Analysis of xx-top500-048-base.sdk
Contents
Original Sudoku
level: medium
position: .9...7..1.62.........3..........25..8.....3......6..8.....4..2.5..8.....3........ initial
Autosolve
position: 493257861.624.8.35...3.62..93.1825.68.6.743.22...63.8.6..745.2352.83.6..3..62..58 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I3: 7,9 => CTR => I3: 4 * DIS # G6: 7,9 => CTR => G6: 1,4 * DIS # G9: 7,9 => CTR => G9: 1,4 * PRF # C9: 4,7 => SOL * PRF # G6: 4,7 => SOL * DIS # G6: 1,9 => CTR => G6: 4,7 * DIS # I6: 4,7 => CTR => I6: 9 * PRF # I6: 9 => SOL * PRF # G6: 4,7 => SOL * DIS # G6: 1,9 => CTR => G6: 4,7 * DIS # I6: 4,7 => CTR => I6: 9 * PRF # I6: 9 => SOL * PRF # H8: 4,7 => SOL * DIS # G6: 1,9 => CTR => G6: 4,7 * PRF # G6: 4,7 => SOL * PRF # H8: 4,7 => SOL * DIS # C7: 9 => CTR => C7: 1,8 * PRF # C9: 4,7 => SOL * PRF # G9: 1,9 => SOL * PRF # C8: 1,9 => SOL * PRF # G9: 1,9 => SOL * PRF # G9: 1,9 => SOL * DIS # C7: 1,9 => CTR => C7: 8 * PRF # C7: 8 => SOL * DIS # G6: 1,9 => CTR => G6: 4,7 * PRF # G6: 4,7 => SOL * CNT 26 HDP CHAINS / 45 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I3: 7,9 => CTR => I3: 4 * DIS I3: 4 # G6: 7,9 => CTR => G6: 1,4 * DIS I3: 4 + G6: 1,4 # G9: 7,9 => CTR => G9: 1,4 * PRF I3: 4 + G6: 1,4 + G9: 1,4 => SOL * STA I3: 4 + G6: 1,4 + G9: 1,4 * CNT 4 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .9...7..1.62.........3..........25..8.....3......6..8.....4..2.5..8.....3........ | initial |
| 493257861.624.8.35...3.62..93.1825.68.6.743.22...63.8.6..745.2352.83.6..3..62..58 | autosolve |
| 493257861162498735785316294934182576856974312271563489618745923529831647347629158 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) A2: 1,7 A3: 1,7 B3: 5,8 C3: 5,8 E2: 1,9 E3: 1,9 G2: 7,9 C4: 4,7 B5: 1,5 B6: 4,7 C6: 1,5 D5: 5,9 D6: 5,9 H4: 4,7 H5: 1,9 B7: 1,8 B9: 4,7 F8: 1,9 F9: 1,9 G7: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,A3: 1.. / A2 = 1 => 17 pairs (_) / A3 = 1 => 0 pairs (X) E2,E3: 1.. / E2 = 1 => 0 pairs (X) / E3 = 1 => 17 pairs (_) B5,C6: 1.. / B5 = 1 => 0 pairs (X) / C6 = 1 => 0 pairs (_) H5,G6: 1.. / H5 = 1 => 0 pairs (*) / G6 = 1 => 0 pairs (X) F8,F9: 1.. / F8 = 1 => 0 pairs (*) / F9 = 1 => 0 pairs (X) A2,E2: 1.. / A2 = 1 => 17 pairs (_) / E2 = 1 => 0 pairs (X) A3,E3: 1.. / A3 = 1 => 0 pairs (X) / E3 = 1 => 17 pairs (_) B5,H5: 1.. / B5 = 1 => 0 pairs (X) / H5 = 1 => 0 pairs (_) C6,G6: 1.. / C6 = 1 => 0 pairs (*) / G6 = 1 => 0 pairs (X) B5,B7: 1.. / B5 = 1 => 0 pairs (X) / B7 = 1 => 0 pairs (_) H5,H8: 1.. / H5 = 1 => 0 pairs (*) / H8 = 1 => 0 pairs (X) H3,I3: 4.. / H3 = 4 => 0 pairs (X) / I3 = 4 => 23 pairs (_) C4,B6: 4.. / C4 = 4 => 0 pairs (*) / B6 = 4 => 0 pairs (X) C4,H4: 4.. / C4 = 4 => 0 pairs (*) / H4 = 4 => 0 pairs (X) B6,B9: 4.. / B6 = 4 => 20 pairs (_) / B9 = 4 => 0 pairs (*) G6,G9: 4.. / G6 = 4 => 0 pairs (*) / G9 = 4 => 0 pairs (X) B3,C3: 5.. / B3 = 5 => 0 pairs (X) / C3 = 5 => 0 pairs (_) B5,C6: 5.. / B5 = 5 => 0 pairs (*) / C6 = 5 => 0 pairs (X) D5,D6: 5.. / D5 = 5 => 0 pairs (X) / D6 = 5 => 0 pairs (_) B5,D5: 5.. / B5 = 5 => 0 pairs (*) / D5 = 5 => 0 pairs (X) C6,D6: 5.. / C6 = 5 => 0 pairs (X) / D6 = 5 => 0 pairs (_) B3,B5: 5.. / B3 = 5 => 0 pairs (X) / B5 = 5 => 0 pairs (_) C3,C6: 5.. / C3 = 5 => 0 pairs (*) / C6 = 5 => 0 pairs (X) A2,A3: 7.. / A2 = 7 => 0 pairs (X) / A3 = 7 => 17 pairs (_) C4,B6: 7.. / C4 = 7 => 20 pairs (_) / B6 = 7 => 0 pairs (*) A2,G2: 7.. / A2 = 7 => 0 pairs (X) / G2 = 7 => 17 pairs (_) C4,H4: 7.. / C4 = 7 => 20 pairs (_) / H4 = 7 => 0 pairs (*) B6,B9: 7.. / B6 = 7 => 0 pairs (*) / B9 = 7 => 0 pairs (X) B3,C3: 8.. / B3 = 8 => 0 pairs (*) / C3 = 8 => 0 pairs (X) B7,C7: 8.. / B7 = 8 => 0 pairs (X) / C7 = 8 => 0 pairs (_) B3,B7: 8.. / B3 = 8 => 0 pairs (*) / B7 = 8 => 0 pairs (X) C3,C7: 8.. / C3 = 8 => 0 pairs (X) / C7 = 8 => 0 pairs (_) E2,E3: 9.. / E2 = 9 => 17 pairs (_) / E3 = 9 => 0 pairs (X) D5,D6: 9.. / D5 = 9 => 0 pairs (*) / D6 = 9 => 0 pairs (X) F8,F9: 9.. / F8 = 9 => 19 pairs (_) / F9 = 9 => 0 pairs (*) E2,G2: 9.. / E2 = 9 => 17 pairs (_) / G2 = 9 => 0 pairs (X) D5,H5: 9.. / D5 = 9 => 0 pairs (*) / H5 = 9 => 0 pairs (X) C7,G7: 9.. / C7 = 9 => 0 pairs (X) / G7 = 9 => 21 pairs (_) * DURATION: 0:01:07.443038 START: 04:18:12.082782 END: 04:19:19.525820 2017-05-04 * CP COUNT: (38) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,B3,B5,B6,B7,B9,C3,C4,C6,D5,D6,E2,E3,F8,F9,G2,G7,H4,H5) * 493257861.624.8.35...3.62..93.1825.68.6.743.22...63.8.6..745.2352.83.6..3..62..58 * PAIR G2: 7,9 BLK 3 H3: 7,9,4 # reduction candidate for 7,9 H3: 7,9 # 23 pairs I3: 7,9,4 # reduction candidate for 7,9 I3: 7,9 => CTR * 4932578617624189351..3962479341825768.6.743.227..634896.9745123527831694341629758 I3: 4 # 23 pairs * PAIR G2: 7,9 COL G G6: 7,9,1,4 # reduction candidate for 7,9 G6: 7,9 => CTR * 493257861.624.8.35...3.62..93.1825.68.6.743122.1563.8.61874592352.83.6..3..62..58 G6: 1,4 # 21 pairs G9: 7,9,1,4 # reduction candidate for 7,9 G9: 7,9 => CTR * 493257861.624.8.35...3.62..9341825768165743922...6348.6..74512352.83.6..34.62..58 G9: 1,4 # 21 pairs * PAIR C4: 4,7 COL C C8: 4,7,1,9 # reduction candidate for 4,7 C8: 4,7 # 23 pairs C9: 4,7,1,9 # reduction candidate for 4,7 C9: 4,7 => SOLVED * 493257861162498735785316294934182576856974312271563489618745923529831647347629158 C9: 1,9 # 23 pairs * PAIR B6: 4,7 ROW 6 G6: 4,7,1,9 # reduction candidate for 4,7 G6: 4,7 => SOLVED * 493257861162498735785316294934182576856974312271563489618745923529831647347629158 G6: 1,9 => CTR * 4932578611624987357..3162949371825468.6974312241.63.876..745.2352483.67937.629458 I6: 4,7,9 # reduction candidate for 4,7 I6: 4,7 => CTR * 4932578611624987357..3162949371825468.6974312241.63.876..745.2352483.67937.629458 I6: 9 => SOLVED * 493257861162498735785316294934182576856974312271563489618745923529831647347629158 * PAIR H4: 4,7 BLK 6 G6: 4,7,1,9 # reduction candidate for 4,7 G6: 4,7 => SOLVED * 493257861162498735785316294934182576856974312271563489618745923529831647347629158 G6: 1,9 => CTR * 4932578611624987357..3162949371825468.6974312241.63.876..745.2352483.67937.629458 I6: 4,7,9 # reduction candidate for 4,7 I6: 4,7 => CTR * 4932578611624987357..3162949371825468.6974312241.63.876..745.2352483.67937.629458 I6: 9 => SOLVED * 493257861162498735785316294934182576856974312271563489618745923529831647347629158 * PAIR H4: 4,7 COL H H3: 4,7,9 # reduction candidate for 4,7 H3: 4,7 # 26 pairs H8: 4,7,1,9 # reduction candidate for 4,7 H8: 4,7 => SOLVED * 493257861162498735785316294934182576856974312271563489618745923529831647347629158 H8: 1,9 # 26 pairs * PAIR H5: 1,9 BLK 6 G6: 1,9,4,7 # reduction candidate for 1,9 G6: 1,9 => CTR * 4932578611624987357..3162949371825468.6974312241.63.876..745.2352483.67937.629458 G6: 4,7 => SOLVED * 493257861162498735785316294934182576856974312271563489618745923529831647347629158 * PAIR H5: 1,9 COL H H8: 1,9,4,7 # reduction candidate for 1,9 H8: 4,7 => SOLVED * 493257861162498735785316294934182576856974312271563489618745923529831647347629158 H8: 1,9 # 26 pairs * PAIR B7: 1,8 BLK 7 C7: 1,8,9 # reduction candidate for 1,8 C7: 9 => CTR * 493257861.624.8.35..83.62..93.1825.68.6.743.22.596318.6..745.2352.83.6..3..62..58 C7: 1,8 # 21 pairs * PAIR B9: 4,7 BLK 7 C8: 4,7,1,9 # reduction candidate for 4,7 C8: 4,7 # 23 pairs C9: 4,7,1,9 # reduction candidate for 4,7 C9: 4,7 => SOLVED * 493257861162498735785316294934182576856974312271563489618745923529831647347629158 C9: 1,9 # 23 pairs * PAIR B9: 4,7 ROW 9 G9: 4,7,1,9 # reduction candidate for 4,7 G9: 1,9 => SOLVED * 493257861162498735785316294934182576856974312271563489618745923529831647347629158 G9: 4,7 # 23 pairs * PAIR F8: 1,9 ROW 8 C8: 1,9,4,7 # reduction candidate for 1,9 C8: 1,9 => SOLVED * 493257861162498735785316294934182576856974312271563489618745923529831647347629158 C8: 4,7 # 23 pairs H8: 1,9,4,7 # reduction candidate for 1,9 H8: 1,9 # 26 pairs * PAIR F9: 1,9 ROW 9 C9: 1,9,4,7 # reduction candidate for 1,9 C9: 1,9 # 23 pairs G9: 1,9,4,7 # reduction candidate for 1,9 G9: 1,9 => SOLVED * 493257861162498735785316294934182576856974312271563489618745923529831647347629158 G9: 4,7 # 23 pairs * PAIR G7: 1,9 BLK 9 H8: 1,9,4,7 # reduction candidate for 1,9 H8: 1,9 # 26 pairs G9: 1,9,4,7 # reduction candidate for 1,9 G9: 1,9 => SOLVED * 493257861162498735785316294934182576856974312271563489618745923529831647347629158 G9: 4,7 # 23 pairs * PAIR G7: 1,9 ROW 7 C7: 1,9,8 # reduction candidate for 1,9 C7: 1,9 => CTR * 493257861.624987357583162.993.182576816.743.22.596318.68174592352.83.61.3..621458 C7: 8 => SOLVED * 493257861162498735785316294934182576856974312271563489618745923529831647347629158 * PAIR G7: 1,9 COL G G6: 1,9,4,7 # reduction candidate for 1,9 G6: 1,9 => CTR * 4932578611624987357..3162949371825468.6974312241.63.876..745.2352483.67937.629458 G6: 4,7 => SOLVED * 493257861162498735785316294934182576856974312271563489618745923529831647347629158 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-048-base-pr-000.dot * REASONING * DIS # I3: 7,9 => CTR => I3: 4 * DIS # G6: 7,9 => CTR => G6: 1,4 * DIS # G9: 7,9 => CTR => G9: 1,4 * PRF # C9: 4,7 => SOL * PRF # G6: 4,7 => SOL * DIS # G6: 1,9 => CTR => G6: 4,7 * DIS # I6: 4,7 => CTR => I6: 9 * PRF # I6: 9 => SOL * PRF # G6: 4,7 => SOL * DIS # G6: 1,9 => CTR => G6: 4,7 * DIS # I6: 4,7 => CTR => I6: 9 * PRF # I6: 9 => SOL * PRF # H8: 4,7 => SOL * DIS # G6: 1,9 => CTR => G6: 4,7 * PRF # G6: 4,7 => SOL * PRF # H8: 4,7 => SOL * DIS # C7: 9 => CTR => C7: 1,8 * PRF # C9: 4,7 => SOL * PRF # G9: 1,9 => SOL * PRF # C8: 1,9 => SOL * PRF # G9: 1,9 => SOL * PRF # G9: 1,9 => SOL * DIS # C7: 1,9 => CTR => C7: 8 * PRF # C7: 8 => SOL * DIS # G6: 1,9 => CTR => G6: 4,7 * PRF # G6: 4,7 => SOL * CNT 26 HDP CHAINS / 45 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,B3,B5,B6,B7,B9,C3,C4,C6,D5,D6,E2,E3,F8,F9,G2,G7,H4,H5) * 493257861.624.8.35...3.62..93.1825.68.6.743.22...63.8.6..745.2352.83.6..3..62..58 * PAIR G2: 7,9 BLK 3 H3: 7,9,4 # reduction candidate for 7,9 H3: 7,9 # 23 pairs I3: 7,9,4 # reduction candidate for 7,9 I3: 7,9 => CTR * 4932578617624189351..3962479341825768.6.743.227..634896.9745123527831694341629758 * RESTART * PAIR G2: 7,9 COL G G6: 7,9,1,4 # reduction candidate for 7,9 G6: 7,9 => CTR * 493257861.624.8.35...3.62.493.1825468.6.74312241563.8.61874592352.83.6..3..62..58 G9: 7,9,1,4 # reduction candidate for 7,9 G9: 7,9 => CTR * 493257861.624.8.35...3.62.49341825768165743922...6348.6..74512352.83.64.34.62..58 G9: 1,4 => SOLVED * 493257861162498735785316294934182576856974312271563489618745923529831647347629158 * DURATION: 0:00:05.132463 START: 04:20:08.677542 END: 04:20:13.810005 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-048-base-pr-001.dot * REASONING * DIS # I3: 7,9 => CTR => I3: 4 * DIS I3: 4 # G6: 7,9 => CTR => G6: 1,4 * DIS I3: 4 + G6: 1,4 # G9: 7,9 => CTR => G9: 1,4 * PRF I3: 4 + G6: 1,4 + G9: 1,4 => SOL * STA I3: 4 + G6: 1,4 + G9: 1,4 * CNT 4 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 048 solution: 493257861162498735785316294934182576856974312271563489618745923529831647347629158 info: 1378 FNBTHWXY S8.f 46142 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 493257861162498735785316294934182576856974312271563489618745923529831647347629158 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 # H3: 7,9 => UNS * DIS # I3: 7,9 => CTR => I3: 4 * INC # I3: 4 => UNS * DIS # G6: 7,9 => CTR => G6: 1,4 * INC # G6: 1,4 => UNS * DIS # G9: 7,9 => CTR => G9: 1,4 * INC # G9: 1,4 => UNS * INC # C8: 4,7 => UNS * PRF # C9: 4,7 => SOL * INC # C9: 1,9 => UNS * PRF # G6: 4,7 => SOL * DIS # G6: 1,9 => CTR => G6: 4,7 * DIS # I6: 4,7 => CTR => I6: 9 * PRF # I6: 9 => SOL * PRF # G6: 4,7 => SOL * DIS # G6: 1,9 => CTR => G6: 4,7 * DIS # I6: 4,7 => CTR => I6: 9 * PRF # I6: 9 => SOL * INC # H3: 4,7 => UNS * PRF # H8: 4,7 => SOL * INC # H8: 1,9 => UNS * DIS # G6: 1,9 => CTR => G6: 4,7 * PRF # G6: 4,7 => SOL * INC # H8: 1,9 => UNS * PRF # H8: 4,7 => SOL * INC # C7: 1,8 => UNS * DIS # C7: 9 => CTR => C7: 1,8 * INC # C8: 4,7 => UNS * PRF # C9: 4,7 => SOL * INC # C9: 1,9 => UNS * INC # G9: 4,7 => UNS * PRF # G9: 1,9 => SOL * PRF # C8: 1,9 => SOL * INC # C8: 4,7 => UNS * INC # H8: 1,9 => UNS * INC # C9: 1,9 => UNS * PRF # G9: 1,9 => SOL * INC # G9: 4,7 => UNS * INC # H8: 1,9 => UNS * PRF # G9: 1,9 => SOL * INC # G9: 4,7 => UNS * DIS # C7: 1,9 => CTR => C7: 8 * PRF # C7: 8 => SOL * DIS # G6: 1,9 => CTR => G6: 4,7 * PRF # G6: 4,7 => SOL * CNT 45 HDP CHAINS / 45 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # H3: 7,9 => UNS * DIS # I3: 7,9 => CTR => I3: 4 * DIS I3: 4 # G6: 7,9 => CTR => G6: 1,4 * DIS I3: 4 + G6: 1,4 # G9: 7,9 => CTR => G9: 1,4 * PRF I3: 4 + G6: 1,4 + G9: 1,4 => SOL * STA I3: 4 + G6: 1,4 + G9: 1,4 * CNT 5 HDP CHAINS / 4 HYP OPENED