Analysis of xx-top500-250-base.sdk
Contents
Original Sudoku
level: medium
position: 6..1......9.....8...........84....9....2..3...7...6.......87...1...3....2.....6.. initial
Autosolve
position: 62.1789.479..6..8284..2976.5847132969162..3783728964154.9.87.2.1.7.328.92.89.16.7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 3,5 => CTR => C2: 1 * PRF # C2: 1 => SOL * PRF # C3: 3,5 => SOL * DIS # C3: 1 => CTR => C3: 3,5 * DIS # D2: 4,5 => CTR => D2: 3 * PRF # D2: 3 => SOL * PRF # D2: 3,5 => SOL * DIS # D2: 4 => CTR => D2: 3,5 * PRF # C3: 3,5 => SOL * DIS # C3: 1 => CTR => C3: 3,5 * DIS # H9: 3,5 => CTR => H9: 4 * PRF # H9: 4 => SOL * PRF # C2: 1,5 => SOL * DIS # C2: 3 => CTR => C2: 1,5 * PRF # C3: 1,3 => SOL * DIS # C3: 5 => CTR => C3: 1,3 * PRF # B7: 5,6 => SOL * DIS # B7: 3 => CTR => B7: 5,6 * DIS # D8: 5,6 => CTR => D8: 4 * PRF # D8: 4 => SOL * DIS # B7: 6 => CTR => B7: 3,5 * DIS # H9: 3,5 => CTR => H9: 4 * PRF # H9: 4 => SOL * DIS # D8: 5,6 => CTR => D8: 4 * PRF # D8: 4 => SOL * PRF # B7: 5,6 => SOL * DIS # B7: 3 => CTR => B7: 5,6 * DIS # D8: 6 => CTR => D8: 4,5 * PRF # H9: 4,5 => SOL * DIS # H9: 3 => CTR => H9: 4,5 * PRF # H9: 4,5 => SOL * DIS # H9: 3 => CTR => H9: 4,5 * DIS # D8: 6 => CTR => D8: 4,5 * CNT 33 HDP CHAINS / 36 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C2: 3,5 => CTR => C2: 1 * PRF C2: 1 => SOL * STA C2: 1 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6..1......9.....8...........84....9....2..3...7...6.......87...1...3....2.....6.. | initial |
| 62.1789.479..6..8284..2976.5847132969162..3783728964154.9.87.2.1.7.328.92.89.16.7 | autosolve |
| 625178934791364582843529761584713296916245378372896415459687123167432859238951647 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) C1: 3,5 F2: 4,5 D3: 3,5 H1: 3,5 G2: 1,5 I3: 1,3 E5: 4,5 F5: 4,5 B8: 5,6 B9: 3,5 D7: 5,6 E9: 4,5 G7: 1,5 I7: 1,3 H8: 4,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,C3: 1.. / C2 = 1 => 0 pairs (*) / C3 = 1 => 0 pairs (X) G2,I3: 1.. / G2 = 1 => 0 pairs (X) / I3 = 1 => 0 pairs (_) G7,I7: 1.. / G7 = 1 => 0 pairs (*) / I7 = 1 => 0 pairs (X) C2,G2: 1.. / C2 = 1 => 0 pairs (*) / G2 = 1 => 0 pairs (X) C3,I3: 1.. / C3 = 1 => 0 pairs (X) / I3 = 1 => 0 pairs (_) G2,G7: 1.. / G2 = 1 => 0 pairs (X) / G7 = 1 => 0 pairs (_) I3,I7: 1.. / I3 = 1 => 0 pairs (*) / I7 = 1 => 0 pairs (X) D2,D3: 3.. / D2 = 3 => 0 pairs (*) / D3 = 3 => 0 pairs (X) H1,I3: 3.. / H1 = 3 => 0 pairs (*) / I3 = 3 => 0 pairs (X) B7,B9: 3.. / B7 = 3 => 0 pairs (X) / B9 = 3 => 0 pairs (_) I7,H9: 3.. / I7 = 3 => 0 pairs (*) / H9 = 3 => 0 pairs (X) C1,H1: 3.. / C1 = 3 => 0 pairs (X) / H1 = 3 => 0 pairs (_) C2,D2: 3.. / C2 = 3 => 0 pairs (X) / D2 = 3 => 0 pairs (_) B7,I7: 3.. / B7 = 3 => 0 pairs (X) / I7 = 3 => 0 pairs (_) B9,H9: 3.. / B9 = 3 => 0 pairs (*) / H9 = 3 => 0 pairs (X) H1,H9: 3.. / H1 = 3 => 0 pairs (*) / H9 = 3 => 0 pairs (X) I3,I7: 3.. / I3 = 3 => 0 pairs (X) / I7 = 3 => 0 pairs (_) D2,F2: 4.. / D2 = 4 => 0 pairs (X) / F2 = 4 => 0 pairs (_) E5,F5: 4.. / E5 = 4 => 0 pairs (*) / F5 = 4 => 0 pairs (X) D8,E9: 4.. / D8 = 4 => 0 pairs (*) / E9 = 4 => 0 pairs (X) H8,H9: 4.. / H8 = 4 => 0 pairs (X) / H9 = 4 => 0 pairs (_) D8,H8: 4.. / D8 = 4 => 0 pairs (*) / H8 = 4 => 0 pairs (X) E9,H9: 4.. / E9 = 4 => 0 pairs (X) / H9 = 4 => 0 pairs (_) D2,D8: 4.. / D2 = 4 => 0 pairs (X) / D8 = 4 => 0 pairs (_) E5,E9: 4.. / E5 = 4 => 0 pairs (*) / E9 = 4 => 0 pairs (X) F2,F5: 4.. / F2 = 4 => 0 pairs (*) / F5 = 4 => 0 pairs (X) H1,G2: 5.. / H1 = 5 => 0 pairs (X) / G2 = 5 => 0 pairs (_) E5,F5: 5.. / E5 = 5 => 0 pairs (X) / F5 = 5 => 0 pairs (_) C1,H1: 5.. / C1 = 5 => 0 pairs (*) / H1 = 5 => 0 pairs (X) C3,D3: 5.. / C3 = 5 => 0 pairs (X) / D3 = 5 => 0 pairs (_) E5,E9: 5.. / E5 = 5 => 0 pairs (X) / E9 = 5 => 0 pairs (_) F2,F5: 5.. / F2 = 5 => 0 pairs (X) / F5 = 5 => 0 pairs (_) G2,G7: 5.. / G2 = 5 => 0 pairs (*) / G7 = 5 => 0 pairs (X) B7,B8: 6.. / B7 = 6 => 0 pairs (X) / B8 = 6 => 15 pairs (_) D7,D8: 6.. / D7 = 6 => 15 pairs (_) / D8 = 6 => 0 pairs (X) B7,D7: 6.. / B7 = 6 => 0 pairs (X) / D7 = 6 => 15 pairs (_) B8,D8: 6.. / B8 = 6 => 15 pairs (_) / D8 = 6 => 0 pairs (X) * DURATION: 0:01:02.519974 START: 11:20:08.454026 END: 11:21:10.974000 2017-05-04 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,B9,C1,D3,D7,E5,E9,F2,F5,G2,G7,H1,H8,I3,I7) * 62.1789.479..6..8284..2976.5847132969162..3783728964154.9.87.2.1.7.328.92.89.16.7 * PAIR C1: 3,5 BLK 1 C2: 3,5,1 # reduction candidate for 3,5 C2: 3,5 => CTR * 62.1789.479..6.1828415297635847132969162.53783728964154396875211.7.328.92.89.16.7 C2: 1 => SOLVED * 625178934791364582843529761584713296916245378372896415459687123167432859238951647 C3: 3,5,1 # reduction candidate for 3,5 C3: 3,5 => SOLVED * 625178934791364582843529761584713296916245378372896415459687123167432859238951647 C3: 1 => CTR * 62.1789.479..6..828415297635847132969162.53783728964154396875211.7.328.92.89.16.7 * PAIR F2: 4,5 BLK 2 D2: 4,5,3 # reduction candidate for 4,5 D2: 4,5 => CTR * 62.1789.4793.6.182841.2976.5847132969162..3783728964154.9.87.2.1.7.328.92.89.16.7 D2: 3 => SOLVED * 625178934791364582843529761584713296916245378372896415459687123167432859238951647 * PAIR D3: 3,5 BLK 2 D2: 3,5,4 # reduction candidate for 3,5 D2: 3,5 => SOLVED * 625178934791364582843529761584713296916245378372896415459687123167432859238951647 D2: 4 => CTR * 62.1789.479346518284..2976.5847132969162..3783728964154.9.87.2.1.7.328.92.89.16.7 * PAIR D3: 3,5 ROW 3 C3: 3,5,1 # reduction candidate for 3,5 C3: 3,5 => SOLVED * 625178934791364582843529761584713296916245378372896415459687123167432859238951647 C3: 1 => CTR * 62.1789.479..6..828415297635847132969162.53783728964154396875211.7.328.92.89.16.7 * PAIR H1: 3,5 COL H H9: 3,5,4 # reduction candidate for 3,5 H9: 3,5 => CTR * 62.1789.479.46518284..2976.5847132969162..3783728964154.9.87.2.1.7.328492.89416.7 H9: 4 => SOLVED * 625178934791364582843529761584713296916245378372896415459687123167432859238951647 * PAIR G2: 1,5 ROW 2 C2: 1,5,3 # reduction candidate for 1,5 C2: 1,5 => SOLVED * 625178934791364582843529761584713296916245378372896415459687123167432859238951647 C2: 3 => CTR * 62.1789.4793.6.182841.2976.5847132969162..3783728964154.9.87.2.1.7.328.92.89.16.7 * PAIR I3: 1,3 ROW 3 C3: 1,3,5 # reduction candidate for 1,3 C3: 1,3 => SOLVED * 625178934791364582843529761584713296916245378372896415459687123167432859238951647 C3: 5 => CTR * 62.1789.479136458284..2976.5847132969162..3783728964154.9.87.2.1.7.328.92.89.16.7 * PAIR B8: 5,6 BLK 7 B7: 5,6,3 # reduction candidate for 5,6 B7: 5,6 => SOLVED * 625178934791364582843529761584713296916245378372896415459687123167432859238951647 B7: 3 => CTR * 62.1789.479..6..8284..2976.5847132969162..378372896415439687521167532849258941637 * PAIR B8: 5,6 ROW 8 D8: 5,6,4 # reduction candidate for 5,6 D8: 5,6 => CTR * 62.1789.479.46518284..2976.5847132969162..3783728964154.9.87.2.1.7.328.92.89.16.7 D8: 4 => SOLVED * 625178934791364582843529761584713296916245378372896415459687123167432859238951647 * PAIR B9: 3,5 BLK 7 B7: 3,5,6 # reduction candidate for 3,5 B7: 6 => CTR * 625178934791.6..8284..2976.5847132969162..378372896415469587123157632849238941657 B7: 3,5 # 15 pairs * PAIR B9: 3,5 ROW 9 H9: 3,5,4 # reduction candidate for 3,5 H9: 3,5 => CTR * 62.1789.479.46518284..2976.5847132969162..3783728964154.9.87.2.1.7.328492.89416.7 H9: 4 => SOLVED * 625178934791364582843529761584713296916245378372896415459687123167432859238951647 * PAIR D7: 5,6 BLK 8 D8: 5,6,4 # reduction candidate for 5,6 D8: 5,6 => CTR * 62.1789.479.46518284..2976.5847132969162..3783728964154.9.87.2.1.7.328.92.89.16.7 D8: 4 => SOLVED * 625178934791364582843529761584713296916245378372896415459687123167432859238951647 * PAIR D7: 5,6 ROW 7 B7: 5,6,3 # reduction candidate for 5,6 B7: 5,6 => SOLVED * 625178934791364582843529761584713296916245378372896415459687123167432859238951647 B7: 3 => CTR * 62.1789.479..6..8284..2976.5847132969162..378372896415439687521167532849258941637 * PAIR E9: 4,5 BLK 8 D8: 4,5,6 # reduction candidate for 4,5 D8: 6 => CTR * 62.1789.479.46518284..2976.5847132969162..3783728964154.9.87.2.1.7.328.92.89.16.7 D8: 4,5 # 15 pairs * PAIR E9: 4,5 ROW 9 H9: 4,5,3 # reduction candidate for 4,5 H9: 4,5 => SOLVED * 625178934791364582843529761584713296916245378372896415459687123167432859238951647 H9: 3 => CTR * 62317895479..6..8284..2976.5847132969162..3783728964154.9.87.2.1.7.328492.8941637 * PAIR H8: 4,5 BLK 9 H9: 4,5,3 # reduction candidate for 4,5 H9: 4,5 => SOLVED * 625178934791364582843529761584713296916245378372896415459687123167432859238951647 H9: 3 => CTR * 62317895479..6..8284..2976.5847132969162..3783728964154.9.87.2.1.7.328492.8941637 * PAIR H8: 4,5 ROW 8 D8: 4,5,6 # reduction candidate for 4,5 D8: 6 => CTR * 62.1789.479.46518284..2976.5847132969162..3783728964154.9.87.2.1.7.328.92.89.16.7 D8: 4,5 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-250-base-pr-000.dot * REASONING * DIS # C2: 3,5 => CTR => C2: 1 * PRF # C2: 1 => SOL * PRF # C3: 3,5 => SOL * DIS # C3: 1 => CTR => C3: 3,5 * DIS # D2: 4,5 => CTR => D2: 3 * PRF # D2: 3 => SOL * PRF # D2: 3,5 => SOL * DIS # D2: 4 => CTR => D2: 3,5 * PRF # C3: 3,5 => SOL * DIS # C3: 1 => CTR => C3: 3,5 * DIS # H9: 3,5 => CTR => H9: 4 * PRF # H9: 4 => SOL * PRF # C2: 1,5 => SOL * DIS # C2: 3 => CTR => C2: 1,5 * PRF # C3: 1,3 => SOL * DIS # C3: 5 => CTR => C3: 1,3 * PRF # B7: 5,6 => SOL * DIS # B7: 3 => CTR => B7: 5,6 * DIS # D8: 5,6 => CTR => D8: 4 * PRF # D8: 4 => SOL * DIS # B7: 6 => CTR => B7: 3,5 * DIS # H9: 3,5 => CTR => H9: 4 * PRF # H9: 4 => SOL * DIS # D8: 5,6 => CTR => D8: 4 * PRF # D8: 4 => SOL * PRF # B7: 5,6 => SOL * DIS # B7: 3 => CTR => B7: 5,6 * DIS # D8: 6 => CTR => D8: 4,5 * PRF # H9: 4,5 => SOL * DIS # H9: 3 => CTR => H9: 4,5 * PRF # H9: 4,5 => SOL * DIS # H9: 3 => CTR => H9: 4,5 * DIS # D8: 6 => CTR => D8: 4,5 * CNT 33 HDP CHAINS / 36 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,B9,C1,D3,D7,E5,E9,F2,F5,G2,G7,H1,H8,I3,I7) * 62.1789.479..6..8284..2976.5847132969162..3783728964154.9.87.2.1.7.328.92.89.16.7 * PAIR C1: 3,5 BLK 1 C2: 3,5,1 # reduction candidate for 3,5 C2: 3,5 => CTR * 62.1789.479..6.1828415297635847132969162.53783728964154396875211.7.328.92.89.16.7 C2: 1 => SOLVED * 625178934791364582843529761584713296916245378372896415459687123167432859238951647 * DURATION: 0:00:01.621903 START: 11:21:50.441698 END: 11:21:52.063601 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-250-base-pr-001.dot * REASONING * DIS # C2: 3,5 => CTR => C2: 1 * PRF C2: 1 => SOL * STA C2: 1 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 250 solution: 625178934791364582843529761584713296916245378372896415459687123167432859238951647 info: 2073 FNBWXY S8.f 34806 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 625178934791364582843529761584713296916245378372896415459687123167432859238951647 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 # C2: 3,5 => CTR => C2: 1 * PRF # C2: 1 => SOL * PRF # C3: 3,5 => SOL * DIS # C3: 1 => CTR => C3: 3,5 * DIS # D2: 4,5 => CTR => D2: 3 * PRF # D2: 3 => SOL * PRF # D2: 3,5 => SOL * DIS # D2: 4 => CTR => D2: 3,5 * PRF # C3: 3,5 => SOL * DIS # C3: 1 => CTR => C3: 3,5 * DIS # H9: 3,5 => CTR => H9: 4 * PRF # H9: 4 => SOL * PRF # C2: 1,5 => SOL * DIS # C2: 3 => CTR => C2: 1,5 * PRF # C3: 1,3 => SOL * DIS # C3: 5 => CTR => C3: 1,3 * PRF # B7: 5,6 => SOL * DIS # B7: 3 => CTR => B7: 5,6 * DIS # D8: 5,6 => CTR => D8: 4 * PRF # D8: 4 => SOL * INC # B7: 3,5 => UNS * DIS # B7: 6 => CTR => B7: 3,5 * DIS # H9: 3,5 => CTR => H9: 4 * PRF # H9: 4 => SOL * DIS # D8: 5,6 => CTR => D8: 4 * PRF # D8: 4 => SOL * PRF # B7: 5,6 => SOL * DIS # B7: 3 => CTR => B7: 5,6 * INC # D8: 4,5 => UNS * DIS # D8: 6 => CTR => D8: 4,5 * PRF # H9: 4,5 => SOL * DIS # H9: 3 => CTR => H9: 4,5 * PRF # H9: 4,5 => SOL * DIS # H9: 3 => CTR => H9: 4,5 * INC # D8: 4,5 => UNS * DIS # D8: 6 => CTR => D8: 4,5 * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C2: 3,5 => CTR => C2: 1 * PRF C2: 1 => SOL * STA C2: 1 * CNT 2 HDP CHAINS / 1 HYP OPENED