Analysis of xx-top500-123-base.sdk
Contents
Original Sudoku
level: medium
position: .3.....2.....1.4..6..7......5.3.2.........8.1.........1.4.5.......4...3.8........ initial
Autosolve
position: 43.5.812.58.21.4.3612734985.51382.4.32694.8.1.481..3.21.48532..2.54.1.388.362.514 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I4: 6,7 => CTR => I4: 9 * PRF # I4: 9 => SOL * PRF # I7: 6,7 => SOL * DIS # I7: 9 => CTR => I7: 6,7 * DIS # H7: 6,7 => CTR => H7: 9 * PRF # H7: 9 => SOL * PRF # I4: 7,9 => SOL * DIS # I4: 6 => CTR => I4: 7,9 * DIS # H6: 7,9 => CTR => H6: 5 * PRF # H6: 5 => SOL * DIS # F6: 5,7 => CTR => F6: 6 * PRF # F6: 6 => SOL * PRF # F6: 6,7 => SOL * DIS # F6: 5 => CTR => F6: 6,7 * DIS # I4: 6,7 => CTR => I4: 9 * PRF # I4: 9 => SOL * PRF # H6: 5,7 => SOL * DIS # H6: 9 => CTR => H6: 5,7 * PRF # B8: 6,7 => SOL * DIS # B8: 9 => CTR => B8: 6,7 * DIS # H7: 6,7 => CTR => H7: 9 * PRF # H7: 9 => SOL * PRF # I7: 6,7 => SOL * DIS # I7: 9 => CTR => I7: 6,7 * DIS # B8: 7,9 => CTR => B8: 6 * PRF # B8: 6 => SOL * DIS # B8: 7,9 => CTR => B8: 6 * PRF # B8: 6 => SOL * DIS # H7: 6,7 => CTR => H7: 9 * PRF # H7: 9 => SOL * PRF # I7: 6,7 => SOL * DIS # I7: 9 => CTR => I7: 6,7 * PRF # B8: 6,7 => SOL * DIS # B8: 9 => CTR => B8: 6,7 * CNT 34 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I4: 6,7 => CTR => I4: 9 * PRF I4: 9 => SOL * STA I4: 9 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .3.....2.....1.4..6..7......5.3.2.........8.1.........1.4.5.......4...3.8........ | initial |
| 43.5.812.58.21.4.3612734985.51382.4.32694.8.1.481..3.21.48532..2.54.1.388.362.514 | autosolve |
| 439568127587219463612734985751382649326945871948176352174853296265491738893627514 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) C1: 7,9 C2: 7,9 E1: 6,9 F2: 6,9 I1: 6,7 H2: 6,7 A4: 7,9 A6: 7,9 F5: 5,7 E6: 6,7 G4: 6,7 H5: 5,7 B7: 6,7 B9: 7,9 E8: 7,9 F9: 7,9 G8: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F5,F6: 5.. / F5 = 5 => 0 pairs (*) / F6 = 5 => 0 pairs (X) H5,H6: 5.. / H5 = 5 => 0 pairs (X) / H6 = 5 => 0 pairs (_) F5,H5: 5.. / F5 = 5 => 0 pairs (*) / H5 = 5 => 0 pairs (X) F6,H6: 5.. / F6 = 5 => 0 pairs (X) / H6 = 5 => 0 pairs (_) E1,F2: 6.. / E1 = 6 => 0 pairs (*) / F2 = 6 => 0 pairs (X) I1,H2: 6.. / I1 = 6 => 0 pairs (X) / H2 = 6 => 0 pairs (_) E6,F6: 6.. / E6 = 6 => 0 pairs (X) / F6 = 6 => 0 pairs (_) G4,I4: 6.. / G4 = 6 => 0 pairs (*) / I4 = 6 => 0 pairs (X) B7,B8: 6.. / B7 = 6 => 0 pairs (X) / B8 = 6 => 0 pairs (_) E1,I1: 6.. / E1 = 6 => 0 pairs (*) / I1 = 6 => 0 pairs (X) F2,H2: 6.. / F2 = 6 => 0 pairs (X) / H2 = 6 => 0 pairs (_) B8,G8: 6.. / B8 = 6 => 0 pairs (*) / G8 = 6 => 0 pairs (X) E1,E6: 6.. / E1 = 6 => 0 pairs (*) / E6 = 6 => 0 pairs (X) F2,F6: 6.. / F2 = 6 => 0 pairs (X) / F6 = 6 => 0 pairs (_) G4,G8: 6.. / G4 = 6 => 0 pairs (*) / G8 = 6 => 0 pairs (X) H2,H7: 6.. / H2 = 6 => 0 pairs (*) / H7 = 6 => 0 pairs (X) C1,C2: 7.. / C1 = 7 => 0 pairs (X) / C2 = 7 => 0 pairs (_) I1,H2: 7.. / I1 = 7 => 0 pairs (*) / H2 = 7 => 0 pairs (X) A4,A6: 7.. / A4 = 7 => 0 pairs (*) / A6 = 7 => 0 pairs (X) E8,F9: 7.. / E8 = 7 => 0 pairs (X) / F9 = 7 => 0 pairs (_) C1,I1: 7.. / C1 = 7 => 0 pairs (X) / I1 = 7 => 0 pairs (_) C2,H2: 7.. / C2 = 7 => 0 pairs (*) / H2 = 7 => 0 pairs (X) F5,H5: 7.. / F5 = 7 => 0 pairs (X) / H5 = 7 => 0 pairs (_) B9,F9: 7.. / B9 = 7 => 0 pairs (X) / F9 = 7 => 0 pairs (_) E6,E8: 7.. / E6 = 7 => 0 pairs (*) / E8 = 7 => 0 pairs (X) G4,G8: 7.. / G4 = 7 => 0 pairs (X) / G8 = 7 => 0 pairs (_) C1,C2: 9.. / C1 = 9 => 0 pairs (*) / C2 = 9 => 0 pairs (X) E1,F2: 9.. / E1 = 9 => 0 pairs (X) / F2 = 9 => 0 pairs (_) A4,A6: 9.. / A4 = 9 => 0 pairs (X) / A6 = 9 => 0 pairs (_) I4,H6: 9.. / I4 = 9 => 0 pairs (*) / H6 = 9 => 0 pairs (X) B8,B9: 9.. / B8 = 9 => 0 pairs (X) / B9 = 9 => 0 pairs (_) E8,F9: 9.. / E8 = 9 => 0 pairs (*) / F9 = 9 => 0 pairs (X) H7,I7: 9.. / H7 = 9 => 0 pairs (*) / I7 = 9 => 0 pairs (X) C1,E1: 9.. / C1 = 9 => 0 pairs (*) / E1 = 9 => 0 pairs (X) C2,F2: 9.. / C2 = 9 => 0 pairs (X) / F2 = 9 => 0 pairs (_) A4,I4: 9.. / A4 = 9 => 0 pairs (X) / I4 = 9 => 0 pairs (_) A6,H6: 9.. / A6 = 9 => 0 pairs (*) / H6 = 9 => 0 pairs (X) B8,E8: 9.. / B8 = 9 => 0 pairs (X) / E8 = 9 => 0 pairs (_) B9,F9: 9.. / B9 = 9 => 0 pairs (*) / F9 = 9 => 0 pairs (X) E1,E8: 9.. / E1 = 9 => 0 pairs (X) / E8 = 9 => 0 pairs (_) F2,F9: 9.. / F2 = 9 => 0 pairs (*) / F9 = 9 => 0 pairs (X) H6,H7: 9.. / H6 = 9 => 0 pairs (X) / H7 = 9 => 0 pairs (_) I4,I7: 9.. / I4 = 9 => 0 pairs (*) / I7 = 9 => 0 pairs (X) * DURATION: 0:01:11.494633 START: 06:58:09.022313 END: 06:59:20.516946 2017-05-04 * CP COUNT: (43) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,B7,B9,C1,C2,E1,E6,E8,F2,F5,F9,G4,G8,H2,H5,I1) * 43.5.812.58.21.4.3612734985.51382.4.32694.8.1.481..3.21.48532..2.54.1.388.362.514 * PAIR I1: 6,7 COL I I4: 6,7,9 # reduction candidate for 6,7 I4: 6,7 => CTR * 43.598126589216473612734985951382.4.32694.8.17481653921.48532.92.5471638873629514 I4: 9 => SOLVED * 439568127587219463612734985751382649326945871948176352174853296265491738893627514 I7: 6,7,9 # reduction candidate for 6,7 I7: 6,7 => SOLVED * 439568127587219463612734985751382649326945871948176352174853296265491738893627514 I7: 9 => CTR * 43.598126589216473612734985951382.4.32694.8.17481653921.48532.92.5471638873629514 * PAIR H2: 6,7 COL H H7: 6,7,9 # reduction candidate for 6,7 H7: 6,7 => CTR * 43.598126589216473612734985951382.4.32694.8517481653921.48532.92.5471638873629514 H7: 9 => SOLVED * 439568127587219463612734985751382649326945871948176352174853296265491738893627514 * PAIR A4: 7,9 ROW 4 I4: 7,9,6 # reduction candidate for 7,9 I4: 7,9 => SOLVED * 439568127587219463612734985751382649326945871948176352174853296265491738893627514 I4: 6 => CTR * 43.5.812.58.21.4.36127349859513827463269478517481653921.48532.92.5471638873629514 * PAIR A6: 7,9 ROW 6 H6: 7,9,5 # reduction candidate for 7,9 H6: 7,9 => CTR * 43.5.812.58.216473612734985.51382.4.3269478517481653921.48532692654.1.388.362.514 H6: 5 => SOLVED * 439568127587219463612734985751382649326945871948176352174853296265491738893627514 * PAIR F5: 5,7 BLK 5 F6: 5,7,6 # reduction candidate for 5,7 F6: 5,7 => CTR * 43.5.812.58.216473612734985.51382.4.3269478517481653921.48532692654.1.388.362.514 F6: 6 => SOLVED * 439568127587219463612734985751382649326945871948176352174853296265491738893627514 * PAIR E6: 6,7 BLK 5 F6: 6,7,5 # reduction candidate for 6,7 F6: 6,7 => SOLVED * 439568127587219463612734985751382649326945871948176352174853296265491738893627514 F6: 5 => CTR * 43.5.812.58.216473612734985.51382.4.3269478517481653921.48532692654.1.388.362.514 * PAIR G4: 6,7 BLK 6 I4: 6,7,9 # reduction candidate for 6,7 I4: 6,7 => CTR * 43.598126589216473612734985951382.4.32694.8.17481653921.48532.92.5471638873629514 I4: 9 => SOLVED * 439568127587219463612734985751382649326945871948176352174853296265491738893627514 * PAIR H5: 5,7 BLK 6 H6: 5,7,9 # reduction candidate for 5,7 H6: 5,7 => SOLVED * 439568127587219463612734985751382649326945871948176352174853296265491738893627514 H6: 9 => CTR * 43.5.812.58.216473612734985951382.473269478517481653921748532692654.1.388.362.514 * PAIR B7: 6,7 BLK 7 B8: 6,7,9 # reduction candidate for 6,7 B8: 6,7 => SOLVED * 439568127587219463612734985751382649326945871948176352174853296265491738893627514 B8: 9 => CTR * 43.598126589216473612734985.5138274932694.8.1.481..3.21648532..295471638873629514 * PAIR B7: 6,7 ROW 7 H7: 6,7,9 # reduction candidate for 6,7 H7: 6,7 => CTR * 43.598126589216473612734985951382.4.32694.8517481653921.48532.92.5471638873629514 H7: 9 => SOLVED * 439568127587219463612734985751382649326945871948176352174853296265491738893627514 I7: 6,7,9 # reduction candidate for 6,7 I7: 6,7 => SOLVED * 439568127587219463612734985751382649326945871948176352174853296265491738893627514 I7: 9 => CTR * 43.598126589216473612734985951382.4.32694.8.17481653921.48532.92.5471638873629514 * PAIR B9: 7,9 BLK 7 B8: 7,9,6 # reduction candidate for 7,9 B8: 7,9 => CTR * 43.5.812.58.21.463612734985.513827463269478517481..3.21648532..2.54.16388.362.514 B8: 6 => SOLVED * 439568127587219463612734985751382649326945871948176352174853296265491738893627514 * PAIR E8: 7,9 ROW 8 B8: 7,9,6 # reduction candidate for 7,9 B8: 7,9 => CTR * 43.5.812.58.21.463612734985.513827463269478517481..3.21648532..2.54.16388.362.514 B8: 6 => SOLVED * 439568127587219463612734985751382649326945871948176352174853296265491738893627514 * PAIR G8: 6,7 BLK 9 H7: 6,7,9 # reduction candidate for 6,7 H7: 6,7 => CTR * 43.598126589216473612734985951382.4.32694.8517481653921.48532.92.5471638873629514 H7: 9 => SOLVED * 439568127587219463612734985751382649326945871948176352174853296265491738893627514 I7: 6,7,9 # reduction candidate for 6,7 I7: 6,7 => SOLVED * 439568127587219463612734985751382649326945871948176352174853296265491738893627514 I7: 9 => CTR * 43.598126589216473612734985951382.4.32694.8.17481653921.48532.92.5471638873629514 * PAIR G8: 6,7 ROW 8 B8: 6,7,9 # reduction candidate for 6,7 B8: 6,7 => SOLVED * 439568127587219463612734985751382649326945871948176352174853296265491738893627514 B8: 9 => CTR * 43.598126589216473612734985.5138274932694.8.1.481..3.21648532..295471638873629514 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-123-base-pr-000.dot * REASONING * DIS # I4: 6,7 => CTR => I4: 9 * PRF # I4: 9 => SOL * PRF # I7: 6,7 => SOL * DIS # I7: 9 => CTR => I7: 6,7 * DIS # H7: 6,7 => CTR => H7: 9 * PRF # H7: 9 => SOL * PRF # I4: 7,9 => SOL * DIS # I4: 6 => CTR => I4: 7,9 * DIS # H6: 7,9 => CTR => H6: 5 * PRF # H6: 5 => SOL * DIS # F6: 5,7 => CTR => F6: 6 * PRF # F6: 6 => SOL * PRF # F6: 6,7 => SOL * DIS # F6: 5 => CTR => F6: 6,7 * DIS # I4: 6,7 => CTR => I4: 9 * PRF # I4: 9 => SOL * PRF # H6: 5,7 => SOL * DIS # H6: 9 => CTR => H6: 5,7 * PRF # B8: 6,7 => SOL * DIS # B8: 9 => CTR => B8: 6,7 * DIS # H7: 6,7 => CTR => H7: 9 * PRF # H7: 9 => SOL * PRF # I7: 6,7 => SOL * DIS # I7: 9 => CTR => I7: 6,7 * DIS # B8: 7,9 => CTR => B8: 6 * PRF # B8: 6 => SOL * DIS # B8: 7,9 => CTR => B8: 6 * PRF # B8: 6 => SOL * DIS # H7: 6,7 => CTR => H7: 9 * PRF # H7: 9 => SOL * PRF # I7: 6,7 => SOL * DIS # I7: 9 => CTR => I7: 6,7 * PRF # B8: 6,7 => SOL * DIS # B8: 9 => CTR => B8: 6,7 * CNT 34 HDP CHAINS / 34 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,B7,B9,C1,C2,E1,E6,E8,F2,F5,F9,G4,G8,H2,H5,I1) * 43.5.812.58.21.4.3612734985.51382.4.32694.8.1.481..3.21.48532..2.54.1.388.362.514 * PAIR I1: 6,7 COL I I4: 6,7,9 # reduction candidate for 6,7 I4: 6,7 => CTR * 43.598126589216473612734985951382.4.32694.8.17481653921.48532.92.5471638873629514 I4: 9 => SOLVED * 439568127587219463612734985751382649326945871948176352174853296265491738893627514 * DURATION: 0:00:01.874621 START: 06:59:59.747723 END: 07:00:01.622344 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-123-base-pr-001.dot * REASONING * DIS # I4: 6,7 => CTR => I4: 9 * PRF I4: 9 => SOL * STA I4: 9 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 123 solution: 439568127587219463612734985751382649326945871948176352174853296265491738893627514 info: 1806 FNBWY S8.f 17385 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 439568127587219463612734985751382649326945871948176352174853296265491738893627514 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 # I4: 6,7 => CTR => I4: 9 * PRF # I4: 9 => SOL * PRF # I7: 6,7 => SOL * DIS # I7: 9 => CTR => I7: 6,7 * DIS # H7: 6,7 => CTR => H7: 9 * PRF # H7: 9 => SOL * PRF # I4: 7,9 => SOL * DIS # I4: 6 => CTR => I4: 7,9 * DIS # H6: 7,9 => CTR => H6: 5 * PRF # H6: 5 => SOL * DIS # F6: 5,7 => CTR => F6: 6 * PRF # F6: 6 => SOL * PRF # F6: 6,7 => SOL * DIS # F6: 5 => CTR => F6: 6,7 * DIS # I4: 6,7 => CTR => I4: 9 * PRF # I4: 9 => SOL * PRF # H6: 5,7 => SOL * DIS # H6: 9 => CTR => H6: 5,7 * PRF # B8: 6,7 => SOL * DIS # B8: 9 => CTR => B8: 6,7 * DIS # H7: 6,7 => CTR => H7: 9 * PRF # H7: 9 => SOL * PRF # I7: 6,7 => SOL * DIS # I7: 9 => CTR => I7: 6,7 * DIS # B8: 7,9 => CTR => B8: 6 * PRF # B8: 6 => SOL * DIS # B8: 7,9 => CTR => B8: 6 * PRF # B8: 6 => SOL * DIS # H7: 6,7 => CTR => H7: 9 * PRF # H7: 9 => SOL * PRF # I7: 6,7 => SOL * DIS # I7: 9 => CTR => I7: 6,7 * PRF # B8: 6,7 => SOL * DIS # B8: 9 => CTR => B8: 6,7 * CNT 34 HDP CHAINS / 34 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # I4: 6,7 => CTR => I4: 9 * PRF I4: 9 => SOL * STA I4: 9 * CNT 2 HDP CHAINS / 1 HYP OPENED