Analysis of xx-top500-372-base.sdk
Contents
Original Sudoku
level: medium
position: .7....85.....12......3.....7......12.4.9.................67.4..3.....6....1...... initial
Autosolve
position: 172469853...7129..6943..1277.9.46.1224.9.17...162.7...92.67.4313.71246..461.9327. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 5,8 => CTR => B2: 3 * PRF # B2: 3 => SOL * PRF # C2: 5,8 => SOL * DIS # C2: 3 => CTR => C2: 5,8 * DIS # E6: 5,8 => CTR => E6: 3 * PRF # E6: 3 => SOL * PRF # B4: 3,5 => SOL * DIS # B4: 8 => CTR => B4: 3,5 * DIS # C2: 3,5 => CTR => C2: 8 * PRF # C2: 8 => SOL * PRF # B4: 5,8 => SOL * DIS # B4: 3 => CTR => B4: 5,8 * DIS # E6: 5,8 => CTR => E6: 3 * PRF # E6: 3 => SOL * DIS # E6: 5,8 => CTR => E6: 3 * PRF # E6: 3 => SOL * PRF # B4: 5,8 => SOL * DIS # B4: 3 => CTR => B4: 5,8 * PRF # E6: 3,5 => SOL * DIS # E6: 8 => CTR => E6: 3,5 * PRF # B4: 3,5 => SOL * DIS # B4: 8 => CTR => B4: 3,5 * PRF # E6: 3,5 => SOL * DIS # E6: 8 => CTR => E6: 3,5 * PRF # C2: 5,8 => SOL * DIS # C2: 3 => CTR => C2: 5,8 * DIS # I8: 9 => CTR => I8: 5,8 * DIS # B2: 5,8 => CTR => B2: 3 * PRF # B2: 3 => SOL * PRF # B4: 5,8 => SOL * DIS # B4: 3 => CTR => B4: 5,8 * DIS # I8: 8,9 => CTR => I8: 5 * PRF # I8: 5 => SOL * DIS # I8: 9 => CTR => I8: 5,8 * CNT 34 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 # B2: 5,8 => CTR => B2: 3 * PRF B2: 3 => SOL * STA B2: 3 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .7....85.....12......3.....7......12.4.9.................67.4..3.....6....1...... | initial |
| 172469853...7129..6943..1277.9.46.1224.9.17...162.7...92.67.4313.71246..461.9327. | autosolve |
| 172469853538712964694385127759846312243951786816237549925678431387124695461593278 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (21) A2: 5,8 E3: 5,8 F3: 5,8 H2: 4,6 I2: 4,6 C5: 3,5 A6: 5,8 D4: 5,8 E5: 3,5 G4: 3,5 H5: 6,8 I5: 6,8 G6: 3,5 H6: 4,9 I6: 4,9 C7: 5,8 B8: 5,8 F7: 5,8 D9: 5,8 H8: 8,9 I9: 5,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,C2: 3.. / B2 = 3 => 0 pairs (*) / C2 = 3 => 0 pairs (X) B4,C5: 3.. / B4 = 3 => 0 pairs (X) / C5 = 3 => 0 pairs (_) E5,E6: 3.. / E5 = 3 => 0 pairs (X) / E6 = 3 => 0 pairs (_) G4,G6: 3.. / G4 = 3 => 0 pairs (*) / G6 = 3 => 0 pairs (X) B4,G4: 3.. / B4 = 3 => 0 pairs (X) / G4 = 3 => 0 pairs (_) C5,E5: 3.. / C5 = 3 => 0 pairs (*) / E5 = 3 => 0 pairs (X) E6,G6: 3.. / E6 = 3 => 0 pairs (*) / G6 = 3 => 0 pairs (X) B2,B4: 3.. / B2 = 3 => 0 pairs (*) / B4 = 3 => 0 pairs (X) C2,C5: 3.. / C2 = 3 => 0 pairs (X) / C5 = 3 => 0 pairs (_) H2,I2: 4.. / H2 = 4 => 0 pairs (X) / I2 = 4 => 15 pairs (_) H6,I6: 4.. / H6 = 4 => 15 pairs (_) / I6 = 4 => 0 pairs (X) H2,H6: 4.. / H2 = 4 => 0 pairs (X) / H6 = 4 => 15 pairs (_) I2,I6: 4.. / I2 = 4 => 15 pairs (_) / I6 = 4 => 0 pairs (X) E3,F3: 5.. / E3 = 5 => 0 pairs (X) / F3 = 5 => 0 pairs (_) G4,G6: 5.. / G4 = 5 => 0 pairs (X) / G6 = 5 => 0 pairs (_) C7,B8: 5.. / C7 = 5 => 0 pairs (*) / B8 = 5 => 0 pairs (X) F7,D9: 5.. / F7 = 5 => 0 pairs (X) / D9 = 5 => 0 pairs (_) I8,I9: 5.. / I8 = 5 => 0 pairs (*) / I9 = 5 => 0 pairs (X) C5,E5: 5.. / C5 = 5 => 0 pairs (X) / E5 = 5 => 0 pairs (_) C7,F7: 5.. / C7 = 5 => 0 pairs (*) / F7 = 5 => 0 pairs (X) B8,I8: 5.. / B8 = 5 => 0 pairs (X) / I8 = 5 => 0 pairs (_) D9,I9: 5.. / D9 = 5 => 0 pairs (*) / I9 = 5 => 0 pairs (X) A2,A6: 5.. / A2 = 5 => 0 pairs (*) / A6 = 5 => 0 pairs (X) D4,D9: 5.. / D4 = 5 => 0 pairs (X) / D9 = 5 => 0 pairs (_) F3,F7: 5.. / F3 = 5 => 0 pairs (*) / F7 = 5 => 0 pairs (X) H2,I2: 6.. / H2 = 6 => 15 pairs (_) / I2 = 6 => 0 pairs (X) H5,I5: 6.. / H5 = 6 => 0 pairs (X) / I5 = 6 => 15 pairs (_) H2,H5: 6.. / H2 = 6 => 15 pairs (_) / H5 = 6 => 0 pairs (X) I2,I5: 6.. / I2 = 6 => 0 pairs (X) / I5 = 6 => 15 pairs (_) E3,F3: 8.. / E3 = 8 => 0 pairs (*) / F3 = 8 => 0 pairs (X) B4,A6: 8.. / B4 = 8 => 0 pairs (X) / A6 = 8 => 0 pairs (_) D4,E6: 8.. / D4 = 8 => 0 pairs (*) / E6 = 8 => 0 pairs (X) H5,I5: 8.. / H5 = 8 => 15 pairs (_) / I5 = 8 => 0 pairs (X) C7,B8: 8.. / C7 = 8 => 0 pairs (X) / B8 = 8 => 0 pairs (_) F7,D9: 8.. / F7 = 8 => 0 pairs (*) / D9 = 8 => 0 pairs (X) B4,D4: 8.. / B4 = 8 => 0 pairs (X) / D4 = 8 => 0 pairs (_) A6,E6: 8.. / A6 = 8 => 0 pairs (*) / E6 = 8 => 0 pairs (X) C7,F7: 8.. / C7 = 8 => 0 pairs (X) / F7 = 8 => 0 pairs (_) D9,I9: 8.. / D9 = 8 => 0 pairs (X) / I9 = 8 => 0 pairs (_) A2,A6: 8.. / A2 = 8 => 0 pairs (X) / A6 = 8 => 0 pairs (_) C2,C7: 8.. / C2 = 8 => 0 pairs (*) / C7 = 8 => 0 pairs (X) D4,D9: 8.. / D4 = 8 => 0 pairs (*) / D9 = 8 => 0 pairs (X) E3,E6: 8.. / E3 = 8 => 0 pairs (*) / E6 = 8 => 0 pairs (X) F3,F7: 8.. / F3 = 8 => 0 pairs (X) / F7 = 8 => 0 pairs (_) H5,H8: 8.. / H5 = 8 => 15 pairs (_) / H8 = 8 => 0 pairs (X) H6,I6: 9.. / H6 = 9 => 0 pairs (X) / I6 = 9 => 15 pairs (_) H8,I8: 9.. / H8 = 9 => 15 pairs (_) / I8 = 9 => 0 pairs (X) H6,H8: 9.. / H6 = 9 => 0 pairs (X) / H8 = 9 => 15 pairs (_) I6,I8: 9.. / I6 = 9 => 15 pairs (_) / I8 = 9 => 0 pairs (X) * DURATION: 0:01:39.477655 START: 15:34:34.245955 END: 15:36:13.723610 2017-05-04 * CP COUNT: (49) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,B8,C5,C7,D4,D9,E3,E5,F3,F7,G4,G6,H2,H5,H6,H8,I2,I5,I6,I9) * 172469853...7129..6943..1277.9.46.1224.9.17...162.7...92.67.4313.71246..461.9327. * PAIR A2: 5,8 BLK 1 B2: 5,8,3 # reduction candidate for 5,8 B2: 5,8 => CTR * 172469853..37129..6943..1277398465122459317..8162573..92867.4313.71246..461.9327. B2: 3 => SOLVED * 172469853538712964694385127759846312243951786816237549925678431387124695461593278 C2: 5,8,3 # reduction candidate for 5,8 C2: 5,8 => SOLVED * 172469853538712964694385127759846312243951786816237549925678431387124695461593278 C2: 3 => CTR * 172469853..37129..6943..1277398465122459317..8162573..92867.4313.71246..461.9327. * PAIR E3: 5,8 COL E E6: 5,8,3 # reduction candidate for 5,8 E6: 5,8 => CTR * 172469853..37129..6943..1277398465122459317..8162573..92867.4313.71246..461.9327. E6: 3 => SOLVED * 172469853538712964694385127759846312243951786816237549925678431387124695461593278 * PAIR C5: 3,5 BLK 4 B4: 3,5,8 # reduction candidate for 3,5 B4: 3,5 => SOLVED * 172469853538712964694385127759846312243951786816237549925678431387124695461593278 B4: 8 => CTR * 172469853.3.7129..6943..12778954631224.9.17...162.7...92.67.4313.71246..461.9327. * PAIR C5: 3,5 COL C C2: 3,5,8 # reduction candidate for 3,5 C2: 3,5 => CTR * 172469853...7129..69435812778954631224.9.17...162.7...9286754313571246..461893275 C2: 8 => SOLVED * 172469853538712964694385127759846312243951786816237549925678431387124695461593278 * PAIR A6: 5,8 BLK 4 B4: 5,8,3 # reduction candidate for 5,8 B4: 5,8 => SOLVED * 172469853538712964694385127759846312243951786816237549925678431387124695461593278 B4: 3 => CTR * 172469853...7129..6943..1277398465122459317..8162573..92867.4313.71246..461.9327. * PAIR A6: 5,8 ROW 6 E6: 5,8,3 # reduction candidate for 5,8 E6: 5,8 => CTR * 172469853..37129..6943..1277398465122459317..8162573..92867.4313.71246..461.9327. E6: 3 => SOLVED * 172469853538712964694385127759846312243951786816237549925678431387124695461593278 * PAIR D4: 5,8 BLK 5 E6: 5,8,3 # reduction candidate for 5,8 E6: 5,8 => CTR * 172469853..37129..6943..1277398465122459317..8162573..92867.4313.71246..461.9327. E6: 3 => SOLVED * 172469853538712964694385127759846312243951786816237549925678431387124695461593278 * PAIR D4: 5,8 ROW 4 B4: 5,8,3 # reduction candidate for 5,8 B4: 5,8 => SOLVED * 172469853538712964694385127759846312243951786816237549925678431387124695461593278 B4: 3 => CTR * 172469853...7129..6943..1277398465122459317..8162573..92867.4313.71246..461.9327. * PAIR E5: 3,5 BLK 5 E6: 3,5,8 # reduction candidate for 3,5 E6: 3,5 => SOLVED * 172469853538712964694385127759846312243951786816237549925678431387124695461593278 E6: 8 => CTR * 172469853...7129..6943..1277.9.46.1224.9317...162873..92.67.4313.71246..461893275 * PAIR G4: 3,5 ROW 4 B4: 3,5,8 # reduction candidate for 3,5 B4: 3,5 => SOLVED * 172469853538712964694385127759846312243951786816237549925678431387124695461593278 B4: 8 => CTR * 172469853.3.7129..6943..12778954631224.9.17...162.7...92.67.4313.71246..461.9327. * PAIR G6: 3,5 ROW 6 E6: 3,5,8 # reduction candidate for 3,5 E6: 3,5 => SOLVED * 172469853538712964694385127759846312243951786816237549925678431387124695461593278 E6: 8 => CTR * 172469853...7129..6943..1277.9.46.1224.9317...162873..92.67.4313.71246..461893275 * PAIR C7: 5,8 COL C C2: 5,8,3 # reduction candidate for 5,8 C2: 5,8 => SOLVED * 172469853538712964694385127759846312243951786816237549925678431387124695461593278 C2: 3 => CTR * 172469853..37129..6943..1277398465122459317..8162573..92867.4313.71246..461.9327. * PAIR B8: 5,8 ROW 8 I8: 5,8,9 # reduction candidate for 5,8 I8: 9 => CTR * 172469853...7129..6943.812778954631224.9.17...162.7...92.67.431357124689461893275 I8: 5,8 # 15 pairs * PAIR B8: 5,8 COL B B2: 5,8,3 # reduction candidate for 5,8 B2: 5,8 => CTR * 172469853..37129..6943..1277398465122459317..8162573..92867.4313.71246..461.9327. B2: 3 => SOLVED * 172469853538712964694385127759846312243951786816237549925678431387124695461593278 B4: 5,8,3 # reduction candidate for 5,8 B4: 5,8 => SOLVED * 172469853538712964694385127759846312243951786816237549925678431387124695461593278 B4: 3 => CTR * 172469853...7129..6943..1277398465122459317..8162573..92867.4313.71246..461.9327. * PAIR H8: 8,9 BLK 9 I8: 8,9,5 # reduction candidate for 8,9 I8: 8,9 => CTR * 172469853...7129..6943..1277.954631224.9.17...162.7...92.67.4313571246..461.93275 I8: 5 => SOLVED * 172469853538712964694385127759846312243951786816237549925678431387124695461593278 * PAIR I9: 5,8 BLK 9 I8: 5,8,9 # reduction candidate for 5,8 I8: 9 => CTR * 172469853...7129..6943.812778954631224.9.17...162.7...92.67.431357124689461893275 I8: 5,8 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-372-base-pr-000.dot * REASONING * DIS # B2: 5,8 => CTR => B2: 3 * PRF # B2: 3 => SOL * PRF # C2: 5,8 => SOL * DIS # C2: 3 => CTR => C2: 5,8 * DIS # E6: 5,8 => CTR => E6: 3 * PRF # E6: 3 => SOL * PRF # B4: 3,5 => SOL * DIS # B4: 8 => CTR => B4: 3,5 * DIS # C2: 3,5 => CTR => C2: 8 * PRF # C2: 8 => SOL * PRF # B4: 5,8 => SOL * DIS # B4: 3 => CTR => B4: 5,8 * DIS # E6: 5,8 => CTR => E6: 3 * PRF # E6: 3 => SOL * DIS # E6: 5,8 => CTR => E6: 3 * PRF # E6: 3 => SOL * PRF # B4: 5,8 => SOL * DIS # B4: 3 => CTR => B4: 5,8 * PRF # E6: 3,5 => SOL * DIS # E6: 8 => CTR => E6: 3,5 * PRF # B4: 3,5 => SOL * DIS # B4: 8 => CTR => B4: 3,5 * PRF # E6: 3,5 => SOL * DIS # E6: 8 => CTR => E6: 3,5 * PRF # C2: 5,8 => SOL * DIS # C2: 3 => CTR => C2: 5,8 * DIS # I8: 9 => CTR => I8: 5,8 * DIS # B2: 5,8 => CTR => B2: 3 * PRF # B2: 3 => SOL * PRF # B4: 5,8 => SOL * DIS # B4: 3 => CTR => B4: 5,8 * DIS # I8: 8,9 => CTR => I8: 5 * PRF # I8: 5 => SOL * DIS # I8: 9 => CTR => I8: 5,8 * CNT 34 HDP CHAINS / 36 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,B8,C5,C7,D4,D9,E3,E5,F3,F7,G4,G6,H2,H5,H6,H8,I2,I5,I6,I9) * 172469853...7129..6943..1277.9.46.1224.9.17...162.7...92.67.4313.71246..461.9327. * PAIR A2: 5,8 BLK 1 B2: 5,8,3 # reduction candidate for 5,8 B2: 5,8 => CTR * 172469853..37129..6943..1277398465122459317..8162573..92867.4313.71246..461.9327. B2: 3 => SOLVED * 172469853538712964694385127759846312243951786816237549925678431387124695461593278 * DURATION: 0:00:01.804336 START: 15:37:00.579709 END: 15:37:02.384045 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-372-base-pr-001.dot * REASONING * DIS # B2: 5,8 => CTR => B2: 3 * PRF B2: 3 => SOL * STA B2: 3 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 372 solution: 172469853538712964694385127759846312243951786816237549925678431387124695461593278 info: 6441 FNBTWY S8.f 22299 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 172469853538712964694385127759846312243951786816237549925678431387124695461593278 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 # B2: 5,8 => CTR => B2: 3 * PRF # B2: 3 => SOL * PRF # C2: 5,8 => SOL * DIS # C2: 3 => CTR => C2: 5,8 * DIS # E6: 5,8 => CTR => E6: 3 * PRF # E6: 3 => SOL * PRF # B4: 3,5 => SOL * DIS # B4: 8 => CTR => B4: 3,5 * DIS # C2: 3,5 => CTR => C2: 8 * PRF # C2: 8 => SOL * PRF # B4: 5,8 => SOL * DIS # B4: 3 => CTR => B4: 5,8 * DIS # E6: 5,8 => CTR => E6: 3 * PRF # E6: 3 => SOL * DIS # E6: 5,8 => CTR => E6: 3 * PRF # E6: 3 => SOL * PRF # B4: 5,8 => SOL * DIS # B4: 3 => CTR => B4: 5,8 * PRF # E6: 3,5 => SOL * DIS # E6: 8 => CTR => E6: 3,5 * PRF # B4: 3,5 => SOL * DIS # B4: 8 => CTR => B4: 3,5 * PRF # E6: 3,5 => SOL * DIS # E6: 8 => CTR => E6: 3,5 * PRF # C2: 5,8 => SOL * DIS # C2: 3 => CTR => C2: 5,8 * INC # I8: 5,8 => UNS * DIS # I8: 9 => CTR => I8: 5,8 * DIS # B2: 5,8 => CTR => B2: 3 * PRF # B2: 3 => SOL * PRF # B4: 5,8 => SOL * DIS # B4: 3 => CTR => B4: 5,8 * DIS # I8: 8,9 => CTR => I8: 5 * PRF # I8: 5 => SOL * INC # I8: 5,8 => UNS * DIS # I8: 9 => CTR => I8: 5,8 * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B2: 5,8 => CTR => B2: 3 * PRF B2: 3 => SOL * STA B2: 3 * CNT 2 HDP CHAINS / 1 HYP OPENED