Analysis of xx-top500-232-base.sdk
Contents
Original Sudoku
level: medium
position: 4..58..........6.7.............1.84...7..3....3....1.....7.6.9.1...........2..... initial
Autosolve
position: 47658.31..981346.73.167..846..9178438174.3...9348.517..837.6.9114.3.87..76.2.1.38 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # G3: 9 => SOL * PRF # G3: 2,9 => SOL * DIS # G3: 5 => CTR => G3: 2,9 * PRF # G3: 2,9 => SOL * DIS # G3: 5 => CTR => G3: 2,9 * PRF # I5: 2,9 => SOL * PRF # G3: 9 => SOL * DIS # C8: 9 => CTR => C8: 2,5 * DIS # I5: 2,6 => CTR => I5: 5,9 * DIS # I5: 2,6 => CTR => I5: 5,9 * PRF # I8: 5 => SOL * DIS # C8: 9 => CTR => C8: 2,5 * DIS # G7: 4 => CTR => G7: 2,5 * DIS # C8: 5,9 => CTR => C8: 2 * PRF # C8: 2 => SOL * DIS # E9: 4 => CTR => E9: 5,9 * DIS # E9: 9 => CTR => E9: 4,5 * DIS # G7: 4,5 => CTR => G7: 2 * PRF # G7: 2 => SOL * DIS # E9: 4 => CTR => E9: 5,9 * DIS # C8: 5,9 => CTR => C8: 2 * PRF # C8: 2 => SOL * DIS # G7: 4,5 => CTR => G7: 2 * PRF # G7: 2 => SOL * DIS # E9: 9 => CTR => E9: 4,5 * CNT 25 HDP CHAINS / 42 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # G3: 9 => SOL * STA G3: 9 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 4..58..........6.7.............1.84...7..3....3....1.....7.6.9.1...........2..... | initial |
| 47658.31..981346.73.167..846..9178438174.3...9348.517..837.6.9114.3.87..76.2.1.38 | autosolve |
| 476589312298134657351672984625917843817463529934825176583746291142398765769251438 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) A2: 2,5 B3: 2,5 F1: 2,9 F3: 2,9 I1: 2,9 H2: 2,5 B4: 2,5 C4: 2,5 E5: 2,6 E6: 2,6 I6: 2,6 A7: 2,5 C9: 5,9 E7: 4,5 E8: 5,9 G9: 4,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,B3: 2.. / A2 = 2 => 0 pairs (*) / B3 = 2 => 0 pairs (X) F1,F3: 2.. / F1 = 2 => 14 pairs (_) / F3 = 2 => 0 pairs (*) B4,C4: 2.. / B4 = 2 => 0 pairs (*) / C4 = 2 => 0 pairs (X) E5,E6: 2.. / E5 = 2 => 14 pairs (_) / E6 = 2 => 15 pairs (_) A7,C8: 2.. / A7 = 2 => 0 pairs (X) / C8 = 2 => 0 pairs (_) F1,I1: 2.. / F1 = 2 => 14 pairs (_) / I1 = 2 => 0 pairs (*) A2,H2: 2.. / A2 = 2 => 0 pairs (*) / H2 = 2 => 0 pairs (X) E6,I6: 2.. / E6 = 2 => 15 pairs (_) / I6 = 2 => 14 pairs (_) A7,G7: 2.. / A7 = 2 => 0 pairs (X) / G7 = 2 => 0 pairs (_) A2,A7: 2.. / A2 = 2 => 0 pairs (*) / A7 = 2 => 0 pairs (X) B3,B4: 2.. / B3 = 2 => 0 pairs (X) / B4 = 2 => 0 pairs (_) C4,C8: 2.. / C4 = 2 => 0 pairs (X) / C8 = 2 => 0 pairs (_) E7,E9: 4.. / E7 = 4 => 16 pairs (_) / E9 = 4 => 0 pairs (X) G7,G9: 4.. / G7 = 4 => 0 pairs (X) / G9 = 4 => 16 pairs (_) E7,G7: 4.. / E7 = 4 => 16 pairs (_) / G7 = 4 => 0 pairs (X) E9,G9: 4.. / E9 = 4 => 0 pairs (X) / G9 = 4 => 16 pairs (_) A2,B3: 5.. / A2 = 5 => 0 pairs (X) / B3 = 5 => 0 pairs (_) H2,G3: 5.. / H2 = 5 => 0 pairs (*) / G3 = 5 => 0 pairs (X) B4,C4: 5.. / B4 = 5 => 0 pairs (X) / C4 = 5 => 0 pairs (_) A2,H2: 5.. / A2 = 5 => 0 pairs (X) / H2 = 5 => 0 pairs (_) B3,G3: 5.. / B3 = 5 => 0 pairs (*) / G3 = 5 => 0 pairs (X) A2,A7: 5.. / A2 = 5 => 0 pairs (X) / A7 = 5 => 0 pairs (_) B3,B4: 5.. / B3 = 5 => 0 pairs (*) / B4 = 5 => 0 pairs (X) I5,I8: 5.. / I5 = 5 => 16 pairs (_) / I8 = 5 => 0 pairs (*) E5,E6: 6.. / E5 = 6 => 15 pairs (_) / E6 = 6 => 14 pairs (_) H8,I8: 6.. / H8 = 6 => 18 pairs (_) / I8 = 6 => 12 pairs (_) E6,I6: 6.. / E6 = 6 => 14 pairs (_) / I6 = 6 => 15 pairs (_) H5,H8: 6.. / H5 = 6 => 12 pairs (_) / H8 = 6 => 18 pairs (_) F1,F3: 9.. / F1 = 9 => 0 pairs (*) / F3 = 9 => 0 pairs (X) I1,G3: 9.. / I1 = 9 => 14 pairs (_) / G3 = 9 => 0 pairs (*) G5,I5: 9.. / G5 = 9 => 14 pairs (_) / I5 = 9 => 0 pairs (*) C8,C9: 9.. / C8 = 9 => 0 pairs (X) / C9 = 9 => 16 pairs (_) E8,E9: 9.. / E8 = 9 => 16 pairs (_) / E9 = 9 => 0 pairs (X) F1,I1: 9.. / F1 = 9 => 0 pairs (*) / I1 = 9 => 0 pairs (X) F3,G3: 9.. / F3 = 9 => 14 pairs (_) / G3 = 9 => 0 pairs (*) C8,E8: 9.. / C8 = 9 => 0 pairs (X) / E8 = 9 => 16 pairs (_) C9,E9: 9.. / C9 = 9 => 16 pairs (_) / E9 = 9 => 0 pairs (X) G3,G5: 9.. / G3 = 9 => 0 pairs (*) / G5 = 9 => 0 pairs (X) I1,I5: 9.. / I1 = 9 => 14 pairs (_) / I5 = 9 => 0 pairs (*) * DURATION: 0:01:05.598324 START: 10:45:44.922601 END: 10:46:50.520925 2017-05-04 * CP COUNT: (39) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,B3,B4,C4,C9,E5,E6,E7,E8,F1,F3,G9,H2,I1,I6) * 47658.31..981346.73.167..846..9178438174.3...9348.517..837.6.9114.3.87..76.2.1.38 * PAIR B3: 2,5 ROW 3 G3: 2,5,9 # reduction candidate for 2,5 G3: 9 => SOLVED * 476589312298134657351672984625917843817463529934825176583746291142398765769251438 G3: 2,5 # 14 pairs * PAIR F3: 2,9 ROW 3 G3: 2,9,5 # reduction candidate for 2,9 G3: 2,9 => SOLVED * 476589312298134657351672984625917843817463529934825176583746291142398765769251438 G3: 5 => CTR * 47658.319.981346273216795846529178438174.39..9348.517.28375649114.3.87..76.2.1.38 * PAIR I1: 2,9 BLK 3 G3: 2,9,5 # reduction candidate for 2,9 G3: 2,9 => SOLVED * 476589312298134657351672984625917843817463529934825176583746291142398765769251438 G3: 5 => CTR * 47658.319.981346273216795846529178438174.39..9348.517.28375649114.3.87..76.2.1.38 * PAIR I1: 2,9 COL I I5: 2,9,5,6 # reduction candidate for 2,9 I5: 2,9 => SOLVED * 476589312298134657351672984625917843817463529934825176583746291142398765769251438 I5: 5,6 # 15 pairs * PAIR H2: 2,5 BLK 3 G3: 2,5,9 # reduction candidate for 2,5 G3: 9 => SOLVED * 476589312298134657351672984625917843817463529934825176583746291142398765769251438 G3: 2,5 # 14 pairs * PAIR H2: 2,5 COL H H5: 2,5,6 # reduction candidate for 2,5 H5: 2,5 # 18 pairs H8: 2,5,6 # reduction candidate for 2,5 H8: 2,5 # 12 pairs * PAIR C4: 2,5 COL C C8: 2,5,9 # reduction candidate for 2,5 C8: 9 => CTR * 47658.31.5981346273216795846.29178438174.3...9348.517.2837.6.911493587..765291438 C8: 2,5 # 16 pairs * PAIR E5: 2,6 ROW 5 H5: 2,6,5 # reduction candidate for 2,6 H5: 2,6 # 19 pairs I5: 2,6,5,9 # reduction candidate for 2,6 I5: 2,6 => CTR * 4765823195981346273216795846529178438174.395.9348.517.2837.6.9114.3.876576.2.1438 I5: 5,9 # 17 pairs * PAIR I6: 2,6 BLK 6 H5: 2,6,5 # reduction candidate for 2,6 H5: 2,6 # 19 pairs I5: 2,6,5,9 # reduction candidate for 2,6 I5: 2,6 => CTR * 4765823195981346273216795846529178438174.395.9348.517.2837.6.9114.3.876576.2.1438 I5: 5,9 # 17 pairs * PAIR I6: 2,6 COL I I8: 2,6,5 # reduction candidate for 2,6 I8: 5 => SOLVED * 476589312298134657351672984625917843817463529934825176583746291142398765769251438 I8: 2,6 # 16 pairs * PAIR A7: 2,5 BLK 7 C8: 2,5,9 # reduction candidate for 2,5 C8: 9 => CTR * 47658.31.5981346273216795846.29178438174.3...9348.517.2837.6.911493587..765291438 C8: 2,5 # 16 pairs * PAIR A7: 2,5 ROW 7 G7: 2,5,4 # reduction candidate for 2,5 G7: 4 => CTR * 47658.31..981346.73.167..846..9178438174.3...9348.517.28375649114.3987..769241538 G7: 2,5 # 16 pairs * PAIR C9: 5,9 BLK 7 C8: 5,9,2 # reduction candidate for 5,9 C8: 5,9 => CTR * 47658.31.5981346273216795846.29178438174.3...9348.517.2837.6.9114.3.87..76.2.1.38 C8: 2 => SOLVED * 476589312298134657351672984625917843817463529934825176583746291142398765769251438 * PAIR C9: 5,9 ROW 9 E9: 5,9,4 # reduction candidate for 5,9 E9: 4 => CTR * 47658.31..9813465735167..846259178438174.3...9348.517..837.6.9114.3987..769241538 E9: 5,9 # 16 pairs * PAIR E7: 4,5 BLK 8 E9: 4,5,9 # reduction candidate for 4,5 E9: 9 => CTR * 47658.3195981346273.167..846..9178438174.3..59348.517..837465911493587..765291438 E9: 4,5 # 16 pairs * PAIR E7: 4,5 ROW 7 G7: 4,5,2 # reduction candidate for 4,5 G7: 4,5 => CTR * 47658.31.5981346273216795846..9178438174.3...9348.517.2837.6.9114.3.87..76.2.1.38 G7: 2 => SOLVED * 476589312298134657351672984625917843817463529934825176583746291142398765769251438 * PAIR E8: 5,9 BLK 8 E9: 5,9,4 # reduction candidate for 5,9 E9: 4 => CTR * 47658.31..9813465735167..846259178438174.3...9348.517..837.6.9114.3987..769241538 E9: 5,9 # 16 pairs * PAIR E8: 5,9 ROW 8 C8: 5,9,2 # reduction candidate for 5,9 C8: 5,9 => CTR * 47658.31.5981346273216795846.29178438174.3...9348.517.2837.6.9114.3.87..76.2.1.38 C8: 2 => SOLVED * 476589312298134657351672984625917843817463529934825176583746291142398765769251438 * PAIR G9: 4,5 BLK 9 G7: 4,5,2 # reduction candidate for 4,5 G7: 4,5 => CTR * 47658.31.5981346273216795846..9178438174.3...9348.517.2837.6.9114.3.87..76.2.1.38 G7: 2 => SOLVED * 476589312298134657351672984625917843817463529934825176583746291142398765769251438 * PAIR G9: 4,5 ROW 9 E9: 4,5,9 # reduction candidate for 4,5 E9: 9 => CTR * 47658.3195981346273.167..846..9178438174.3..59348.517..837465911493587..765291438 E9: 4,5 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-232-base-pr-000.dot * REASONING * PRF # G3: 9 => SOL * PRF # G3: 2,9 => SOL * DIS # G3: 5 => CTR => G3: 2,9 * PRF # G3: 2,9 => SOL * DIS # G3: 5 => CTR => G3: 2,9 * PRF # I5: 2,9 => SOL * PRF # G3: 9 => SOL * DIS # C8: 9 => CTR => C8: 2,5 * DIS # I5: 2,6 => CTR => I5: 5,9 * DIS # I5: 2,6 => CTR => I5: 5,9 * PRF # I8: 5 => SOL * DIS # C8: 9 => CTR => C8: 2,5 * DIS # G7: 4 => CTR => G7: 2,5 * DIS # C8: 5,9 => CTR => C8: 2 * PRF # C8: 2 => SOL * DIS # E9: 4 => CTR => E9: 5,9 * DIS # E9: 9 => CTR => E9: 4,5 * DIS # G7: 4,5 => CTR => G7: 2 * PRF # G7: 2 => SOL * DIS # E9: 4 => CTR => E9: 5,9 * DIS # C8: 5,9 => CTR => C8: 2 * PRF # C8: 2 => SOL * DIS # G7: 4,5 => CTR => G7: 2 * PRF # G7: 2 => SOL * DIS # E9: 9 => CTR => E9: 4,5 * CNT 25 HDP CHAINS / 42 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,B3,B4,C4,C9,E5,E6,E7,E8,F1,F3,G9,H2,I1,I6) * 47658.31..981346.73.167..846..9178438174.3...9348.517..837.6.9114.3.87..76.2.1.38 * PAIR B3: 2,5 ROW 3 G3: 2,5,9 # reduction candidate for 2,5 G3: 9 => SOLVED * 476589312298134657351672984625917843817463529934825176583746291142398765769251438 * DURATION: 0:00:02.833934 START: 10:47:32.106301 END: 10:47:34.940235 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-232-base-pr-001.dot * REASONING * PRF # G3: 9 => SOL * STA G3: 9 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 232 solution: 476589312298134657351672984625917843817463529934825176583746291142398765769251438 info: 2065 FNWXY S8.f 31085 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 476589312298134657351672984625917843817463529934825176583746291142398765769251438 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 # G3: 2,5 => UNS * PRF # G3: 9 => SOL * PRF # G3: 2,9 => SOL * DIS # G3: 5 => CTR => G3: 2,9 * PRF # G3: 2,9 => SOL * DIS # G3: 5 => CTR => G3: 2,9 * PRF # I5: 2,9 => SOL * INC # I5: 5,6 => UNS * INC # G3: 2,5 => UNS * PRF # G3: 9 => SOL * INC # H5: 2,5 => UNS * INC # H8: 2,5 => UNS * INC # C8: 2,5 => UNS * DIS # C8: 9 => CTR => C8: 2,5 * INC # H5: 2,6 => UNS * DIS # I5: 2,6 => CTR => I5: 5,9 * INC # I5: 5,9 => UNS * INC # H5: 2,6 => UNS * DIS # I5: 2,6 => CTR => I5: 5,9 * INC # I5: 5,9 => UNS * INC # I8: 2,6 => UNS * PRF # I8: 5 => SOL * INC # C8: 2,5 => UNS * DIS # C8: 9 => CTR => C8: 2,5 * INC # G7: 2,5 => UNS * DIS # G7: 4 => CTR => G7: 2,5 * DIS # C8: 5,9 => CTR => C8: 2 * PRF # C8: 2 => SOL * INC # E9: 5,9 => UNS * DIS # E9: 4 => CTR => E9: 5,9 * INC # E9: 4,5 => UNS * DIS # E9: 9 => CTR => E9: 4,5 * DIS # G7: 4,5 => CTR => G7: 2 * PRF # G7: 2 => SOL * INC # E9: 5,9 => UNS * DIS # E9: 4 => CTR => E9: 5,9 * DIS # C8: 5,9 => CTR => C8: 2 * PRF # C8: 2 => SOL * DIS # G7: 4,5 => CTR => G7: 2 * PRF # G7: 2 => SOL * INC # E9: 4,5 => UNS * DIS # E9: 9 => CTR => E9: 4,5 * CNT 42 HDP CHAINS / 42 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G3: 2,5 => UNS * PRF # G3: 9 => SOL * STA G3: 9 * CNT 2 HDP CHAINS / 2 HYP OPENED