Analysis of xx-top500-298-base.sdk
Contents
Original Sudoku
level: medium
position: .1.7.........5.4..........34..3.....2.....5.....1...8.5...2.6...3.....7......4... initial
Autosolve
position: .1.7.........5.4..........34..3.....2.....5.....1...8.5...2.6...3.....7.1....4... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D8: 8,9 => CTR => D8: 5,6 * DIS # E8: 8,9 => CTR => E8: 1,6 * DIS # B7: 8,9 => CTR => B7: 4,7 * PRF # I7: 8,9 => SOL * DIS # D2: 8,9 => CTR => D2: 2,6 * DIS # D3: 8,9 => CTR => D3: 2,4,6 * DIS # D5: 8,9 => CTR => D5: 4,6 * CNT 7 HDP CHAINS / 17 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D8: 8,9 => CTR => D8: 5,6 * DIS D8: 5,6 # E8: 8,9 => CTR => E8: 1,6 * DIS D8: 5,6 + E8: 1,6 # B7: 8,9 => CTR => B7: 4,7 * PRF D8: 5,6 + E8: 1,6 + B7: 4,7 # I7: 8,9 => SOL * STA D8: 5,6 + E8: 1,6 + B7: 4,7 + I7: 8,9 * CNT 4 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .1.7.........5.4..........34..3.....2.....5.....1...8.5...2.6...3.....7......4... | initial |
| .1.7.........5.4..........34..3.....2.....5.....1...8.5...2.6...3.....7.1....4... | autosolve |
| 614739852398251467752468193461385729283697541975142386547923618839516274126874935 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) F4: 2,5 F6: 2,5 D7: 8,9 F7: 3,7 E9: 3,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C4,C5: 1.. / C4 = 1 => 0 pairs (*) / C5 = 1 => 0 pairs (X) E8,F8: 1.. / E8 = 1 => 5 pairs (_) / F8 = 1 => 0 pairs (X) H7,I7: 1.. / H7 = 1 => 0 pairs (*) / I7 = 1 => 0 pairs (X) E3,E8: 1.. / E3 = 1 => 0 pairs (X) / E8 = 1 => 5 pairs (_) G3,G4: 1.. / G3 = 1 => 6 pairs (_) / G4 = 1 => 0 pairs (X) D2,D3: 2.. / D2 = 2 => 5 pairs (_) / D3 = 2 => 0 pairs (X) F4,F6: 2.. / F4 = 2 => 3 pairs (_) / F6 = 2 => 3 pairs (_) H5,G6: 3.. / H5 = 3 => 0 pairs (X) / G6 = 3 => 0 pairs (_) F7,E9: 3.. / F7 = 3 => 0 pairs (*) / E9 = 3 => 0 pairs (X) C5,H5: 3.. / C5 = 3 => 0 pairs (*) / H5 = 3 => 0 pairs (X) F7,H7: 3.. / F7 = 3 => 0 pairs (*) / H7 = 3 => 0 pairs (X) E1,E9: 3.. / E1 = 3 => 0 pairs (*) / E9 = 3 => 0 pairs (X) G6,G9: 3.. / G6 = 3 => 0 pairs (*) / G9 = 3 => 0 pairs (X) C1,E1: 4.. / C1 = 4 => 0 pairs (*) / E1 = 4 => 0 pairs (X) E6,I6: 4.. / E6 = 4 => 0 pairs (*) / I6 = 4 => 0 pairs (X) C8,I8: 4.. / C8 = 4 => 0 pairs (X) / I8 = 4 => 0 pairs (_) B3,B7: 4.. / B3 = 4 => 0 pairs (X) / B7 = 4 => 0 pairs (_) D3,D5: 4.. / D3 = 4 => 0 pairs (*) / D5 = 4 => 0 pairs (X) H5,H7: 4.. / H5 = 4 => 0 pairs (*) / H7 = 4 => 0 pairs (X) F4,F6: 5.. / F4 = 5 => 3 pairs (_) / F6 = 5 => 3 pairs (_) D8,D9: 5.. / D8 = 5 => 5 pairs (_) / D9 = 5 => 0 pairs (X) D8,I8: 5.. / D8 = 5 => 5 pairs (_) / I8 = 5 => 0 pairs (X) I2,G3: 7.. / I2 = 7 => 5 pairs (_) / G3 = 7 => 0 pairs (X) F7,E9: 7.. / F7 = 7 => 0 pairs (X) / E9 = 7 => 0 pairs (_) F5,F7: 7.. / F5 = 7 => 0 pairs (*) / F7 = 7 => 0 pairs (X) * DURATION: 0:00:37.504709 START: 13:09:31.152105 END: 13:10:08.656814 2017-05-04 * CP COUNT: (25) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D7,E9,F4,F6,F7) * .1.7.........5.4..........34..3.....2.....5.....1...8.5...2.6...3.....7.1....4... * PAIR D7: 8,9 BLK 8 D8: 8,9,5,6 # reduction candidate for 8,9 D8: 8,9 => CTR * .1.74........5.4...4......34..3.....2..4..5.....1...845...2.641.34...2751..534.98 D8: 5,6 # 6 pairs E8: 8,9,1,6 # reduction candidate for 8,9 E8: 8,9 => CTR * .1.7.........5.4......1...34..3..1..2.1...53....1...8.5...23641.34..1.7.1...74... E8: 1,6 # 6 pairs F8: 8,9,1,6 # reduction candidate for 8,9 F8: 8,9 # 8 pairs D9: 8,9,5,6 # reduction candidate for 8,9 D9: 8,9 # 11 pairs * PAIR D7: 8,9 ROW 7 B7: 8,9,4,7 # reduction candidate for 8,9 B7: 8,9 => CTR * .1.74........5.4...4......34..3.....2..4..5.....1...845...23641.34....7.1...74... B7: 4,7 # 6 pairs C7: 8,9,4,7 # reduction candidate for 8,9 C7: 8,9 # 8 pairs I7: 8,9,1,4 # reduction candidate for 8,9 I7: 8,9 => SOLVED * 614739852398251467752468193461385729283697541975142386547923618839516274126874935 I7: 1,4 # 6 pairs * PAIR D7: 8,9 COL D D2: 8,9,2,6 # reduction candidate for 8,9 D2: 8,9 => CTR * .1.74........5.4...4.2....34..3.....2..4..5.....1...845...23641.34....7.1...74... D2: 2,6 # 6 pairs D3: 8,9,2,4,6 # reduction candidate for 8,9 D3: 8,9 => CTR * .1.74.......25.4...4......34..3.....2..4..5.....1...845...23641.34....7.12..74... D3: 2,4,6 # 5 pairs D5: 8,9,4,6 # reduction candidate for 8,9 D5: 8,9 => CTR * .1473..523.82514.7...4..1.34.13..72.2.3..7541...14238.547.23618836519.741..674.35 D5: 4,6 # 6 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-298-base-pr-000.dot * REASONING * DIS # D8: 8,9 => CTR => D8: 5,6 * DIS # E8: 8,9 => CTR => E8: 1,6 * DIS # B7: 8,9 => CTR => B7: 4,7 * PRF # I7: 8,9 => SOL * DIS # D2: 8,9 => CTR => D2: 2,6 * DIS # D3: 8,9 => CTR => D3: 2,4,6 * DIS # D5: 8,9 => CTR => D5: 4,6 * CNT 7 HDP CHAINS / 17 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D7,E9,F4,F6,F7) * .1.7.........5.4..........34..3.....2.....5.....1...8.5...2.6...3.....7.1....4... * PAIR D7: 8,9 BLK 8 D8: 8,9,5,6 # reduction candidate for 8,9 D8: 8,9 => CTR * .1.74........5.4...4......34..3.....2..4..5.....1...845...2.641.34...2751..534.98 E8: 8,9,1,6 # reduction candidate for 8,9 E8: 8,9 => CTR * .1.7.........5.4......1...34..3..1..2.1...53....1...8.5...23641.34..1.7.1...74... F8: 8,9,1,6 # reduction candidate for 8,9 F8: 8,9 # 8 pairs D9: 8,9,5,6 # reduction candidate for 8,9 D9: 8,9 # 11 pairs * PAIR D7: 8,9 ROW 7 B7: 8,9,4,7 # reduction candidate for 8,9 B7: 8,9 => CTR * .1.74........5.4...4......34..3.....2..4..5.....1...845...23641.34....7.1...74... C7: 8,9,4,7 # reduction candidate for 8,9 C7: 8,9 # 10 pairs I7: 8,9,1,4 # reduction candidate for 8,9 I7: 8,9 => SOLVED * 614739852398251467752468193461385729283697541975142386547923618839516274126874935 * DURATION: 0:00:07.137687 START: 13:10:20.966712 END: 13:10:28.104399 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-298-base-pr-001.dot * REASONING * DIS # D8: 8,9 => CTR => D8: 5,6 * DIS D8: 5,6 # E8: 8,9 => CTR => E8: 1,6 * DIS D8: 5,6 + E8: 1,6 # B7: 8,9 => CTR => B7: 4,7 * PRF D8: 5,6 + E8: 1,6 + B7: 4,7 # I7: 8,9 => SOL * STA D8: 5,6 + E8: 1,6 + B7: 4,7 + I7: 8,9 * CNT 4 HDP CHAINS / 7 HYP OPENED
Header Info
Top 500 Minimum 17 298 solution: 614739852398251467752468193461385729283697541975142386547923618839516274126874935 info: 2530 FNBHWXY S8.f 15709 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 614739852398251467752468193461385729283697541975142386547923618839516274126874935 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 # D8: 8,9 => CTR => D8: 5,6 * INC # D8: 5,6 => UNS * DIS # E8: 8,9 => CTR => E8: 1,6 * INC # E8: 1,6 => UNS * INC # F8: 8,9 => UNS * INC # D9: 8,9 => UNS * DIS # B7: 8,9 => CTR => B7: 4,7 * INC # B7: 4,7 => UNS * INC # C7: 8,9 => UNS * PRF # I7: 8,9 => SOL * INC # I7: 1,4 => UNS * DIS # D2: 8,9 => CTR => D2: 2,6 * INC # D2: 2,6 => UNS * DIS # D3: 8,9 => CTR => D3: 2,4,6 * INC # D3: 2,4,6 => UNS * DIS # D5: 8,9 => CTR => D5: 4,6 * INC # D5: 4,6 => UNS * CNT 17 HDP CHAINS / 17 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D8: 8,9 => CTR => D8: 5,6 * DIS D8: 5,6 # E8: 8,9 => CTR => E8: 1,6 * INC D8: 5,6 + E8: 1,6 # F8: 8,9 => UNS * INC D8: 5,6 + E8: 1,6 # D9: 8,9 => UNS * DIS D8: 5,6 + E8: 1,6 # B7: 8,9 => CTR => B7: 4,7 * INC D8: 5,6 + E8: 1,6 + B7: 4,7 # C7: 8,9 => UNS * PRF D8: 5,6 + E8: 1,6 + B7: 4,7 # I7: 8,9 => SOL * STA D8: 5,6 + E8: 1,6 + B7: 4,7 + I7: 8,9 * CNT 7 HDP CHAINS / 7 HYP OPENED