Analysis of xx-top500-127-base.sdk
Contents
Original Sudoku
level: medium
position: ..3.5.......8..4...7............8.73.2.....5.9..1.....8.....1..4....6.......7.... initial
Autosolve
position: .83754.195198..4.7.74.1.3851465.8.73728....519351.78..8.72.51..451.867.23.2.715.8 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E5: 3,6 => CTR => E5: 4,9 * DIS # D5: 6,9 => CTR => D5: 3,4 * PRF # D5: 3,4 => SOL * PRF # H6: 2,6 => SOL * DIS # H6: 4 => CTR => H6: 2,6 * DIS # D5: 3,9 => CTR => D5: 4,6 * PRF # E5: 3,9 => SOL * PRF # H6: 2,6 => SOL * DIS # H6: 4 => CTR => H6: 2,6 * DIS # D5: 6,9 => CTR => D5: 3,4 * PRF # D5: 3,4 => SOL * PRF # E5: 6,9 => SOL * DIS # H6: 4,6 => CTR => H6: 2 * PRF # H6: 2 => SOL * DIS # H7: 6,9 => CTR => H7: 3,4 * PRF # H9: 4 => SOL * PRF # E7: 4 => SOL * DIS # D5: 3,9 => CTR => D5: 4,6 * DIS # E7: 3 => CTR => E7: 4,9 * PRF # H9: 4,9 => SOL * DIS # H9: 6 => CTR => H9: 4,9 * PRF # D5: 4,9 => SOL * DIS # H7: 4,6 => CTR => H7: 3,9 * DIS # H7: 4,6 => CTR => H7: 3,9 * CNT 24 HDP CHAINS / 37 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E5: 3,6 => CTR => E5: 4,9 * DIS E5: 4,9 # D5: 6,9 => CTR => D5: 3,4 * PRF E5: 4,9 + D5: 3,4 => SOL * STA E5: 4,9 + D5: 3,4 * CNT 3 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..3.5.......8..4...7............8.73.2.....5.9..1.....8.....1..4....6.......7.... | initial |
| .83754.195198..4.7.74.1.3851465.8.73728....519351.78..8.72.51..451.867.23.2.715.8 | autosolve |
| 683754219519832467274619385146528973728493651935167824897245136451386792362971548 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) A1: 2,6 A3: 2,6 E2: 3,6 F2: 2,3 D3: 6,9 F3: 2,9 G1: 2,6 H2: 2,6 E4: 2,9 F5: 3,9 E6: 2,6 G4: 2,9 G5: 6,9 I6: 4,6 B7: 6,9 B9: 6,9 D8: 3,9 D9: 4,9 I7: 4,6 H8: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A3: 2.. / A1 = 2 => 0 pairs (X) / A3 = 2 => 0 pairs (_) F2,F3: 2.. / F2 = 2 => 0 pairs (*) / F3 = 2 => 0 pairs (X) G1,H2: 2.. / G1 = 2 => 0 pairs (*) / H2 = 2 => 0 pairs (X) E4,E6: 2.. / E4 = 2 => 0 pairs (*) / E6 = 2 => 0 pairs (X) G4,H6: 2.. / G4 = 2 => 0 pairs (X) / H6 = 2 => 0 pairs (_) A1,G1: 2.. / A1 = 2 => 0 pairs (X) / G1 = 2 => 0 pairs (_) F2,H2: 2.. / F2 = 2 => 0 pairs (*) / H2 = 2 => 0 pairs (X) A3,F3: 2.. / A3 = 2 => 0 pairs (*) / F3 = 2 => 0 pairs (X) E4,G4: 2.. / E4 = 2 => 0 pairs (*) / G4 = 2 => 0 pairs (X) E6,H6: 2.. / E6 = 2 => 0 pairs (X) / H6 = 2 => 0 pairs (_) G1,G4: 2.. / G1 = 2 => 0 pairs (*) / G4 = 2 => 0 pairs (X) H2,H6: 2.. / H2 = 2 => 0 pairs (X) / H6 = 2 => 0 pairs (_) E2,F2: 3.. / E2 = 3 => 0 pairs (*) / F2 = 3 => 0 pairs (X) E7,D8: 3.. / E7 = 3 => 0 pairs (X) / D8 = 3 => 20 pairs (_) H7,H8: 3.. / H7 = 3 => 20 pairs (_) / H8 = 3 => 0 pairs (X) E7,H7: 3.. / E7 = 3 => 0 pairs (X) / H7 = 3 => 20 pairs (_) D8,H8: 3.. / D8 = 3 => 20 pairs (_) / H8 = 3 => 0 pairs (X) D5,D8: 3.. / D5 = 3 => 0 pairs (X) / D8 = 3 => 20 pairs (_) F2,F5: 3.. / F2 = 3 => 0 pairs (X) / F5 = 3 => 0 pairs (_) D5,E5: 4.. / D5 = 4 => 0 pairs (*) / E5 = 4 => 0 pairs (X) H6,I6: 4.. / H6 = 4 => 0 pairs (X) / I6 = 4 => 0 pairs (_) E7,D9: 4.. / E7 = 4 => 0 pairs (*) / D9 = 4 => 0 pairs (X) D9,H9: 4.. / D9 = 4 => 21 pairs (_) / H9 = 4 => 0 pairs (*) D5,D9: 4.. / D5 = 4 => 0 pairs (*) / D9 = 4 => 0 pairs (X) E5,E7: 4.. / E5 = 4 => 21 pairs (_) / E7 = 4 => 0 pairs (*) I6,I7: 4.. / I6 = 4 => 0 pairs (*) / I7 = 4 => 0 pairs (X) A1,A3: 6.. / A1 = 6 => 0 pairs (*) / A3 = 6 => 0 pairs (X) E2,D3: 6.. / E2 = 6 => 0 pairs (X) / D3 = 6 => 0 pairs (_) G1,H2: 6.. / G1 = 6 => 0 pairs (X) / H2 = 6 => 0 pairs (_) B7,B9: 6.. / B7 = 6 => 0 pairs (X) / B9 = 6 => 0 pairs (_) A1,G1: 6.. / A1 = 6 => 0 pairs (*) / G1 = 6 => 0 pairs (X) E2,H2: 6.. / E2 = 6 => 0 pairs (X) / H2 = 6 => 0 pairs (_) A3,D3: 6.. / A3 = 6 => 0 pairs (X) / D3 = 6 => 0 pairs (_) B9,H9: 6.. / B9 = 6 => 0 pairs (*) / H9 = 6 => 0 pairs (X) D3,D5: 6.. / D3 = 6 => 0 pairs (*) / D5 = 6 => 0 pairs (X) G1,G5: 6.. / G1 = 6 => 0 pairs (X) / G5 = 6 => 0 pairs (_) I6,I7: 6.. / I6 = 6 => 0 pairs (X) / I7 = 6 => 0 pairs (_) D3,F3: 9.. / D3 = 9 => 0 pairs (X) / F3 = 9 => 0 pairs (_) G4,G5: 9.. / G4 = 9 => 0 pairs (*) / G5 = 9 => 0 pairs (X) B7,B9: 9.. / B7 = 9 => 0 pairs (*) / B9 = 9 => 0 pairs (X) E4,G4: 9.. / E4 = 9 => 0 pairs (X) / G4 = 9 => 0 pairs (_) D8,H8: 9.. / D8 = 9 => 0 pairs (X) / H8 = 9 => 20 pairs (_) F3,F5: 9.. / F3 = 9 => 0 pairs (*) / F5 = 9 => 0 pairs (X) * DURATION: 0:01:12.919026 START: 07:06:00.858171 END: 07:07:13.777197 2017-05-04 * CP COUNT: (43) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B7,B9,D3,D8,D9,E2,E4,E6,F2,F3,F5,G1,G4,G5,H2,H8,I6,I7) * .83754.195198..4.7.74.1.3851465.8.73728....519351.78..8.72.51..451.867.23.2.715.8 * PAIR E2: 3,6 COL E E5: 3,6,4,9 # reduction candidate for 3,6 E5: 3,6 => CTR * .83754.195198..4.7.746193851465982737284.395193512786.8.7245136451386792362971548 E5: 4,9 # 21 pairs * PAIR D3: 6,9 COL D D5: 6,9,3,4 # reduction candidate for 6,9 D5: 6,9 => CTR * .83754.195198..4.7.74.1.3851465.8.73728.43.519351.78..8.72.51..4513867923.2471568 D5: 3,4 => SOLVED * 683754219519832467274619385146528973728493651935167824897245136451386792362971548 * PAIR H2: 2,6 COL H H6: 2,6,4 # reduction candidate for 2,6 H6: 2,6 => SOLVED * 683754219519832467274619385146528973728493651935167824897245136451386792362971548 H6: 4 => CTR * .83754.195198..427.74.123851465.8273728..9.519351.78..8.72.51..451.867.23.2.715.8 * PAIR F5: 3,9 BLK 5 D5: 3,9,4,6 # reduction candidate for 3,9 D5: 3,9 => CTR * .83754.195198..4.7.746193851465.8.73728.436519351678248.72.51464513867923.2.715.8 D5: 4,6 # 21 pairs E5: 3,9,4,6 # reduction candidate for 3,9 E5: 3,9 => SOLVED * 683754219519832467274619385146528973728493651935167824897245136451386792362971548 E5: 4,6 # 21 pairs * PAIR E6: 2,6 ROW 6 H6: 2,6,4 # reduction candidate for 2,6 H6: 2,6 => SOLVED * 683754219519832467274619385146528973728493651935167824897245136451386792362971548 H6: 4 => CTR * .83754.195198..427.74.123851465.8273728..9.519351.78..8.72.51..451.867.23.2.715.8 * PAIR G5: 6,9 ROW 5 D5: 6,9,3,4 # reduction candidate for 6,9 D5: 6,9 => CTR * .83754.195198..4.7.74.1.3851465.8.73728.43.519351.78..8.72.51..4513867923.2471568 D5: 3,4 => SOLVED * 683754219519832467274619385146528973728493651935167824897245136451386792362971548 E5: 6,9,3,4 # reduction candidate for 6,9 E5: 6,9 => SOLVED * 683754219519832467274619385146528973728493651935167824897245136451386792362971548 E5: 3,4 # 21 pairs * PAIR I6: 4,6 BLK 6 H6: 4,6,2 # reduction candidate for 4,6 H6: 4,6 => CTR * .83754.195198..427.74.123851465.8273728..9.519351.78..8.72.51..451.867.23.2.715.8 H6: 2 => SOLVED * 683754219519832467274619385146528973728493651935167824897245136451386792362971548 * PAIR B7: 6,9 ROW 7 H7: 6,9,3,4 # reduction candidate for 6,9 H7: 6,9 => CTR * .83754.195198..4.7.74.1.3851465.8.73728....519351.78..8.72351.44519867323.24715.8 H7: 3,4 # 21 pairs * PAIR B9: 6,9 ROW 9 H9: 6,9,4 # reduction candidate for 6,9 H9: 4 => SOLVED * 683754219519832467274619385146528973728493651935167824897245136451386792362971548 H9: 6,9 # 21 pairs * PAIR D8: 3,9 BLK 8 E7: 3,9,4 # reduction candidate for 3,9 E7: 4 => SOLVED * 683754219519832467274619385146528973728493651935167824897245136451386792362971548 E7: 3,9 # 21 pairs * PAIR D8: 3,9 COL D D5: 3,9,4,6 # reduction candidate for 3,9 D5: 3,9 => CTR * .83754.195198..4.7.746193851465.8.73728.436519351678248.72.51464513867923.2.715.8 D5: 4,6 # 21 pairs * PAIR D9: 4,9 BLK 8 E7: 4,9,3 # reduction candidate for 4,9 E7: 3 => CTR * .83754.195198..4.7.74.1.3851465.8.73728.4..519351.78..8.72351..4519867323.24715.8 E7: 4,9 # 20 pairs * PAIR D9: 4,9 ROW 9 H9: 4,9,6 # reduction candidate for 4,9 H9: 4,9 => SOLVED * 683754219519832467274619385146528973728493651935167824897245136451386792362971548 H9: 6 => CTR * .837546195198634276749123851465.82737286...519351.78..8.72.51..451.867.23.2471568 * PAIR D9: 4,9 COL D D5: 4,9,3,6 # reduction candidate for 4,9 D5: 4,9 => SOLVED * 683754219519832467274619385146528973728493651935167824897245136451386792362971548 D5: 3,6 # 22 pairs * PAIR I7: 4,6 BLK 9 H7: 4,6,3,9 # reduction candidate for 4,6 H7: 4,6 => CTR * .83754.195198..4.7.74.1.3851465.8.73728....519351.78..8.72351..4519867323.2471598 H7: 3,9 # 22 pairs H9: 4,6,9 # reduction candidate for 4,6 H9: 4,6 # 22 pairs * PAIR H8: 3,9 BLK 9 H7: 3,9,4,6 # reduction candidate for 3,9 H7: 4,6 => CTR * .83754.195198..4.7.74.1.3851465.8.73728....519351.78..8.72351..4519867323.2471598 H7: 3,9 # 22 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-127-base-pr-000.dot * REASONING * DIS # E5: 3,6 => CTR => E5: 4,9 * DIS # D5: 6,9 => CTR => D5: 3,4 * PRF # D5: 3,4 => SOL * PRF # H6: 2,6 => SOL * DIS # H6: 4 => CTR => H6: 2,6 * DIS # D5: 3,9 => CTR => D5: 4,6 * PRF # E5: 3,9 => SOL * PRF # H6: 2,6 => SOL * DIS # H6: 4 => CTR => H6: 2,6 * DIS # D5: 6,9 => CTR => D5: 3,4 * PRF # D5: 3,4 => SOL * PRF # E5: 6,9 => SOL * DIS # H6: 4,6 => CTR => H6: 2 * PRF # H6: 2 => SOL * DIS # H7: 6,9 => CTR => H7: 3,4 * PRF # H9: 4 => SOL * PRF # E7: 4 => SOL * DIS # D5: 3,9 => CTR => D5: 4,6 * DIS # E7: 3 => CTR => E7: 4,9 * PRF # H9: 4,9 => SOL * DIS # H9: 6 => CTR => H9: 4,9 * PRF # D5: 4,9 => SOL * DIS # H7: 4,6 => CTR => H7: 3,9 * DIS # H7: 4,6 => CTR => H7: 3,9 * CNT 24 HDP CHAINS / 37 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B7,B9,D3,D8,D9,E2,E4,E6,F2,F3,F5,G1,G4,G5,H2,H8,I6,I7) * .83754.195198..4.7.74.1.3851465.8.73728....519351.78..8.72.51..451.867.23.2.715.8 * PAIR E2: 3,6 COL E E5: 3,6,4,9 # reduction candidate for 3,6 E5: 3,6 => CTR * .83754.195198..4.7.746193851465982737284.395193512786.8.7245136451386792362971548 * PAIR RESTART * PAIR D3: 6,9 COL D D5: 6,9,3,4 # reduction candidate for 6,9 D5: 6,9 => CTR * .83754.195198..4.7.74.1.3851465.8.73728.43.519351.78..8.72.51..4513867923.2471568 D5: 3,4 => SOLVED * 683754219519832467274619385146528973728493651935167824897245136451386792362971548 * DURATION: 0:00:05.002275 START: 07:07:52.979336 END: 07:07:57.981611 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-127-base-pr-001.dot * REASONING * DIS # E5: 3,6 => CTR => E5: 4,9 * DIS E5: 4,9 # D5: 6,9 => CTR => D5: 3,4 * PRF E5: 4,9 + D5: 3,4 => SOL * STA E5: 4,9 + D5: 3,4 * CNT 3 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 127 solution: 683754219519832467274619385146528973728493651935167824897245136451386792362971548 info: 1809 FNBWY S8.f 13471 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 683754219519832467274619385146528973728493651935167824897245136451386792362971548 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 # E5: 3,6 => CTR => E5: 4,9 * INC # E5: 4,9 => UNS * DIS # D5: 6,9 => CTR => D5: 3,4 * PRF # D5: 3,4 => SOL * PRF # H6: 2,6 => SOL * DIS # H6: 4 => CTR => H6: 2,6 * DIS # D5: 3,9 => CTR => D5: 4,6 * INC # D5: 4,6 => UNS * PRF # E5: 3,9 => SOL * INC # E5: 4,6 => UNS * PRF # H6: 2,6 => SOL * DIS # H6: 4 => CTR => H6: 2,6 * DIS # D5: 6,9 => CTR => D5: 3,4 * PRF # D5: 3,4 => SOL * PRF # E5: 6,9 => SOL * INC # E5: 3,4 => UNS * DIS # H6: 4,6 => CTR => H6: 2 * PRF # H6: 2 => SOL * DIS # H7: 6,9 => CTR => H7: 3,4 * INC # H7: 3,4 => UNS * INC # H9: 6,9 => UNS * PRF # H9: 4 => SOL * INC # E7: 3,9 => UNS * PRF # E7: 4 => SOL * DIS # D5: 3,9 => CTR => D5: 4,6 * INC # D5: 4,6 => UNS * INC # E7: 4,9 => UNS * DIS # E7: 3 => CTR => E7: 4,9 * PRF # H9: 4,9 => SOL * DIS # H9: 6 => CTR => H9: 4,9 * PRF # D5: 4,9 => SOL * INC # D5: 3,6 => UNS * DIS # H7: 4,6 => CTR => H7: 3,9 * INC # H7: 3,9 => UNS * INC # H9: 4,6 => UNS * INC # H7: 3,9 => UNS * DIS # H7: 4,6 => CTR => H7: 3,9 * CNT 37 HDP CHAINS / 37 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # E5: 3,6 => CTR => E5: 4,9 * DIS E5: 4,9 # D5: 6,9 => CTR => D5: 3,4 * PRF E5: 4,9 + D5: 3,4 => SOL * STA E5: 4,9 + D5: 3,4 * CNT 3 HDP CHAINS / 2 HYP OPENED