Analysis of xx-top500-401-base.sdk
Contents
Original Sudoku
level: medium
position: ...6..31...2..4....5....7...9.81............2......6..3.67............9.2........ initial
Autosolve
position: 978625314162374.5.453...726697812435.3......2.2....6..3.675924.7.52...932.9...567 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B8: 1,8 => SOL * PRF # B8: 1,8 => SOL * CNT 2 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B8: 1,8 => SOL * STA B8: 1,8 * CNT 1 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...6..31...2..4....5....7...9.81............2......6..3.67............9.2........ | initial |
| 978625314162374.5.453...726697812435.3......2.2....6..3.675924.7.52...932.9...567 | autosolve |
| 978625314162374859453981726697812435531467982824593671316759248785246193249138567 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) D3: 1,9 E3: 8,9 F3: 1,8 G2: 8,9 I2: 8,9 A5: 5,8 C5: 1,4 A6: 5,8 C6: 1,4 F5: 6,7 F6: 3,7 G5: 1,9 H5: 7,8 H6: 7,8 I6: 1,9 B7: 1,8 D9: 1,4 I7: 1,8 G8: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D3,F3: 1.. / D3 = 1 => 24 pairs (_) / F3 = 1 => 24 pairs (_) C5,C6: 1.. / C5 = 1 => 17 pairs (_) / C6 = 1 => 20 pairs (_) G5,I6: 1.. / G5 = 1 => 20 pairs (_) / I6 = 1 => 17 pairs (_) I7,G8: 1.. / I7 = 1 => 20 pairs (_) / G8 = 1 => 17 pairs (_) C5,G5: 1.. / C5 = 1 => 17 pairs (_) / G5 = 1 => 20 pairs (_) C6,I6: 1.. / C6 = 1 => 20 pairs (_) / I6 = 1 => 17 pairs (_) B7,I7: 1.. / B7 = 1 => 17 pairs (_) / I7 = 1 => 20 pairs (_) D3,D9: 1.. / D3 = 1 => 24 pairs (_) / D9 = 1 => 24 pairs (_) G5,G8: 1.. / G5 = 1 => 20 pairs (_) / G8 = 1 => 17 pairs (_) I6,I7: 1.. / I6 = 1 => 17 pairs (_) / I7 = 1 => 20 pairs (_) E6,F6: 3.. / E6 = 3 => 18 pairs (_) / F6 = 3 => 18 pairs (_) E9,F9: 3.. / E9 = 3 => 18 pairs (_) / F9 = 3 => 18 pairs (_) E6,E9: 3.. / E6 = 3 => 18 pairs (_) / E9 = 3 => 18 pairs (_) F6,F9: 3.. / F6 = 3 => 18 pairs (_) / F9 = 3 => 18 pairs (_) C5,C6: 4.. / C5 = 4 => 20 pairs (_) / C6 = 4 => 17 pairs (_) B8,B9: 4.. / B8 = 4 => 21 pairs (_) / B9 = 4 => 0 pairs (*) B8,E8: 4.. / B8 = 4 => 21 pairs (_) / E8 = 4 => 0 pairs (*) A5,A6: 5.. / A5 = 5 => 18 pairs (_) / A6 = 5 => 18 pairs (_) D5,D6: 5.. / D5 = 5 => 18 pairs (_) / D6 = 5 => 18 pairs (_) A5,D5: 5.. / A5 = 5 => 18 pairs (_) / D5 = 5 => 18 pairs (_) A6,D6: 5.. / A6 = 5 => 18 pairs (_) / D6 = 5 => 18 pairs (_) E5,F5: 6.. / E5 = 6 => 18 pairs (_) / F5 = 6 => 18 pairs (_) E8,F8: 6.. / E8 = 6 => 18 pairs (_) / F8 = 6 => 18 pairs (_) E5,E8: 6.. / E5 = 6 => 18 pairs (_) / E8 = 6 => 18 pairs (_) F5,F8: 6.. / F5 = 6 => 18 pairs (_) / F8 = 6 => 18 pairs (_) F5,F6: 7.. / F5 = 7 => 18 pairs (_) / F6 = 7 => 18 pairs (_) H5,H6: 7.. / H5 = 7 => 18 pairs (_) / H6 = 7 => 18 pairs (_) F5,H5: 7.. / F5 = 7 => 18 pairs (_) / H5 = 7 => 18 pairs (_) F6,H6: 7.. / F6 = 7 => 18 pairs (_) / H6 = 7 => 18 pairs (_) E3,F3: 8.. / E3 = 8 => 24 pairs (_) / F3 = 8 => 24 pairs (_) G2,I2: 8.. / G2 = 8 => 17 pairs (_) / I2 = 8 => 20 pairs (_) A5,A6: 8.. / A5 = 8 => 18 pairs (_) / A6 = 8 => 18 pairs (_) H5,H6: 8.. / H5 = 8 => 18 pairs (_) / H6 = 8 => 18 pairs (_) I7,G8: 8.. / I7 = 8 => 17 pairs (_) / G8 = 8 => 20 pairs (_) A5,H5: 8.. / A5 = 8 => 18 pairs (_) / H5 = 8 => 18 pairs (_) A6,H6: 8.. / A6 = 8 => 18 pairs (_) / H6 = 8 => 18 pairs (_) B7,I7: 8.. / B7 = 8 => 20 pairs (_) / I7 = 8 => 17 pairs (_) G2,G8: 8.. / G2 = 8 => 17 pairs (_) / G8 = 8 => 20 pairs (_) I2,I7: 8.. / I2 = 8 => 20 pairs (_) / I7 = 8 => 17 pairs (_) D3,E3: 9.. / D3 = 9 => 24 pairs (_) / E3 = 9 => 24 pairs (_) G2,I2: 9.. / G2 = 9 => 20 pairs (_) / I2 = 9 => 17 pairs (_) G5,I6: 9.. / G5 = 9 => 17 pairs (_) / I6 = 9 => 20 pairs (_) G2,G5: 9.. / G2 = 9 => 20 pairs (_) / G5 = 9 => 17 pairs (_) I2,I6: 9.. / I2 = 9 => 17 pairs (_) / I6 = 9 => 20 pairs (_) * DURATION: 0:01:33.267560 START: 16:30:17.765068 END: 16:31:51.032628 2017-05-04 * CP COUNT: (44) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B7,C5,C6,D3,D9,E3,F3,F5,F6,G2,G5,G8,H5,H6,I2,I6,I7) * 978625314162374.5.453...726697812435.3......2.2....6..3.675924.7.52...932.9...567 * PAIR F3: 1,8 COL F F8: 1,8,6 # reduction candidate for 1,8 F8: 1,8 # 18 pairs F9: 1,8,3 # reduction candidate for 1,8 F9: 1,8 # 18 pairs * PAIR B7: 1,8 BLK 7 B8: 1,8,4 # reduction candidate for 1,8 B8: 1,8 => SOLVED * 978625314162374859453981726697812435531467982824593671316759248785246193249138567 B8: 4 # 21 pairs B9: 1,8,4 # reduction candidate for 1,8 B9: 1,8 # 21 pairs * PAIR D9: 1,4 ROW 9 B9: 1,4,8 # reduction candidate for 1,4 B9: 1,4 # 24 pairs B9: 8 # 18 pairs * PAIR G8: 1,8 ROW 8 B8: 1,8,4 # reduction candidate for 1,8 B8: 1,8 => SOLVED * 978625314162374859453981726697812435531467982824593671316759248785246193249138567 B8: 4 # 21 pairs F8: 1,8,6 # reduction candidate for 1,8 F8: 1,8 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-401-base-pr-000.dot * REASONING * PRF # B8: 1,8 => SOL * PRF # B8: 1,8 => SOL * CNT 2 HDP CHAINS / 10 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B7,C5,C6,D3,D9,E3,F3,F5,F6,G2,G5,G8,H5,H6,I2,I6,I7) * 978625314162374.5.453...726697812435.3......2.2....6..3.675924.7.52...932.9...567 * PAIR F3: 1,8 COL F F8: 1,8,6 # reduction candidate for 1,8 F8: 1,8 # 18 pairs F9: 1,8,3 # reduction candidate for 1,8 F9: 1,8 # 18 pairs * PAIR B7: 1,8 BLK 7 B8: 1,8,4 # reduction candidate for 1,8 B8: 1,8 => SOLVED * 978625314162374859453981726697812435531467982824593671316759248785246193249138567 * DURATION: 0:00:04.961408 START: 16:32:03.608341 END: 16:32:08.569749 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-401-base-pr-001.dot * REASONING * PRF # B8: 1,8 => SOL * STA B8: 1,8 * CNT 1 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 401 solution: 978625314162374859453981726697812435531467982824593671316759248785246193249138567 info: 90174 FNBY S8.f 40086 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 978625314162374859453981726697812435531467982824593671316759248785246193249138567 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 # F8: 1,8 => UNS * INC # F9: 1,8 => UNS * PRF # B8: 1,8 => SOL * INC # B8: 4 => UNS * INC # B9: 1,8 => UNS * INC # B9: 1,4 => UNS * INC # B9: 8 => UNS * PRF # B8: 1,8 => SOL * INC # B8: 4 => UNS * INC # F8: 1,8 => UNS * CNT 10 HDP CHAINS / 10 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F8: 1,8 => UNS * INC # F9: 1,8 => UNS * PRF # B8: 1,8 => SOL * STA B8: 1,8 * CNT 3 HDP CHAINS / 3 HYP OPENED