Analysis of xx-top500-378-base.sdk
Contents
Original Sudoku
level: medium
position: .4.....315..72...................26..3...1...8..4.......2.6.7.......34........... initial
Autosolve
position: 2476...3151372.6.....3145721.4.3726.7362.1...82.4.63174.216.7.3..1.7342.37..421.6 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B3: 8 => SOL * DIS # F1: 8,9 => CTR => F1: 5 * DIS # F7: 5 => CTR => F7: 8,9 * DIS # F1: 8,9 => CTR => F1: 5 * PRF # C9: 8 => SOL * DIS # H5: 8,9 => CTR => H5: 4,5 * PRF # I5: 8,9 => SOL * PRF # E5: 5 => SOL * CNT 8 HDP CHAINS / 37 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B3: 8 => SOL * STA B3: 8 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .4.....315..72...................26..3...1...8..4.......2.6.7.......34........... | initial |
| 2476...3151372.6.....3145721.4.3726.7362.1...82.4.63174.216.7.3..1.7342.37..421.6 | autosolve |
| 247685931513729684689314572194837265736251849825496317452168793961573428378942156 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) A3: 6,9 C3: 8,9 F2: 8,9 G1: 8,9 B4: 5,9 C6: 5,9 E6: 5,9 G5: 8,9 A8: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H2,I2: 4.. / H2 = 4 => 10 pairs (_) / I2 = 4 => 11 pairs (_) H5,I5: 4.. / H5 = 4 => 11 pairs (_) / I5 = 4 => 10 pairs (_) H2,H5: 4.. / H2 = 4 => 10 pairs (_) / H5 = 4 => 11 pairs (_) I2,I5: 4.. / I2 = 4 => 11 pairs (_) / I5 = 4 => 10 pairs (_) E1,F1: 5.. / E1 = 5 => 0 pairs (X) / F1 = 5 => 12 pairs (_) B4,C6: 5.. / B4 = 5 => 16 pairs (_) / C6 = 5 => 19 pairs (_) C6,E6: 5.. / C6 = 5 => 19 pairs (_) / E6 = 5 => 16 pairs (_) C6,C9: 5.. / C6 = 5 => 19 pairs (_) / C9 = 5 => 16 pairs (_) F1,F7: 5.. / F1 = 5 => 12 pairs (_) / F7 = 5 => 0 pairs (X) A3,B3: 6.. / A3 = 6 => 13 pairs (_) / B3 = 6 => 7 pairs (_) A8,B8: 6.. / A8 = 6 => 7 pairs (_) / B8 = 6 => 13 pairs (_) A3,A8: 6.. / A3 = 6 => 13 pairs (_) / A8 = 6 => 7 pairs (_) B3,B8: 6.. / B3 = 6 => 7 pairs (_) / B8 = 6 => 13 pairs (_) B3,C3: 8.. / B3 = 8 => 0 pairs (*) / C3 = 8 => 0 pairs (X) D4,E5: 8.. / D4 = 8 => 16 pairs (_) / E5 = 8 => 15 pairs (_) D4,I4: 8.. / D4 = 8 => 16 pairs (_) / I4 = 8 => 15 pairs (_) C3,C9: 8.. / C3 = 8 => 10 pairs (_) / C9 = 8 => 0 pairs (*) E1,E5: 8.. / E1 = 8 => 16 pairs (_) / E5 = 8 => 15 pairs (_) G1,G5: 8.. / G1 = 8 => 15 pairs (_) / G5 = 8 => 16 pairs (_) B4,C6: 9.. / B4 = 9 => 19 pairs (_) / C6 = 9 => 16 pairs (_) C6,E6: 9.. / C6 = 9 => 16 pairs (_) / E6 = 9 => 19 pairs (_) A3,A8: 9.. / A3 = 9 => 7 pairs (_) / A8 = 9 => 13 pairs (_) G1,G5: 9.. / G1 = 9 => 16 pairs (_) / G5 = 9 => 15 pairs (_) * DURATION: 0:00:48.059379 START: 15:48:25.430044 END: 15:49:13.489423 2017-05-04 * CP COUNT: (23) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A8,B4,C3,C6,E6,F2,G1,G5) * 2476...3151372.6.....3145721.4.3726.7362.1...82.4.63174.216.7.3..1.7342.37..421.6 * PAIR A3: 6,9 BLK 1 B3: 6,9,8 # reduction candidate for 6,9 B3: 8 => SOLVED * 247685931513729684689314572194837265736251849825496317452168793961573428378942156 B3: 6,9 # 10 pairs * PAIR C3: 8,9 BLK 1 B3: 8,9,6 # reduction candidate for 8,9 B3: 8,9 # 13 pairs B3: 6 # 7 pairs * PAIR C3: 8,9 COL C C9: 8,9,5 # reduction candidate for 8,9 C9: 8,9 # 19 pairs C9: 5 # 16 pairs * PAIR F2: 8,9 BLK 2 E1: 8,9,5 # reduction candidate for 8,9 E1: 8,9 # 12 pairs F1: 8,9,5 # reduction candidate for 8,9 F1: 8,9 => CTR * 2476598315137286949683145721.45372687362819..8254963174.21657.3.5187342937.942156 F1: 5 # 12 pairs * PAIR F2: 8,9 ROW 2 H2: 8,9,4 # reduction candidate for 8,9 H2: 8,9 # 11 pairs I2: 8,9,4 # reduction candidate for 8,9 I2: 8,9 # 10 pairs * PAIR F2: 8,9 COL F F7: 8,9,5 # reduction candidate for 8,9 F7: 5 => CTR * 2476598315137286949683145721.45372687362819..8254963174.21657.3.5187342937.942156 F7: 8,9 # 12 pairs * PAIR G1: 8,9 BLK 3 H2: 8,9,4 # reduction candidate for 8,9 H2: 8,9 # 11 pairs I2: 8,9,4 # reduction candidate for 8,9 I2: 8,9 # 10 pairs * PAIR G1: 8,9 ROW 1 E1: 8,9,5 # reduction candidate for 8,9 E1: 8,9 # 12 pairs F1: 8,9,5 # reduction candidate for 8,9 F1: 8,9 => CTR * 2476598315137286949683145721.45372687362819..8254963174.21657.3.5187342937.942156 F1: 5 # 12 pairs * PAIR B4: 5,9 ROW 4 D4: 5,9,8 # reduction candidate for 5,9 D4: 5,9 # 15 pairs I4: 5,9,8 # reduction candidate for 5,9 I4: 5,9 # 16 pairs * PAIR B4: 5,9 COL B B7: 5,9,8 # reduction candidate for 5,9 B7: 5,9 # 12 pairs B8: 5,9,6,8 # reduction candidate for 5,9 B8: 5,9 # 16 pairs * PAIR C6: 5,9 COL C C9: 5,9,8 # reduction candidate for 5,9 C9: 8 => SOLVED * 247685931513729684689314572194837265736251849825496317452168793961573428378942156 C9: 5,9 # 10 pairs * PAIR E6: 5,9 BLK 5 D4: 5,9,8 # reduction candidate for 5,9 D4: 5,9 # 15 pairs E5: 5,9,8 # reduction candidate for 5,9 E5: 5,9 # 16 pairs * PAIR E6: 5,9 COL E E1: 5,9,8 # reduction candidate for 5,9 E1: 8 # 16 pairs E1: 5,9 # 15 pairs * PAIR G5: 8,9 BLK 6 I4: 8,9,5 # reduction candidate for 8,9 I4: 8,9 # 13 pairs H5: 8,9,4,5 # reduction candidate for 8,9 H5: 8,9 => CTR * 247685931513729648...3145721948372657362518948254963174.2168753..1.7342.37..421.6 H5: 4,5 # 10 pairs I5: 8,9,4,5 # reduction candidate for 8,9 I5: 8,9 => SOLVED * 247685931513729684689314572194837265736251849825496317452168793961573428378942156 I5: 4,5 # 10 pairs * PAIR G5: 8,9 ROW 5 E5: 8,9,5 # reduction candidate for 8,9 E5: 5 => SOLVED * 247685931513729684689314572194837265736251849825496317452168793961573428378942156 E5: 8,9 # 13 pairs * PAIR A8: 6,9 BLK 7 B8: 6,9,5,8 # reduction candidate for 6,9 B8: 6,9 # 15 pairs B8: 5,8 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-378-base-pr-000.dot * REASONING * PRF # B3: 8 => SOL * DIS # F1: 8,9 => CTR => F1: 5 * DIS # F7: 5 => CTR => F7: 8,9 * DIS # F1: 8,9 => CTR => F1: 5 * PRF # C9: 8 => SOL * DIS # H5: 8,9 => CTR => H5: 4,5 * PRF # I5: 8,9 => SOL * PRF # E5: 5 => SOL * CNT 8 HDP CHAINS / 37 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A8,B4,C3,C6,E6,F2,G1,G5) * 2476...3151372.6.....3145721.4.3726.7362.1...82.4.63174.216.7.3..1.7342.37..421.6 * PAIR A3: 6,9 BLK 1 B3: 6,9,8 # reduction candidate for 6,9 B3: 8 => SOLVED * 247685931513729684689314572194837265736251849825496317452168793961573428378942156 * DURATION: 0:00:03.135897 START: 15:49:56.409112 END: 15:49:59.545009 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-378-base-pr-001.dot * REASONING * PRF # B3: 8 => SOL * STA B3: 8 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 378 solution: 247685931513729684689314572194837265736251849825496317452168793961573428378942156 info: 18976 FNBTWXYK S8.f 18573 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 247685931513729684689314572194837265736251849825496317452168793961573428378942156 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 # B3: 6,9 => UNS * PRF # B3: 8 => SOL * INC # B3: 8,9 => UNS * INC # B3: 6 => UNS * INC # C9: 8,9 => UNS * INC # C9: 5 => UNS * INC # E1: 8,9 => UNS * DIS # F1: 8,9 => CTR => F1: 5 * INC # F1: 5 => UNS * INC # H2: 8,9 => UNS * INC # I2: 8,9 => UNS * INC # F7: 8,9 => UNS * DIS # F7: 5 => CTR => F7: 8,9 * INC # H2: 8,9 => UNS * INC # I2: 8,9 => UNS * INC # E1: 8,9 => UNS * DIS # F1: 8,9 => CTR => F1: 5 * INC # F1: 5 => UNS * INC # D4: 5,9 => UNS * INC # I4: 5,9 => UNS * INC # B7: 5,9 => UNS * INC # B8: 5,9 => UNS * INC # C9: 5,9 => UNS * PRF # C9: 8 => SOL * INC # D4: 5,9 => UNS * INC # E5: 5,9 => UNS * INC # E1: 5,9 => UNS * INC # E1: 8 => UNS * INC # I4: 8,9 => UNS * DIS # H5: 8,9 => CTR => H5: 4,5 * INC # H5: 4,5 => UNS * PRF # I5: 8,9 => SOL * INC # I5: 4,5 => UNS * INC # E5: 8,9 => UNS * PRF # E5: 5 => SOL * INC # B8: 6,9 => UNS * INC # B8: 5,8 => UNS * CNT 37 HDP CHAINS / 37 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B3: 6,9 => UNS * PRF # B3: 8 => SOL * STA B3: 8 * CNT 2 HDP CHAINS / 2 HYP OPENED