Analysis of xx-top500-162-base.sdk
Contents
Original Sudoku
level: medium
position: ....29.........1......3......9....2..8...4....5.7........1..8.53..8..6..2........ initial
Autosolve
position: 831.295..92.5781.35...31289..9385.2..8321495..527963.8.9.162835315847692268953... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C3: 4,6 => SOL * DIS # C3: 7 => CTR => C3: 4,6 * DIS # C3: 4,7 => CTR => C3: 6 * PRF # C3: 6 => SOL * DIS # H1: 4,6 => CTR => H1: 7 * PRF # H1: 7 => SOL * PRF # C3: 4,6 => SOL * DIS # C3: 7 => CTR => C3: 4,6 * PRF # H1: 4,7 => SOL * DIS # H1: 6 => CTR => H1: 4,7 * PRF # I9: 4,7 => SOL * DIS # I9: 1 => CTR => I9: 4,7 * DIS # H1: 4,6 => CTR => H1: 7 * PRF # H1: 7 => SOL * PRF # H9: 1,4 => SOL * DIS # H9: 7 => CTR => H9: 1,4 * DIS # C3: 4,7 => CTR => C3: 6 * PRF # C3: 6 => SOL * DIS # H9: 4,7 => CTR => H9: 1 * PRF # H9: 1 => SOL * PRF # I9: 4,7 => SOL * DIS # I9: 1 => CTR => I9: 4,7 * CNT 22 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C3: 4,6 => SOL * STA C3: 4,6 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....29.........1......3......9....2..8...4....5.7........1..8.53..8..6..2........ | initial |
| 831.295..92.5781.35...31289..9385.2..8321495..527963.8.9.162835315847692268953... | autosolve |
| 831629574924578163576431289649385721783214956152796348497162835315847692268953417 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) C2: 4,6 B3: 4,7 D1: 4,6 D3: 4,6 I1: 4,7 H2: 4,6 A4: 1,6 B4: 4,7 A5: 6,7 A6: 1,4 G4: 4,7 I4: 1,6 I5: 6,7 H6: 1,4 A7: 4,7 C7: 4,7 G9: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A4,A6: 1.. / A4 = 1 => 0 pairs (X) / A6 = 1 => 0 pairs (_) I4,H6: 1.. / I4 = 1 => 0 pairs (*) / H6 = 1 => 0 pairs (X) H9,I9: 1.. / H9 = 1 => 0 pairs (*) / I9 = 1 => 0 pairs (X) A4,I4: 1.. / A4 = 1 => 0 pairs (X) / I4 = 1 => 0 pairs (_) A6,H6: 1.. / A6 = 1 => 0 pairs (*) / H6 = 1 => 0 pairs (X) H6,H9: 1.. / H6 = 1 => 0 pairs (X) / H9 = 1 => 0 pairs (_) I4,I9: 1.. / I4 = 1 => 0 pairs (*) / I9 = 1 => 0 pairs (X) D1,D3: 4.. / D1 = 4 => 0 pairs (X) / D3 = 4 => 0 pairs (_) B4,A6: 4.. / B4 = 4 => 0 pairs (*) / A6 = 4 => 0 pairs (X) G4,H6: 4.. / G4 = 4 => 0 pairs (X) / H6 = 4 => 0 pairs (_) A7,C7: 4.. / A7 = 4 => 0 pairs (*) / C7 = 4 => 0 pairs (X) C2,H2: 4.. / C2 = 4 => 0 pairs (*) / H2 = 4 => 0 pairs (X) B4,G4: 4.. / B4 = 4 => 0 pairs (*) / G4 = 4 => 0 pairs (X) A6,H6: 4.. / A6 = 4 => 0 pairs (X) / H6 = 4 => 0 pairs (_) A6,A7: 4.. / A6 = 4 => 0 pairs (X) / A7 = 4 => 0 pairs (_) B3,B4: 4.. / B3 = 4 => 0 pairs (X) / B4 = 4 => 0 pairs (_) G4,G9: 4.. / G4 = 4 => 0 pairs (X) / G9 = 4 => 0 pairs (_) I1,I9: 4.. / I1 = 4 => 0 pairs (*) / I9 = 4 => 0 pairs (X) C2,C3: 6.. / C2 = 6 => 0 pairs (X) / C3 = 6 => 0 pairs (_) D1,D3: 6.. / D1 = 6 => 0 pairs (*) / D3 = 6 => 0 pairs (X) H1,H2: 6.. / H1 = 6 => 0 pairs (X) / H2 = 6 => 0 pairs (_) A4,A5: 6.. / A4 = 6 => 0 pairs (*) / A5 = 6 => 0 pairs (X) I4,I5: 6.. / I4 = 6 => 0 pairs (X) / I5 = 6 => 0 pairs (_) D1,H1: 6.. / D1 = 6 => 0 pairs (*) / H1 = 6 => 0 pairs (X) C2,H2: 6.. / C2 = 6 => 0 pairs (X) / H2 = 6 => 0 pairs (_) C3,D3: 6.. / C3 = 6 => 0 pairs (*) / D3 = 6 => 0 pairs (X) A4,I4: 6.. / A4 = 6 => 0 pairs (*) / I4 = 6 => 0 pairs (X) A5,I5: 6.. / A5 = 6 => 0 pairs (X) / I5 = 6 => 0 pairs (_) B3,C3: 7.. / B3 = 7 => 0 pairs (*) / C3 = 7 => 0 pairs (X) H1,I1: 7.. / H1 = 7 => 0 pairs (*) / I1 = 7 => 0 pairs (X) B4,A5: 7.. / B4 = 7 => 0 pairs (X) / A5 = 7 => 0 pairs (_) G4,I5: 7.. / G4 = 7 => 0 pairs (*) / I5 = 7 => 0 pairs (X) A7,C7: 7.. / A7 = 7 => 0 pairs (X) / C7 = 7 => 0 pairs (_) B4,G4: 7.. / B4 = 7 => 0 pairs (X) / G4 = 7 => 0 pairs (_) A5,I5: 7.. / A5 = 7 => 0 pairs (*) / I5 = 7 => 0 pairs (X) A5,A7: 7.. / A5 = 7 => 0 pairs (*) / A7 = 7 => 0 pairs (X) B3,B4: 7.. / B3 = 7 => 0 pairs (*) / B4 = 7 => 0 pairs (X) C3,C7: 7.. / C3 = 7 => 0 pairs (X) / C7 = 7 => 0 pairs (_) G4,G9: 7.. / G4 = 7 => 0 pairs (*) / G9 = 7 => 0 pairs (X) H1,H9: 7.. / H1 = 7 => 0 pairs (*) / H9 = 7 => 0 pairs (X) * DURATION: 0:01:06.710634 START: 08:17:16.807018 END: 08:18:23.517652 2017-05-04 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,A6,A7,B3,B4,C2,C7,D1,D3,G4,G9,H2,H6,I1,I4,I5) * 831.295..92.5781.35...31289..9385.2..8321495..527963.8.9.162835315847692268953... * PAIR C2: 4,6 BLK 1 C3: 4,6,7 # reduction candidate for 4,6 C3: 4,6 => SOLVED * 831629574924578163576431289649385721783214956152796348497162835315847692268953417 C3: 7 => CTR * 831.295..926578143547631289.7938542.683214957.527963.8.9.162835315847692268953... * PAIR B3: 4,7 BLK 1 C3: 4,7,6 # reduction candidate for 4,7 C3: 4,7 => CTR * 831.295..9265781435..631289..938542..83214957.527963.8.9.162835315847692268953... C3: 6 => SOLVED * 831629574924578163576431289649385721783214956152796348497162835315847692268953417 * PAIR D1: 4,6 ROW 1 H1: 4,6,7 # reduction candidate for 4,6 H1: 4,6 => CTR * 831.295.792.5781.35...31289..938572.783214956.527963484971628353158476922689534.. H1: 7 => SOLVED * 831629574924578163576431289649385721783214956152796348497162835315847692268953417 * PAIR D3: 4,6 ROW 3 C3: 4,6,7 # reduction candidate for 4,6 C3: 4,6 => SOLVED * 831629574924578163576431289649385721783214956152796348497162835315847692268953417 C3: 7 => CTR * 831.295..926578143547631289.7938542.683214957.527963.8.9.162835315847692268953... * PAIR I1: 4,7 BLK 3 H1: 4,7,6 # reduction candidate for 4,7 H1: 4,7 => SOLVED * 831629574924578163576431289649385721783214956152796348497162835315847692268953417 H1: 6 => CTR * 831.295679265781435..631289..9385.2..8321495..527963.8.9.162835315847692268953... * PAIR I1: 4,7 COL I I9: 4,7,1 # reduction candidate for 4,7 I9: 4,7 => SOLVED * 831629574924578163576431289649385721783214956152796348497162835315847692268953417 I9: 1 => CTR * 831.295.4924578163576431289.4938572.783214956152796348.9.162835315847692268953... * PAIR H2: 4,6 BLK 3 H1: 4,6,7 # reduction candidate for 4,6 H1: 4,6 => CTR * 831.295.792.5781.35...31289..938572.783214956.527963484971628353158476922689534.. H1: 7 => SOLVED * 831629574924578163576431289649385721783214956152796348497162835315847692268953417 * PAIR H6: 1,4 COL H H9: 1,4,7 # reduction candidate for 1,4 H9: 1,4 => SOLVED * 831629574924578163576431289649385721783214956152796348497162835315847692268953417 H9: 7 => CTR * 831.295..92.5781.35...31289..9385.2..8321495..52796318.9.162835315847692268953.71 * PAIR C7: 4,7 COL C C3: 4,7,6 # reduction candidate for 4,7 C3: 4,7 => CTR * 831.295..9265781435..631289..938542..83214957.527963.8.9.162835315847692268953... C3: 6 => SOLVED * 831629574924578163576431289649385721783214956152796348497162835315847692268953417 * PAIR G9: 4,7 BLK 9 H9: 4,7,1 # reduction candidate for 4,7 H9: 4,7 => CTR * 831.295.49245781635764312891.9385.2..8321495..52796318.9.162835315847692268953..1 H9: 1 => SOLVED * 831629574924578163576431289649385721783214956152796348497162835315847692268953417 I9: 4,7,1 # reduction candidate for 4,7 I9: 4,7 => SOLVED * 831629574924578163576431289649385721783214956152796348497162835315847692268953417 I9: 1 => CTR * 831.295.4924578163576431289.4938572.783214956152796348.9.162835315847692268953... * INCONCLUSIVE * SAVE PR GRAPH xx-top500-162-base-pr-000.dot * REASONING * PRF # C3: 4,6 => SOL * DIS # C3: 7 => CTR => C3: 4,6 * DIS # C3: 4,7 => CTR => C3: 6 * PRF # C3: 6 => SOL * DIS # H1: 4,6 => CTR => H1: 7 * PRF # H1: 7 => SOL * PRF # C3: 4,6 => SOL * DIS # C3: 7 => CTR => C3: 4,6 * PRF # H1: 4,7 => SOL * DIS # H1: 6 => CTR => H1: 4,7 * PRF # I9: 4,7 => SOL * DIS # I9: 1 => CTR => I9: 4,7 * DIS # H1: 4,6 => CTR => H1: 7 * PRF # H1: 7 => SOL * PRF # H9: 1,4 => SOL * DIS # H9: 7 => CTR => H9: 1,4 * DIS # C3: 4,7 => CTR => C3: 6 * PRF # C3: 6 => SOL * DIS # H9: 4,7 => CTR => H9: 1 * PRF # H9: 1 => SOL * PRF # I9: 4,7 => SOL * DIS # I9: 1 => CTR => I9: 4,7 * CNT 22 HDP CHAINS / 22 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,A6,A7,B3,B4,C2,C7,D1,D3,G4,G9,H2,H6,I1,I4,I5) * 831.295..92.5781.35...31289..9385.2..8321495..527963.8.9.162835315847692268953... * PAIR C2: 4,6 BLK 1 C3: 4,6,7 # reduction candidate for 4,6 C3: 4,6 => SOLVED * 831629574924578163576431289649385721783214956152796348497162835315847692268953417 * DURATION: 0:00:01.894408 START: 08:18:49.544597 END: 08:18:51.439005 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-162-base-pr-001.dot * REASONING * PRF # C3: 4,6 => SOL * STA C3: 4,6 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 162 solution: 831629574924578163576431289649385721783214956152796348497162835315847692268953417 info: 1821 FNBTWY S8.f 3648 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 831629574924578163576431289649385721783214956152796348497162835315847692268953417 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:
* PRF # C3: 4,6 => SOL * DIS # C3: 7 => CTR => C3: 4,6 * DIS # C3: 4,7 => CTR => C3: 6 * PRF # C3: 6 => SOL * DIS # H1: 4,6 => CTR => H1: 7 * PRF # H1: 7 => SOL * PRF # C3: 4,6 => SOL * DIS # C3: 7 => CTR => C3: 4,6 * PRF # H1: 4,7 => SOL * DIS # H1: 6 => CTR => H1: 4,7 * PRF # I9: 4,7 => SOL * DIS # I9: 1 => CTR => I9: 4,7 * DIS # H1: 4,6 => CTR => H1: 7 * PRF # H1: 7 => SOL * PRF # H9: 1,4 => SOL * DIS # H9: 7 => CTR => H9: 1,4 * DIS # C3: 4,7 => CTR => C3: 6 * PRF # C3: 6 => SOL * DIS # H9: 4,7 => CTR => H9: 1 * PRF # H9: 1 => SOL * PRF # I9: 4,7 => SOL * DIS # I9: 1 => CTR => I9: 4,7 * CNT 22 HDP CHAINS / 22 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C3: 4,6 => SOL * STA C3: 4,6 * CNT 1 HDP CHAINS / 1 HYP OPENED