Analysis of xx-top500-176-base.sdk
Contents
Original Sudoku
level: medium
position: 3.....67....5.1....4.......2......856.1.3..............854.........6.3........... initial
Autosolve
position: 35928467182657143914739652823461..856.18352..5.8.42163.85423.16.12.6835..6315.8.2 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A8: 7,9 => CTR => A8: 4 * PRF # A8: 4 => SOL * PRF # A9: 7,9 => SOL * DIS # A9: 4 => CTR => A9: 7,9 * DIS # A8: 7,9 => CTR => A8: 4 * PRF # A8: 4 => SOL * PRF # A9: 7,9 => SOL * DIS # A9: 4 => CTR => A9: 7,9 * PRF # A8: 4,7 => SOL * DIS # A8: 9 => CTR => A8: 4,7 * PRF # A9: 4,9 => SOL * DIS # A9: 7 => CTR => A9: 4,9 * CNT 12 HDP CHAINS / 12 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A8: 7,9 => CTR => A8: 4 * PRF A8: 4 => SOL * STA A8: 4 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 3.....67....5.1....4.......2......856.1.3..............854.........6.3........... | initial |
| 35928467182657143914739652823461..856.18352..5.8.42163.85423.16.12.6835..6315.8.2 | autosolve |
| 359284671826571439147396528234619785671835294598742163785423916412968357963157842 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) B5: 7,9 B6: 7,9 F4: 7,9 D6: 7,9 G4: 7,9 H5: 4,9 I5: 4,7 A7: 7,9 D8: 7,9 F9: 7,9 G7: 7,9 I8: 4,7 H9: 4,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H5,I5: 4.. / H5 = 4 => 0 pairs (X) / I5 = 4 => 0 pairs (_) A8,A9: 4.. / A8 = 4 => 0 pairs (*) / A9 = 4 => 0 pairs (X) I8,H9: 4.. / I8 = 4 => 0 pairs (X) / H9 = 4 => 0 pairs (_) A8,I8: 4.. / A8 = 4 => 0 pairs (*) / I8 = 4 => 0 pairs (X) A9,H9: 4.. / A9 = 4 => 0 pairs (X) / H9 = 4 => 0 pairs (_) H5,H9: 4.. / H5 = 4 => 0 pairs (X) / H9 = 4 => 0 pairs (_) I5,I8: 4.. / I5 = 4 => 0 pairs (*) / I8 = 4 => 0 pairs (X) B5,B6: 7.. / B5 = 7 => 0 pairs (*) / B6 = 7 => 0 pairs (X) F4,D6: 7.. / F4 = 7 => 0 pairs (X) / D6 = 7 => 0 pairs (_) G4,I5: 7.. / G4 = 7 => 0 pairs (*) / I5 = 7 => 0 pairs (X) D8,F9: 7.. / D8 = 7 => 0 pairs (X) / F9 = 7 => 0 pairs (_) G7,I8: 7.. / G7 = 7 => 0 pairs (X) / I8 = 7 => 0 pairs (_) F4,G4: 7.. / F4 = 7 => 0 pairs (X) / G4 = 7 => 0 pairs (_) B5,I5: 7.. / B5 = 7 => 0 pairs (*) / I5 = 7 => 0 pairs (X) B6,D6: 7.. / B6 = 7 => 0 pairs (X) / D6 = 7 => 0 pairs (_) A7,G7: 7.. / A7 = 7 => 0 pairs (*) / G7 = 7 => 0 pairs (X) A9,F9: 7.. / A9 = 7 => 0 pairs (X) / F9 = 7 => 0 pairs (_) D6,D8: 7.. / D6 = 7 => 0 pairs (*) / D8 = 7 => 0 pairs (X) F4,F9: 7.. / F4 = 7 => 0 pairs (X) / F9 = 7 => 0 pairs (_) G4,G7: 7.. / G4 = 7 => 0 pairs (*) / G7 = 7 => 0 pairs (X) I5,I8: 7.. / I5 = 7 => 0 pairs (X) / I8 = 7 => 0 pairs (_) B5,B6: 9.. / B5 = 9 => 0 pairs (X) / B6 = 9 => 0 pairs (_) F4,D6: 9.. / F4 = 9 => 0 pairs (*) / D6 = 9 => 0 pairs (X) G4,H5: 9.. / G4 = 9 => 0 pairs (X) / H5 = 9 => 0 pairs (_) D8,F9: 9.. / D8 = 9 => 0 pairs (*) / F9 = 9 => 0 pairs (X) G7,H9: 9.. / G7 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) F4,G4: 9.. / F4 = 9 => 0 pairs (*) / G4 = 9 => 0 pairs (X) B5,H5: 9.. / B5 = 9 => 0 pairs (X) / H5 = 9 => 0 pairs (_) B6,D6: 9.. / B6 = 9 => 0 pairs (*) / D6 = 9 => 0 pairs (X) A7,G7: 9.. / A7 = 9 => 0 pairs (X) / G7 = 9 => 0 pairs (_) A8,D8: 9.. / A8 = 9 => 0 pairs (X) / D8 = 9 => 0 pairs (_) D6,D8: 9.. / D6 = 9 => 0 pairs (X) / D8 = 9 => 0 pairs (_) F4,F9: 9.. / F4 = 9 => 0 pairs (*) / F9 = 9 => 0 pairs (X) G4,G7: 9.. / G4 = 9 => 0 pairs (X) / G7 = 9 => 0 pairs (_) H5,H9: 9.. / H5 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) * DURATION: 0:01:04.341622 START: 08:42:59.256466 END: 08:44:03.598088 2017-05-04 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B5,B6,D6,D8,F4,F9,G4,G7,H5,H9,I5,I8) * 35928467182657143914739652823461..856.18352..5.8.42163.85423.16.12.6835..6315.8.2 * PAIR A7: 7,9 BLK 7 A8: 7,9,4 # reduction candidate for 7,9 A8: 7,9 => CTR * 35928467182657143914739652823461..856.18352..5.8.42163.85423.16.12.68354463157892 A8: 4 => SOLVED * 359284671826571439147396528234619785671835294598742163785423916412968357963157842 A9: 7,9,4 # reduction candidate for 7,9 A9: 7,9 => SOLVED * 359284671826571439147396528234619785671835294598742163785423916412968357963157842 A9: 4 => CTR * 35928467182657143914739652823461..856.18352..5.8.42163.85423.16.12.6835.463157892 * PAIR D8: 7,9 ROW 8 A8: 7,9,4 # reduction candidate for 7,9 A8: 7,9 => CTR * 35928467182657143914739652823461..856.18352..5.8.42163.85423.16.12.68354463157892 A8: 4 => SOLVED * 359284671826571439147396528234619785671835294598742163785423916412968357963157842 * PAIR F9: 7,9 ROW 9 A9: 7,9,4 # reduction candidate for 7,9 A9: 7,9 => SOLVED * 359284671826571439147396528234619785671835294598742163785423916412968357963157842 A9: 4 => CTR * 35928467182657143914739652823461..856.18352..5.8.42163.85423.16.12.6835.463157892 * PAIR I8: 4,7 ROW 8 A8: 4,7,9 # reduction candidate for 4,7 A8: 4,7 => SOLVED * 359284671826571439147396528234619785671835294598742163785423916412968357963157842 A8: 9 => CTR * 35928467182657143914739652823461..856.18352..5.8.42163.85423.16912768354.6315.8.2 * PAIR H9: 4,9 ROW 9 A9: 4,9,7 # reduction candidate for 4,9 A9: 4,9 => SOLVED * 359284671826571439147396528234619785671835294598742163785423916412968357963157842 A9: 7 => CTR * 35928467182657143914739652823461..856.18352..5.8.42163.85423.16412968357.6315.8.2 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-176-base-pr-000.dot * REASONING * DIS # A8: 7,9 => CTR => A8: 4 * PRF # A8: 4 => SOL * PRF # A9: 7,9 => SOL * DIS # A9: 4 => CTR => A9: 7,9 * DIS # A8: 7,9 => CTR => A8: 4 * PRF # A8: 4 => SOL * PRF # A9: 7,9 => SOL * DIS # A9: 4 => CTR => A9: 7,9 * PRF # A8: 4,7 => SOL * DIS # A8: 9 => CTR => A8: 4,7 * PRF # A9: 4,9 => SOL * DIS # A9: 7 => CTR => A9: 4,9 * CNT 12 HDP CHAINS / 12 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B5,B6,D6,D8,F4,F9,G4,G7,H5,H9,I5,I8) * 35928467182657143914739652823461..856.18352..5.8.42163.85423.16.12.6835..6315.8.2 * PAIR A7: 7,9 BLK 7 A8: 7,9,4 # reduction candidate for 7,9 A8: 7,9 => CTR * 35928467182657143914739652823461..856.18352..5.8.42163.85423.16.12.68354463157892 A8: 4 => SOLVED * 359284671826571439147396528234619785671835294598742163785423916412968357963157842 * DURATION: 0:00:01.828804 START: 08:44:19.105793 END: 08:44:20.934597 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-176-base-pr-001.dot * REASONING * DIS # A8: 7,9 => CTR => A8: 4 * PRF A8: 4 => SOL * STA A8: 4 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 176 solution: 359284671826571439147396528234619785671835294598742163785423916412968357963157842 info: 1827 FNTWX S8.f 28962 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 359284671826571439147396528234619785671835294598742163785423916412968357963157842 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 # A8: 7,9 => CTR => A8: 4 * PRF # A8: 4 => SOL * PRF # A9: 7,9 => SOL * DIS # A9: 4 => CTR => A9: 7,9 * DIS # A8: 7,9 => CTR => A8: 4 * PRF # A8: 4 => SOL * PRF # A9: 7,9 => SOL * DIS # A9: 4 => CTR => A9: 7,9 * PRF # A8: 4,7 => SOL * DIS # A8: 9 => CTR => A8: 4,7 * PRF # A9: 4,9 => SOL * DIS # A9: 7 => CTR => A9: 4,9 * CNT 12 HDP CHAINS / 12 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A8: 7,9 => CTR => A8: 4 * PRF A8: 4 => SOL * STA A8: 4 * CNT 2 HDP CHAINS / 1 HYP OPENED