Analysis of xx-top500-069-base.sdk
Contents
Original Sudoku
level: medium
position: ...6.5...2.....9............76....4....1..2.....83...........57.....4..61...2.... initial
Autosolve
position: ...6.57.225....96.6.....5...76....415..14627.4..837695....6..577....4.2616572.4.9 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D3: 2,9 => CTR => D3: 3,4 * DIS # I2: 8 => CTR => I2: 3,4 * DIS # A1: 3,8 => CTR => A1: 9 * DIS # D4: 5,9 => CTR => D4: 2 * DIS # E8: 5,9 => CTR => E8: 1,8 * DIS # D4: 5 => CTR => D4: 2,9 * DIS # F3: 1,3,8 => CTR => F3: 2,9 * DIS # F7: 3,9 => CTR => F7: 1,8 * DIS # D8: 3,9 => CTR => D8: 5 * PRF # A7: 8 => SOL * DIS # F3: 3,8 => CTR => F3: 1,2,9 * CNT 11 HDP CHAINS / 40 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D3: 2,9 => CTR => D3: 3,4 * DIS D3: 3,4 # I2: 8 => CTR => I2: 3,4 * PRF D3: 3,4 + I2: 3,4 # G7: 3,8 => SOL * STA D3: 3,4 + I2: 3,4 + G7: 3,8 * CNT 3 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...6.5...2.....9............76....4....1..2.....83...........57.....4..61...2.... | initial |
| ...6.57.225....96.6.....5...76....415..14627.4..837695....6..577....4.2616572.4.9 | autosolve |
| 948615732251378964637492518376259841589146273412837695824961357793584126165723489 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) D2: 3,4 A4: 3,8 B6: 1,2 C6: 1,2 E4: 5,9 F4: 2,9 G4: 3,8 I5: 3,8 B7: 2,4 C7: 2,4 D7: 3,9 F9: 3,8 H9: 3,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H1,H3: 1.. / H1 = 1 => 15 pairs (_) / H3 = 1 => 15 pairs (_) B6,C6: 1.. / B6 = 1 => 9 pairs (_) / C6 = 1 => 10 pairs (_) F7,E8: 1.. / F7 = 1 => 18 pairs (_) / E8 = 1 => 17 pairs (_) G7,G8: 1.. / G7 = 1 => 17 pairs (_) / G8 = 1 => 18 pairs (_) F7,G7: 1.. / F7 = 1 => 18 pairs (_) / G7 = 1 => 17 pairs (_) E8,G8: 1.. / E8 = 1 => 17 pairs (_) / G8 = 1 => 18 pairs (_) D3,F3: 2.. / D3 = 2 => 0 pairs (X) / F3 = 2 => 11 pairs (_) B6,C6: 2.. / B6 = 2 => 10 pairs (_) / C6 = 2 => 9 pairs (_) D4,F4: 2.. / D4 = 2 => 11 pairs (_) / F4 = 2 => 0 pairs (X) B7,C7: 2.. / B7 = 2 => 9 pairs (_) / C7 = 2 => 10 pairs (_) B6,B7: 2.. / B6 = 2 => 10 pairs (_) / B7 = 2 => 9 pairs (_) C6,C7: 2.. / C6 = 2 => 9 pairs (_) / C7 = 2 => 10 pairs (_) D3,D4: 2.. / D3 = 2 => 0 pairs (X) / D4 = 2 => 11 pairs (_) F3,F4: 2.. / F3 = 2 => 11 pairs (_) / F4 = 2 => 0 pairs (X) G4,I5: 3.. / G4 = 3 => 0 pairs (X) / I5 = 3 => 0 pairs (_) A4,G4: 3.. / A4 = 3 => 0 pairs (*) / G4 = 3 => 0 pairs (X) F9,H9: 3.. / F9 = 3 => 0 pairs (*) / H9 = 3 => 0 pairs (X) B1,C1: 4.. / B1 = 4 => 9 pairs (_) / C1 = 4 => 10 pairs (_) D2,D3: 4.. / D2 = 4 => 13 pairs (_) / D3 = 4 => 15 pairs (_) I2,I3: 4.. / I2 = 4 => 15 pairs (_) / I3 = 4 => 13 pairs (_) B7,C7: 4.. / B7 = 4 => 10 pairs (_) / C7 = 4 => 9 pairs (_) D2,I2: 4.. / D2 = 4 => 13 pairs (_) / I2 = 4 => 15 pairs (_) D3,I3: 4.. / D3 = 4 => 15 pairs (_) / I3 = 4 => 13 pairs (_) B1,B7: 4.. / B1 = 4 => 9 pairs (_) / B7 = 4 => 10 pairs (_) C1,C7: 4.. / C1 = 4 => 10 pairs (_) / C7 = 4 => 9 pairs (_) D4,E4: 5.. / D4 = 5 => 0 pairs (X) / E4 = 5 => 13 pairs (_) D8,E8: 5.. / D8 = 5 => 13 pairs (_) / E8 = 5 => 0 pairs (X) D4,D8: 5.. / D4 = 5 => 0 pairs (X) / D8 = 5 => 13 pairs (_) E4,E8: 5.. / E4 = 5 => 13 pairs (_) / E8 = 5 => 0 pairs (X) C2,C3: 7.. / C2 = 7 => 15 pairs (_) / C3 = 7 => 13 pairs (_) E2,E3: 7.. / E2 = 7 => 13 pairs (_) / E3 = 7 => 15 pairs (_) C2,E2: 7.. / C2 = 7 => 15 pairs (_) / E2 = 7 => 13 pairs (_) C3,E3: 7.. / C3 = 7 => 13 pairs (_) / E3 = 7 => 15 pairs (_) G4,I5: 8.. / G4 = 8 => 0 pairs (*) / I5 = 8 => 0 pairs (X) A4,G4: 8.. / A4 = 8 => 0 pairs (X) / G4 = 8 => 0 pairs (_) F9,H9: 8.. / F9 = 8 => 0 pairs (X) / H9 = 8 => 0 pairs (_) B5,C5: 9.. / B5 = 9 => 15 pairs (_) / C5 = 9 => 15 pairs (_) A1,A7: 9.. / A1 = 9 => 16 pairs (_) / A7 = 9 => 0 pairs (X) * DURATION: 0:01:11.384271 START: 05:02:05.095481 END: 05:03:16.479752 2017-05-04 * CP COUNT: (38) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B6,B7,C6,C7,D2,D7,E4,F4,F9,G4,H9,I5) * ...6.57.225....96.6.....5...76....415..14627.4..837695....6..577....4.2616572.4.9 * PAIR D2: 3,4 BLK 2 D3: 3,4,2,9 # reduction candidate for 3,4 D3: 2,9 => CTR * 9..685712258471963617293584876..23415..1462784..837695....691577...14826165728439 D3: 3,4 # 15 pairs * PAIR D2: 3,4 ROW 2 I2: 3,4,8 # reduction candidate for 3,4 I2: 8 => CTR * ...6.57.22534719686.73.25143762598415..1462734..837695...96..577....4.26165723489 I2: 3,4 # 20 pairs * PAIR A4: 3,8 BLK 4 B5: 3,8,9 # reduction candidate for 3,8 B5: 3,8 # 15 pairs C5: 3,8,9 # reduction candidate for 3,8 C5: 3,8 # 15 pairs * PAIR A4: 3,8 COL A A1: 3,8,9 # reduction candidate for 3,8 A1: 3,8 => CTR * ...6.57.225.4..96.6.....5.4.76...3415..1462784..8376959..3618577....4126165728439 A1: 9 # 16 pairs A7: 3,8,9 # reduction candidate for 3,8 A7: 3,8 # 16 pairs * PAIR E4: 5,9 BLK 5 D4: 5,9,2 # reduction candidate for 5,9 D4: 5,9 => CTR * 9..685712258471963617293584876..23415..1462784..837695....691577...14826165728439 D4: 2 # 11 pairs * PAIR E4: 5,9 COL E E8: 5,9,1,8 # reduction candidate for 5,9 E8: 5,9 => CTR * ...6.57.225...396.6.....5.3.76...3415..1462784..837695....618577....4126165728439 E8: 1,8 # 16 pairs * PAIR F4: 2,9 BLK 5 D4: 2,9,5 # reduction candidate for 2,9 D4: 5 => CTR * ...6.57.225.4.39686..2.9514.76592.415..14627.4..837695....61.577...54126165728439 D4: 2,9 # 13 pairs * PAIR F4: 2,9 COL F F3: 2,9,1,3,8 # reduction candidate for 2,9 F3: 1,3,8 => CTR * 9..68571225.47.9636.7293584.769523415..1462784..837695....691577...14.26165728439 F3: 2,9 # 14 pairs * PAIR G4: 3,8 COL G G7: 3,8,1 # reduction candidate for 3,8 G7: 3,8 # 18 pairs G8: 3,8,1 # reduction candidate for 3,8 G8: 3,8 # 17 pairs * PAIR I5: 3,8 ROW 5 B5: 3,8,9 # reduction candidate for 3,8 B5: 3,8 # 15 pairs C5: 3,8,9 # reduction candidate for 3,8 C5: 3,8 # 15 pairs * PAIR I5: 3,8 COL I I2: 3,8,4 # reduction candidate for 3,8 I2: 3,8 # 13 pairs I3: 3,8,4 # reduction candidate for 3,8 I3: 3,8 # 15 pairs * PAIR D7: 3,9 BLK 8 F7: 3,9,1,8 # reduction candidate for 3,9 F7: 3,9 => CTR * ...6.57.225....96.6.....5...76.5.3415..1462784..8376958...6.1577...14.26165728439 F7: 1,8 # 15 pairs D8: 3,9,5 # reduction candidate for 3,9 D8: 3,9 => CTR * ...6.57.225.4.39686..2.9514.76592.415..14627.4..837695....61.577...54126165728439 D8: 5 # 13 pairs * PAIR D7: 3,9 ROW 7 A7: 3,9,8 # reduction candidate for 3,9 A7: 8 => SOLVED * 948615732251378964637492518376259841589146273412837695824961357793584126165723489 A7: 3,9 # 19 pairs * PAIR D7: 3,9 COL D D3: 3,9,2,4 # reduction candidate for 3,9 D3: 2,4 # 14 pairs D3: 3,9 # 12 pairs * PAIR F9: 3,8 BLK 8 F7: 3,8,1,9 # reduction candidate for 3,8 F7: 3,8 # 17 pairs F7: 1,9 # 14 pairs * PAIR F9: 3,8 COL F F2: 3,8,1 # reduction candidate for 3,8 F2: 3,8 # 17 pairs F3: 3,8,1,2,9 # reduction candidate for 3,8 F3: 3,8 => CTR * 9..68571225.4719636.7293584.769523415..1462784.1837695....691577...14.26165728439 F3: 1,2,9 # 13 pairs * PAIR H9: 3,8 BLK 9 G7: 3,8,1 # reduction candidate for 3,8 G7: 3,8 # 18 pairs G8: 3,8,1 # reduction candidate for 3,8 G8: 3,8 # 17 pairs * PAIR H9: 3,8 COL H H1: 3,8,1 # reduction candidate for 3,8 H1: 3,8 # 15 pairs H3: 3,8,1 # reduction candidate for 3,8 H3: 3,8 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-069-base-pr-000.dot * REASONING * DIS # D3: 2,9 => CTR => D3: 3,4 * DIS # I2: 8 => CTR => I2: 3,4 * DIS # A1: 3,8 => CTR => A1: 9 * DIS # D4: 5,9 => CTR => D4: 2 * DIS # E8: 5,9 => CTR => E8: 1,8 * DIS # D4: 5 => CTR => D4: 2,9 * DIS # F3: 1,3,8 => CTR => F3: 2,9 * DIS # F7: 3,9 => CTR => F7: 1,8 * DIS # D8: 3,9 => CTR => D8: 5 * PRF # A7: 8 => SOL * DIS # F3: 3,8 => CTR => F3: 1,2,9 * CNT 11 HDP CHAINS / 40 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B6,B7,C6,C7,D2,D7,E4,F4,F9,G4,H9,I5) * ...6.57.225....96.6.....5...76....415..14627.4..837695....6..577....4.2616572.4.9 * PAIR D2: 3,4 BLK 2 D3: 3,4,2,9 # reduction candidate for 3,4 D3: 2,9 => CTR * 9..685712258471963617293584876..23415..1462784..837695....691577...14826165728439 * PAIR D2: 3,4 ROW 2 I2: 3,4,8 # reduction candidate for 3,4 I2: 8 => CTR * 9..6.57.225.47.968687392514.762598415.81462734..8376958..96..577.9584126165723489 * PAIR RESTART * PAIR A4: 3,8 BLK 4 B5: 3,8,9 # reduction candidate for 3,8 B5: 3,8 # 19 pairs C5: 3,8,9 # reduction candidate for 3,8 C5: 3,8 # 19 pairs * PAIR G4: 3,8 COL G G7: 3,8,1 # reduction candidate for 3,8 G7: 3,8 => SOLVED * 948615732251378964637492518376259841589146273412837695824961357793584126165723489 * DURATION: 0:00:09.892202 START: 05:03:57.517545 END: 05:04:07.409747 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-069-base-pr-001.dot * REASONING * DIS # D3: 2,9 => CTR => D3: 3,4 * DIS D3: 3,4 # I2: 8 => CTR => I2: 3,4 * PRF D3: 3,4 + I2: 3,4 # G7: 3,8 => SOL * STA D3: 3,4 + I2: 3,4 + G7: 3,8 * CNT 3 HDP CHAINS / 7 HYP OPENED
Header Info
Top 500 Minimum 17 069 solution: 948615732251378964637492518376259841589146273412837695824961357793584126165723489 info: 1448 FNBTHWX S8.f 10910 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 948615732251378964637492518376259841589146273412837695824961357793584126165723489 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 # D3: 3,4 => UNS * DIS # D3: 2,9 => CTR => D3: 3,4 * INC # I2: 3,4 => UNS * DIS # I2: 8 => CTR => I2: 3,4 * INC # B5: 3,8 => UNS * INC # C5: 3,8 => UNS * DIS # A1: 3,8 => CTR => A1: 9 * INC # A1: 9 => UNS * INC # A7: 3,8 => UNS * DIS # D4: 5,9 => CTR => D4: 2 * INC # D4: 2 => UNS * DIS # E8: 5,9 => CTR => E8: 1,8 * INC # E8: 1,8 => UNS * INC # D4: 2,9 => UNS * DIS # D4: 5 => CTR => D4: 2,9 * INC # F3: 2,9 => UNS * DIS # F3: 1,3,8 => CTR => F3: 2,9 * INC # G7: 3,8 => UNS * INC # G8: 3,8 => UNS * INC # B5: 3,8 => UNS * INC # C5: 3,8 => UNS * INC # I2: 3,8 => UNS * INC # I3: 3,8 => UNS * DIS # F7: 3,9 => CTR => F7: 1,8 * INC # F7: 1,8 => UNS * DIS # D8: 3,9 => CTR => D8: 5 * INC # D8: 5 => UNS * INC # A7: 3,9 => UNS * PRF # A7: 8 => SOL * INC # D3: 3,9 => UNS * INC # D3: 2,4 => UNS * INC # F7: 3,8 => UNS * INC # F7: 1,9 => UNS * INC # F2: 3,8 => UNS * DIS # F3: 3,8 => CTR => F3: 1,2,9 * INC # F3: 1,2,9 => UNS * INC # G7: 3,8 => UNS * INC # G8: 3,8 => UNS * INC # H1: 3,8 => UNS * INC # H3: 3,8 => UNS * CNT 40 HDP CHAINS / 40 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D3: 3,4 => UNS * DIS # D3: 2,9 => CTR => D3: 3,4 * INC D3: 3,4 # I2: 3,4 => UNS * DIS D3: 3,4 # I2: 8 => CTR => I2: 3,4 * INC D3: 3,4 + I2: 3,4 # B5: 3,8 => UNS * INC D3: 3,4 + I2: 3,4 # C5: 3,8 => UNS * PRF D3: 3,4 + I2: 3,4 # G7: 3,8 => SOL * STA D3: 3,4 + I2: 3,4 + G7: 3,8 * CNT 7 HDP CHAINS / 7 HYP OPENED