 B1: 1,9,8 # reduction candidate for 1,9 B1: 1,9 # 14 pairs C1: 1,9,3,8 # reduction candidate for 1,9 C1: 1,9 => CTR * 28.435.76.547.63.27632.15.45.6827.43.7236485.3485192678376524..6...43725425.7863. C1: 3,8 # 12 pairs * PAIR H3: 8,9 BLK 3 H2: 8,9,1 # reduction candidate for 8,9 H2: 8,9 => CTR * 2..4.51761547.63.27..2.15.45...279439723648513485192678376524196..843725425.7.63. H2: 1 => SOLVED * 218435976954786312763291584586927143172364859349518267837652491691843725425179638 * PAIR H3: 8,9 ROW 3 B3: 8,9,6 # reduction candidate for 8,9 B3: 8,9 # 14 pairs C3: 8,9,3,6 # reduction candidate for 8,9 C3: 8,9 # 17 pairs E3: 8,9,3 # reduction candidate for 8,9 E3: 8,9 => SOLVED * 218435976954786312763291584586927143172364859349518267837652491691843725425179638 E3: 3 # 12 pairs * PAIR A5: 1,9 BLK 4 B4: 1,9,6,8 # reduction candidate for 1,9 B4: 1,9 => CTR * 2..485.7685479631276.2315845.6827143172364859348519267.376524..68..43725425.7863. B4: 6,8 # 12 pairs C4: 1,9,6,8 # reduction candidate for 1,9 C4: 1,9 => CTR * 213485976854796312796231584569827143172364859348519267.376524..68..43725425.7863. C4: 6,8 # 12 pairs * PAIR A5: 1,9 COL A A2: 1,9,8 # reduction candidate for 1,9 A2: 1,9 => SOLVED * 218435976954786312763291584586927143172364859349518267837652491691843725425179638 A2: 8 => CTR * 2..4.5.768547963127..2.15845...2714317236485934.51.267.376524..6...43725425.7.63. A7: 1,9,8 # reduction candidate for 1,9 A7: 1,9 => CTR * 2..4.5.768547963127..2.15845...2714317236485934.51.267.376524..6...43725425.7.63. A7: 8 => SOLVED * 218435976954786312763291584586927143172364859349518267837652491691843725425179638 * PAIR C6: 8,9 BLK 4 B4: 8,9,1,6 # reduction candidate for 8,9 B4: 8,9 => SOLVED * 218435976954786312763291584586927143172364859349518267837652491691843725425179638 B4: 1,6 # 13 pairs C4: 8,9,1,6 # reduction candidate for 8,9 C4: 8,9 => CTR * 2.34.59769547863.27.62315.456..2714317236485934.51.267.376524916...43725425179638 C4: 1,6 # 12 pairs * PAIR C6: 8,9 COL C C1: 8,9,1,3 # reduction candidate for 8,9 C1: 8,9 => SOLVED * 218435976954786312763291584586927143172364859349518267837652491691843725425179638 C1: 1,3 # 12 pairs C3: 8,9,3,6 # reduction candidate for 8,9 C3: 8,9 # 17 pairs C8: 8,9,1 # reduction candidate for 8,9 C8: 8,9 # 15 pairs * PAIR D4: 8,9 ROW 4 B4: 8,9,1,6 # reduction candidate for 8,9 B4: 8,9 => SOLVED * 218435976954786312763291584586927143172364859349518267837652491691843725425179638 B4: 1,6 # 13 pairs C4: 8,9,1,6 # reduction candidate for 8,9 C4: 8,9 => CTR * 2.34.59769547863.27.62315.456..2714317236485934.51.267.376524916...43725425179638 C4: 1,6 # 12 pairs * PAIR D4: 8,9 COL D D8: 8,9,1 # reduction candidate for 8,9 D8: 8,9 # 14 pairs D9: 8,9,1 # reduction candidate for 8,9 D9: 8,9 => CTR * 2..4.5.76.547.63127..2.15845...2714317236485934.51.267.376524986..143725425.7.631 D9: 1 # 14 pairs * PAIR G4: 1,9 ROW 4 B4: 1,9,6,8 # reduction candidate for 1,9 B4: 1,9 => CTR * 2..485.7685479631276.2315845.6827143172364859348519267.376524..68..43725425.7863. B4: 6,8 # 12 pairs C4: 1,9,6,8 # reduction candidate for 1,9 C4: 1,9 => CTR * 213485976854796312796231584569827143172364859348519267.376524..68..43725425.7863. C4: 6,8 # 12 pairs * PAIR I5: 1,9 COL I I7: 1,9,8 # reduction candidate for 1,9 I7: 1,9 => SOLVED * 218435976954786312763291584586927143172364859349518267837652491691843725425179638 I7: 8 => CTR * 2..4.5.768547963127..2.15845...2714317236485934.51.2679376524.86...43725425.7.63. I9: 1,9,8 # reduction candidate for 1,9 I9: 1,9 => CTR * 2..4.5.768547963127..2.15845...2714317236485934.51.2679376524.86...43725425.7.63. I9: 8 => SOLVED * 218435976954786312763291584586927143172364859349518267837652491691843725425179638 * PAIR F9: 8,9 BLK 8 D8: 8,9,1 # reduction candidate for 8,9 D8: 8,9 # 14 pairs D9: 8,9,1 # reduction candidate for 8,9 D9: 8,9 => CTR * 2..4.5.76.547.63127..2.15845...2714317236485934.51.267.376524986..143725425.7.631 D9: 1 # 14 pairs * PAIR F9: 8,9 ROW 9 I9: 8,9,1 # reduction candidate for 8,9 I9: 1 => CTR * 2..4.5.768547963127..2.15845...2714317236485934.51.2679376524.86...43725425.7.631 I9: 8,9 # 14 pairs * PAIR H7: 1,9 BLK 9 I7: 1,9,8 # reduction candidate for 1,9 I7: 1,9 => SOLVED * 218435976954786312763291584586927143172364859349518267837652491691843725425179638 I7: 8 => CTR * 2..4.5.768547963127..2.15845...2714317236485934.51.2679376524.86...43725425.7.63. I9: 1,9,8 # reduction candidate for 1,9 I9: 1,9 => CTR * 2..4.5.768547963127..2.15845...2714317236485934.51.2679376524.86...43725425.7.63. I9: 8 => SOLVED * 218435976954786312763291584586927143172364859349518267837652491691843725425179638 * PAIR H7: 1,9 ROW 7 A7: 1,9,8 # reduction candidate for 1,9 A7: 1,9 => CTR * 2..4.5.768547963127..2.15845...2714317236485934.51.267.376524..6...43725425.7.63. A7: 8 => SOLVED * 218435976954786312763291584586927143172364859349518267837652491691843725425179638 * PAIR H7: 1,9 COL H H2: 1,9,8 # reduction candidate for 1,9 H2: 8 => CTR * 2..4.51761547963827..2.15945...279439723648513485192678376524196..843725425.7.63. H2: 1,9 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-313-base-pr-000.dot * REASONING * PRF # E3: 8,9 => SOL * PRF # A2: 8,9 => SOL * DIS # A2: 1 => CTR => A2: 8,9 * DIS # H2: 8,9 => CTR => H2: 1 * PRF # H2: 1 => SOL * DIS # H2: 8 => CTR => H2: 1,9 * DIS # C1: 1,9 => CTR => C1: 3,8 * DIS # H2: 8,9 => CTR => H2: 1 * PRF # H2: 1 => SOL * PRF # E3: 8,9 => SOL * DIS # B4: 1,9 => CTR => B4: 6,8 * DIS # C4: 1,9 => CTR => C4: 6,8 * PRF # A2: 1,9 => SOL * DIS # A2: 8 => CTR => A2: 1,9 * DIS # A7: 1,9 => CTR => A7: 8 * PRF # A7: 8 => SOL * PRF # B4: 8,9 => SOL * DIS # C4: 8,9 => CTR => C4: 1,6 * PRF # C1: 8,9 => SOL * PRF # B4: 8,9 => SOL * DIS # C4: 8,9 => CTR => C4: 1,6 * DIS # D9: 8,9 => CTR => D9: 1 * DIS # B4: 1,9 => CTR => B4: 6,8 * DIS # C4: 1,9 => CTR => C4: 6,8 * PRF # I7: 1,9 => SOL * DIS # I7: 8 => CTR => I7: 1,9 * DIS # I9: 1,9 => CTR => I9: 8 * PRF # I9: 8 => SOL * DIS # D9: 8,9 => CTR => D9: 1 * DIS # I9: 1 => CTR => I9: 8,9 * PRF # I7: 1,9 => SOL * DIS # I7: 8 => CTR => I7: 1,9 * DIS # I9: 1,9 => CTR => I9: 8 * PRF # I9: 8 => SOL * DIS # A7: 1,9 => CTR => A7: 8 * PRF # A7: 8 => SOL * DIS # H2: 8 => CTR => H2: 1,9 * CNT 37 HDP CHAINS / 62 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,C6,D4,E2,F6,F9,G1,G4,H3,H7,I5) * 2..4.5.76.547.63.27..2.15.45...27.43.7236485.34.51.267.376524..6...43725425.7.63. * PAIR E2: 8,9 BLK 2 E1: 8,9,3 # reduction candidate for 8,9 E1: 8,9 # 12 pairs E3: 8,9,3 # reduction candidate for 8,9 E3: 8,9 => SOLVED * 218435976954786312763291584586927143172364859349518267837652491691843725425179638 * DURATION: 0:00:03.090823 START: 13:42:49.456575 END: 13:42:52.547398 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-313-base-pr-001.dot * REASONING * PRF # E3: 8,9 => SOL * STA E3: 8,9 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 313 solution: 218435976954786312763291584586927143172364859349518267837652491691843725425179638 info: 2847 FNBWX S8.f 26681 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 218435976954786312763291584586927143172364859349518267837652491691843725425179638 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 # E1: 8,9 => UNS * PRF # E3: 8,9 => SOL * INC # E3: 3 => UNS * PRF # A2: 8,9 => SOL * DIS # A2: 1 => CTR => A2: 8,9 * DIS # H2: 8,9 => CTR => H2: 1 * PRF # H2: 1 => SOL * INC # H2: 1,9 => UNS * DIS # H2: 8 => CTR => H2: 1,9 * INC # B1: 1,9 => UNS * DIS # C1: 1,9 => CTR => C1: 3,8 * INC # C1: 3,8 => UNS * DIS # H2: 8,9 => CTR => H2: 1 * PRF # H2: 1 => SOL * INC # B3: 8,9 => UNS * INC # C3: 8,9 => UNS * PRF # E3: 8,9 => SOL * INC # E3: 3 => UNS * DIS # B4: 1,9 => CTR => B4: 6,8 * INC # B4: 6,8 => UNS * DIS # C4: 1,9 => CTR => C4: 6,8 * INC # C4: 6,8 => UNS * PRF # A2: 1,9 => SOL * DIS # A2: 8 => CTR => A2: 1,9 * DIS # A7: 1,9 => CTR => A7: 8 * PRF # A7: 8 => SOL * PRF # B4: 8,9 => SOL * INC # B4: 1,6 => UNS * DIS # C4: 8,9 => CTR => C4: 1,6 * INC # C4: 1,6 => UNS * PRF # C1: 8,9 => SOL * INC # C1: 1,3 => UNS * INC # C3: 8,9 => UNS * INC # C8: 8,9 => UNS * PRF # B4: 8,9 => SOL * INC # B4: 1,6 => UNS * DIS # C4: 8,9 => CTR => C4: 1,6 * INC # C4: 1,6 => UNS * INC # D8: 8,9 => UNS * DIS # D9: 8,9 => CTR => D9: 1 * INC # D9: 1 => UNS * DIS # B4: 1,9 => CTR => B4: 6,8 * INC # B4: 6,8 => UNS * DIS # C4: 1,9 => CTR => C4: 6,8 * INC # C4: 6,8 => UNS * PRF # I7: 1,9 => SOL * DIS # I7: 8 => CTR => I7: 1,9 * DIS # I9: 1,9 => CTR => I9: 8 * PRF # I9: 8 => SOL * INC # D8: 8,9 => UNS * DIS # D9: 8,9 => CTR => D9: 1 * INC # D9: 1 => UNS * INC # I9: 8,9 => UNS * DIS # I9: 1 => CTR => I9: 8,9 * PRF # I7: 1,9 => SOL * DIS # I7: 8 => CTR => I7: 1,9 * DIS # I9: 1,9 => CTR => I9: 8 * PRF # I9: 8 => SOL * DIS # A7: 1,9 => CTR => A7: 8 * PRF # A7: 8 => SOL * INC # H2: 1,9 => UNS * DIS # H2: 8 => CTR => H2: 1,9 * CNT 62 HDP CHAINS / 62 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E1: 8,9 => UNS * PRF # E3: 8,9 => SOL * STA E3: 8,9 * CNT 2 HDP CHAINS / 2 HYP OPENED