Analysis of xx-top500-025-base.sdk
Contents
Original Sudoku
level: medium
position: 6...43.........1.......9.....71..2..3...6.....2.......4......35...8...6....2..... initial
Autosolve
position: 6.174352.....281..2...193...671.52433..462...1243.765.412976835...8.1462..62.4... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B5: 8,9 => CTR => B5: 5 * DIS # B3: 5,8 => CTR => B3: 4,7 * PRF # C5: 9 => SOL * DIS # B2: 7,9 => CTR => B2: 3,4,5 * DIS # B3: 7,8 => CTR => B3: 4,5 * PRF # B3: 4,5 => SOL * DIS # B5: 8,9 => CTR => B5: 5 * DIS # H5: 1 => CTR => H5: 8,9 * DIS # B9: 3 => CTR => B9: 5,8 * DIS # B9: 3,5 => CTR => B9: 8 * PRF # B9: 8 => SOL * DIS # H5: 1,9 => CTR => H5: 8 * PRF # H5: 8 => SOL * CNT 13 HDP CHAINS / 24 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B5: 8,9 => CTR => B5: 5 * DIS B5: 5 # B2: 7,9 => CTR => B2: 3,4 * DIS B5: 5 + B2: 3,4 # A2: 5 => CTR => A2: 7,9 * DIS B5: 5 + B2: 3,4 + A2: 7,9 # B3: 7,8 => CTR => B3: 4 * PRF B5: 5 + B2: 3,4 + A2: 7,9 + B3: 4 => SOL * STA B5: 5 + B2: 3,4 + A2: 7,9 + B3: 4 * CNT 5 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6...43.........1.......9.....71..2..3...6.....2.......4......35...8...6....2..... | initial |
| 6.174352.....281..2...193...671.52433..462...1243.765.412976835...8.1462..62.4... | autosolve |
| 691743528735628194248519376867195243359462781124387659412976835973851462586234917 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (21) B1: 8,9 C3: 5,8 D2: 5,6 D3: 5,6 I1: 8,9 H2: 7,9 I2: 4,6 H3: 7,8 I3: 4,6 A4: 8,9 E4: 8,9 E6: 8,9 G5: 7,9 I5: 1,7 I6: 8,9 A9: 5,8 E8: 3,5 E9: 3,5 G9: 7,9 H9: 1,9 I9: 1,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H5,I5: 1.. / H5 = 1 => 0 pairs (X) / I5 = 1 => 17 pairs (_) H9,I9: 1.. / H9 = 1 => 17 pairs (_) / I9 = 1 => 0 pairs (X) H5,H9: 1.. / H5 = 1 => 0 pairs (X) / H9 = 1 => 17 pairs (_) I5,I9: 1.. / I5 = 1 => 17 pairs (_) / I9 = 1 => 0 pairs (X) B2,C2: 3.. / B2 = 3 => 0 pairs (*) / C2 = 3 => 0 pairs (X) E8,E9: 3.. / E8 = 3 => 0 pairs (X) / E9 = 3 => 24 pairs (_) B9,E9: 3.. / B9 = 3 => 0 pairs (X) / E9 = 3 => 24 pairs (_) C2,C8: 3.. / C2 = 3 => 22 pairs (_) / C8 = 3 => 0 pairs (*) B2,B3: 4.. / B2 = 4 => 22 pairs (_) / B3 = 4 => 0 pairs (*) I2,I3: 4.. / I2 = 4 => 0 pairs (*) / I3 = 4 => 0 pairs (X) B2,I2: 4.. / B2 = 4 => 22 pairs (_) / I2 = 4 => 0 pairs (*) B3,I3: 4.. / B3 = 4 => 0 pairs (*) / I3 = 4 => 0 pairs (X) D2,D3: 5.. / D2 = 5 => 22 pairs (_) / D3 = 5 => 0 pairs (*) B5,C5: 5.. / B5 = 5 => 23 pairs (_) / C5 = 5 => 0 pairs (X) E8,E9: 5.. / E8 = 5 => 24 pairs (_) / E9 = 5 => 0 pairs (X) D2,D3: 6.. / D2 = 6 => 0 pairs (*) / D3 = 6 => 0 pairs (X) I2,I3: 6.. / I2 = 6 => 22 pairs (_) / I3 = 6 => 0 pairs (*) D2,I2: 6.. / D2 = 6 => 0 pairs (*) / I2 = 6 => 0 pairs (X) D3,I3: 6.. / D3 = 6 => 22 pairs (_) / I3 = 6 => 0 pairs (*) H2,H3: 7.. / H2 = 7 => 0 pairs (X) / H3 = 7 => 0 pairs (_) G5,I5: 7.. / G5 = 7 => 17 pairs (_) / I5 = 7 => 0 pairs (X) A8,B8: 7.. / A8 = 7 => 25 pairs (_) / B8 = 7 => 0 pairs (*) G9,I9: 7.. / G9 = 7 => 0 pairs (X) / I9 = 7 => 17 pairs (_) B3,H3: 7.. / B3 = 7 => 0 pairs (X) / H3 = 7 => 0 pairs (_) A2,A8: 7.. / A2 = 7 => 0 pairs (*) / A8 = 7 => 0 pairs (X) G5,G9: 7.. / G5 = 7 => 17 pairs (_) / G9 = 7 => 0 pairs (X) I5,I9: 7.. / I5 = 7 => 0 pairs (X) / I9 = 7 => 17 pairs (_) I1,H3: 8.. / I1 = 8 => 0 pairs (*) / H3 = 8 => 0 pairs (X) E4,E6: 8.. / E4 = 8 => 0 pairs (X) / E6 = 8 => 0 pairs (_) H5,I6: 8.. / H5 = 8 => 0 pairs (*) / I6 = 8 => 0 pairs (X) A9,B9: 8.. / A9 = 8 => 0 pairs (X) / B9 = 8 => 0 pairs (_) B1,I1: 8.. / B1 = 8 => 0 pairs (X) / I1 = 8 => 0 pairs (_) A4,E4: 8.. / A4 = 8 => 0 pairs (*) / E4 = 8 => 0 pairs (X) E6,I6: 8.. / E6 = 8 => 0 pairs (*) / I6 = 8 => 0 pairs (X) A4,A9: 8.. / A4 = 8 => 0 pairs (*) / A9 = 8 => 0 pairs (X) C3,C5: 8.. / C3 = 8 => 0 pairs (*) / C5 = 8 => 0 pairs (X) H3,H5: 8.. / H3 = 8 => 0 pairs (X) / H5 = 8 => 0 pairs (_) I1,I6: 8.. / I1 = 8 => 0 pairs (*) / I6 = 8 => 0 pairs (X) I1,H2: 9.. / I1 = 9 => 0 pairs (X) / H2 = 9 => 0 pairs (_) E4,E6: 9.. / E4 = 9 => 0 pairs (*) / E6 = 9 => 0 pairs (X) G9,H9: 9.. / G9 = 9 => 17 pairs (_) / H9 = 9 => 0 pairs (X) B1,I1: 9.. / B1 = 9 => 0 pairs (*) / I1 = 9 => 0 pairs (X) A4,E4: 9.. / A4 = 9 => 0 pairs (X) / E4 = 9 => 0 pairs (_) E6,I6: 9.. / E6 = 9 => 0 pairs (X) / I6 = 9 => 0 pairs (_) G5,G9: 9.. / G5 = 9 => 0 pairs (X) / G9 = 9 => 17 pairs (_) I1,I6: 9.. / I1 = 9 => 0 pairs (X) / I6 = 9 => 0 pairs (_) * DURATION: 0:01:25.715749 START: 03:27:17.184895 END: 03:28:42.900644 2017-05-04 * CP COUNT: (46) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A9,B1,C3,D2,D3,E4,E6,E8,E9,G5,G9,H2,H3,H9,I1,I2,I3,I5,I6,I9) * 6.174352.....281..2...193...671.52433..462...1243.765.412976835...8.1462..62.4... * PAIR B1: 8,9 COL B B5: 8,9,5 # reduction candidate for 8,9 B5: 8,9 => CTR * 6.174352.....281..2.8.1937..671.52433.5462.81124387659412976835...8.1462.86234917 B5: 5 # 23 pairs * PAIR C3: 5,8 BLK 1 B3: 5,8,4,7 # reduction candidate for 5,8 B3: 5,8 => CTR * 6917435287435281962856193748671.52433..462.81124387659412976835.7.831462.36254917 B3: 4,7 # 22 pairs * PAIR C3: 5,8 COL C C5: 5,8,9 # reduction candidate for 5,8 C5: 9 => SOLVED * 691743528735628194248519376867195243359462781124387659412976835973851462586234917 C5: 5,8 # 24 pairs * PAIR H2: 7,9 ROW 2 A2: 7,9,5 # reduction candidate for 7,9 A2: 7,9 # 25 pairs B2: 7,9,3,4,5 # reduction candidate for 7,9 B2: 7,9 => CTR * 691743528.73628194248519376867195243359462781124387659412976835...8.1462..62.4917 B2: 3,4,5 # 21 pairs * PAIR H3: 7,8 ROW 3 B3: 7,8,4,5 # reduction candidate for 7,8 B3: 7,8 => CTR * 6.174352..435281.62.56193.4.671.5243358462...1243.7658412976835..98.14628362.4... B3: 4,5 => SOLVED * 691743528735628194248519376867195243359462781124387659412976835973851462586234917 * PAIR A4: 8,9 BLK 4 B5: 8,9,5 # reduction candidate for 8,9 B5: 8,9 => CTR * 6.174352.....281..2.8.1937..671.52433.5462.81124387659412976835...8.1462.86234917 B5: 5 # 23 pairs C5: 8,9,5 # reduction candidate for 8,9 C5: 8,9 # 23 pairs * PAIR I6: 8,9 BLK 6 H5: 8,9,1 # reduction candidate for 8,9 H5: 1 => CTR * 681743529....2817.2756193849671.52433.8462.171243.7658412976835...8.14628.62.4791 H5: 8,9 # 17 pairs * PAIR A9: 5,8 BLK 7 B9: 5,8,3 # reduction candidate for 5,8 B9: 3 => CTR * 681743529.93.281742...193..9671852433..462...124397658412976835..9831462836254... B9: 5,8 # 24 pairs * PAIR E8: 3,5 ROW 8 B8: 3,5,7,9 # reduction candidate for 3,5 B8: 3,5 # 26 pairs C8: 3,5,9 # reduction candidate for 3,5 C8: 3,5 # 24 pairs * PAIR E9: 3,5 ROW 9 B9: 3,5,8 # reduction candidate for 3,5 B9: 3,5 => CTR * 681743529....2817.275.193..9671852433..462...124397658412976835...8.14628.62.4... B9: 8 => SOLVED * 691743528735628194248519376867195243359462781124387659412976835973851462586234917 * PAIR H9: 1,9 COL H H5: 1,9,8 # reduction candidate for 1,9 H5: 1,9 => CTR * 681743529....2817.2756193849671.52433.8462...1243.7658412976835...8.14628.62.4... H5: 8 => SOLVED * 691743528735628194248519376867195243359462781124387659412976835973851462586234917 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-025-base-pr-000.dot * REASONING * DIS # B5: 8,9 => CTR => B5: 5 * DIS # B3: 5,8 => CTR => B3: 4,7 * PRF # C5: 9 => SOL * DIS # B2: 7,9 => CTR => B2: 3,4,5 * DIS # B3: 7,8 => CTR => B3: 4,5 * PRF # B3: 4,5 => SOL * DIS # B5: 8,9 => CTR => B5: 5 * DIS # H5: 1 => CTR => H5: 8,9 * DIS # B9: 3 => CTR => B9: 5,8 * DIS # B9: 3,5 => CTR => B9: 8 * PRF # B9: 8 => SOL * DIS # H5: 1,9 => CTR => H5: 8 * PRF # H5: 8 => SOL * CNT 13 HDP CHAINS / 24 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A9,B1,C3,D2,D3,E4,E6,E8,E9,G5,G9,H2,H3,H9,I1,I2,I3,I5,I6,I9) * 6.174352.....281..2...193...671.52433..462...1243.765.412976835...8.1462..62.4... * PAIR B1: 8,9 COL B B5: 8,9,5 # reduction candidate for 8,9 B5: 8,9 => CTR * 6.174352.....281..2.8.1937..671.52433.5462.81124387659412976835...8.1462.86234917 * PAIR RESTART * PAIR H2: 7,9 ROW 2 A2: 7,9,5 # reduction candidate for 7,9 A2: 7,9 # 27 pairs B2: 7,9,3,4 # reduction candidate for 7,9 B2: 7,9 => CTR * 691743528.73628194248519376867195243359462781124387659412976835...8.1462..62.4917 * RESTART * PAIR H2: 7,9 ROW 2 A2: 7,9,5 # reduction candidate for 7,9 A2: 5 => CTR * 6.174352.5..6281742...193...671.524335.462...1243.765.412976835...8.1462..62.4... * PAIR RESTART * PAIR H3: 7,8 ROW 3 B3: 7,8,4 # reduction candidate for 7,8 B3: 7,8 => CTR * 6.174352..435281.62.56193.4.671.5243358462...1243.7658412976835..98.14628362.4... B3: 4 => SOLVED * 691743528735628194248519376867195243359462781124387659412976835973851462586234917 * DURATION: 0:00:09.699346 START: 03:29:09.409334 END: 03:29:19.108680 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-025-base-pr-001.dot * REASONING * DIS # B5: 8,9 => CTR => B5: 5 * DIS B5: 5 # B2: 7,9 => CTR => B2: 3,4 * DIS B5: 5 + B2: 3,4 # A2: 5 => CTR => A2: 7,9 * DIS B5: 5 + B2: 3,4 + A2: 7,9 # B3: 7,8 => CTR => B3: 4 * PRF B5: 5 + B2: 3,4 + A2: 7,9 + B3: 4 => SOL * STA B5: 5 + B2: 3,4 + A2: 7,9 + B3: 4 * CNT 5 HDP CHAINS / 6 HYP OPENED
Header Info
Top 500 Minimum 17 025 solution: 691743528735628194248519376867195243359462781124387659412976835973851462586234917 info: 1321 FNBTWXY S8.f 39507 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 691743528735628194248519376867195243359462781124387659412976835973851462586234917 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 # B5: 8,9 => CTR => B5: 5 * INC # B5: 5 => UNS * DIS # B3: 5,8 => CTR => B3: 4,7 * INC # B3: 4,7 => UNS * INC # C5: 5,8 => UNS * PRF # C5: 9 => SOL * INC # A2: 7,9 => UNS * DIS # B2: 7,9 => CTR => B2: 3,4,5 * INC # B2: 3,4,5 => UNS * DIS # B3: 7,8 => CTR => B3: 4,5 * PRF # B3: 4,5 => SOL * DIS # B5: 8,9 => CTR => B5: 5 * INC # B5: 5 => UNS * INC # C5: 8,9 => UNS * INC # H5: 8,9 => UNS * DIS # H5: 1 => CTR => H5: 8,9 * INC # B9: 5,8 => UNS * DIS # B9: 3 => CTR => B9: 5,8 * INC # B8: 3,5 => UNS * INC # C8: 3,5 => UNS * DIS # B9: 3,5 => CTR => B9: 8 * PRF # B9: 8 => SOL * DIS # H5: 1,9 => CTR => H5: 8 * PRF # H5: 8 => SOL * CNT 24 HDP CHAINS / 24 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B5: 8,9 => CTR => B5: 5 * INC B5: 5 # A2: 7,9 => UNS * DIS B5: 5 # B2: 7,9 => CTR => B2: 3,4 * INC B5: 5 + B2: 3,4 # A2: 7,9 => UNS * DIS B5: 5 + B2: 3,4 # A2: 5 => CTR => A2: 7,9 * DIS B5: 5 + B2: 3,4 + A2: 7,9 # B3: 7,8 => CTR => B3: 4 * PRF B5: 5 + B2: 3,4 + A2: 7,9 + B3: 4 => SOL * STA B5: 5 + B2: 3,4 + A2: 7,9 + B3: 4 * CNT 7 HDP CHAINS / 6 HYP OPENED