Analysis of xx-top500-122-base.sdk
Contents
Original Sudoku
level: medium
position: 1.8.....6...7.34............4....57.5...1...........3..7.5.........8...12........ initial
Autosolve
position: 138.5.7.6.5.7.34187.41683.53418.657.5.731.68..8..7513.879541263463287951215639847 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I5: 2,9 => CTR => I5: 4 * PRF # I5: 4 => SOL * PRF # I5: 2,4 => SOL * DIS # I5: 9 => CTR => I5: 2,4 * PRF # I6: 4,9 => SOL * DIS # I6: 2 => CTR => I6: 4,9 * DIS # I5: 2,9 => CTR => I5: 4 * PRF # I5: 4 => SOL * PRF # I6: 2,9 => SOL * DIS # I6: 4 => CTR => I6: 2,9 * CNT 10 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I5: 2,9 => CTR => I5: 4 * PRF I5: 4 => SOL * STA I5: 4 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1.8.....6...7.34............4....57.5...1...........3..7.5.........8...12........ | initial |
| 138.5.7.6.5.7.34187.41683.53418.657.5.731.68..8..7513.879541263463287951215639847 | autosolve |
| 138954726956723418724168395341896572597312684682475139879541263463287951215639847 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) A2: 6,9 C2: 2,6 B3: 2,9 D1: 4,9 F1: 2,4 E2: 2,9 H1: 2,9 H3: 2,9 B5: 2,9 A6: 6,9 C6: 2,6 E4: 2,9 F5: 2,4 D6: 4,9 I4: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,B3: 2.. / C2 = 2 => 0 pairs (X) / B3 = 2 => 0 pairs (_) F1,E2: 2.. / F1 = 2 => 0 pairs (X) / E2 = 2 => 0 pairs (_) H1,H3: 2.. / H1 = 2 => 0 pairs (*) / H3 = 2 => 0 pairs (X) B5,C6: 2.. / B5 = 2 => 0 pairs (X) / C6 = 2 => 0 pairs (_) E4,F5: 2.. / E4 = 2 => 0 pairs (X) / F5 = 2 => 0 pairs (_) F1,H1: 2.. / F1 = 2 => 0 pairs (X) / H1 = 2 => 0 pairs (_) C2,E2: 2.. / C2 = 2 => 0 pairs (X) / E2 = 2 => 0 pairs (_) B3,H3: 2.. / B3 = 2 => 0 pairs (*) / H3 = 2 => 0 pairs (X) E4,I4: 2.. / E4 = 2 => 0 pairs (X) / I4 = 2 => 0 pairs (_) C6,I6: 2.. / C6 = 2 => 0 pairs (*) / I6 = 2 => 0 pairs (X) B3,B5: 2.. / B3 = 2 => 0 pairs (*) / B5 = 2 => 0 pairs (X) C2,C6: 2.. / C2 = 2 => 0 pairs (X) / C6 = 2 => 0 pairs (_) E2,E4: 2.. / E2 = 2 => 0 pairs (*) / E4 = 2 => 0 pairs (X) F1,F5: 2.. / F1 = 2 => 0 pairs (X) / F5 = 2 => 0 pairs (_) D1,F1: 4.. / D1 = 4 => 0 pairs (X) / F1 = 4 => 0 pairs (_) F5,D6: 4.. / F5 = 4 => 0 pairs (X) / D6 = 4 => 0 pairs (_) I5,I6: 4.. / I5 = 4 => 0 pairs (*) / I6 = 4 => 0 pairs (X) F5,I5: 4.. / F5 = 4 => 0 pairs (X) / I5 = 4 => 0 pairs (_) D6,I6: 4.. / D6 = 4 => 0 pairs (*) / I6 = 4 => 0 pairs (X) D1,D6: 4.. / D1 = 4 => 0 pairs (X) / D6 = 4 => 0 pairs (_) F1,F5: 4.. / F1 = 4 => 0 pairs (*) / F5 = 4 => 0 pairs (X) A2,C2: 6.. / A2 = 6 => 0 pairs (X) / C2 = 6 => 0 pairs (_) A6,C6: 6.. / A6 = 6 => 0 pairs (*) / C6 = 6 => 0 pairs (X) A2,A6: 6.. / A2 = 6 => 0 pairs (X) / A6 = 6 => 0 pairs (_) C2,C6: 6.. / C2 = 6 => 0 pairs (*) / C6 = 6 => 0 pairs (X) A2,B3: 9.. / A2 = 9 => 0 pairs (*) / B3 = 9 => 0 pairs (X) D1,E2: 9.. / D1 = 9 => 0 pairs (*) / E2 = 9 => 0 pairs (X) H1,H3: 9.. / H1 = 9 => 0 pairs (X) / H3 = 9 => 0 pairs (_) B5,A6: 9.. / B5 = 9 => 0 pairs (*) / A6 = 9 => 0 pairs (X) E4,D6: 9.. / E4 = 9 => 0 pairs (*) / D6 = 9 => 0 pairs (X) D1,H1: 9.. / D1 = 9 => 0 pairs (*) / H1 = 9 => 0 pairs (X) A2,E2: 9.. / A2 = 9 => 0 pairs (*) / E2 = 9 => 0 pairs (X) B3,H3: 9.. / B3 = 9 => 0 pairs (X) / H3 = 9 => 0 pairs (_) E4,I4: 9.. / E4 = 9 => 0 pairs (*) / I4 = 9 => 0 pairs (X) B5,I5: 9.. / B5 = 9 => 0 pairs (*) / I5 = 9 => 0 pairs (X) A2,A6: 9.. / A2 = 9 => 0 pairs (*) / A6 = 9 => 0 pairs (X) B3,B5: 9.. / B3 = 9 => 0 pairs (X) / B5 = 9 => 0 pairs (_) D1,D6: 9.. / D1 = 9 => 0 pairs (*) / D6 = 9 => 0 pairs (X) E2,E4: 9.. / E2 = 9 => 0 pairs (X) / E4 = 9 => 0 pairs (_) * DURATION: 0:01:04.854525 START: 06:56:33.979423 END: 06:57:38.833948 2017-05-04 * CP COUNT: (39) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,B3,B5,C2,C6,D1,D6,E2,E4,F1,F5,H1,H3,I4) * 138.5.7.6.5.7.34187.41683.53418.657.5.731.68..8..7513.879541263463287951215639847 * PAIR B5: 2,9 ROW 5 I5: 2,9,4 # reduction candidate for 2,9 I5: 2,9 => CTR * 13845279695.7.34187.41683.53418.657.5.731468..8.975134879541263463287951215639847 I5: 4 => SOLVED * 138954726956723418724168395341896572597312684682475139879541263463287951215639847 * PAIR F5: 2,4 ROW 5 I5: 2,4,9 # reduction candidate for 2,4 I5: 2,4 => SOLVED * 138954726956723418724168395341896572597312684682475139879541263463287951215639847 I5: 9 => CTR * 138.5.7.6.5.7.34187.41683.53418.657.5.731468998..7513.879541263463287951215639847 * PAIR D6: 4,9 ROW 6 I6: 4,9,2 # reduction candidate for 4,9 I6: 4,9 => SOLVED * 138954726956723418724168395341896572597312684682475139879541263463287951215639847 I6: 2 => CTR * 138.5.7.6.5.7.34187.41683.53418.657.5.731.684.8.475132879541263463287951215639847 * PAIR I4: 2,9 BLK 6 I5: 2,9,4 # reduction candidate for 2,9 I5: 2,9 => CTR * 13845279695.7.34187.41683.53418.657.5.731468..8.975134879541263463287951215639847 I5: 4 => SOLVED * 138954726956723418724168395341896572597312684682475139879541263463287951215639847 I6: 2,9,4 # reduction candidate for 2,9 I6: 2,9 => SOLVED * 138954726956723418724168395341896572597312684682475139879541263463287951215639847 I6: 4 => CTR * 1384527.6.5.7.34187.41683.53418.657.5.731.68..82.75134879541263463287951215639847 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-122-base-pr-000.dot * REASONING * DIS # I5: 2,9 => CTR => I5: 4 * PRF # I5: 4 => SOL * PRF # I5: 2,4 => SOL * DIS # I5: 9 => CTR => I5: 2,4 * PRF # I6: 4,9 => SOL * DIS # I6: 2 => CTR => I6: 4,9 * DIS # I5: 2,9 => CTR => I5: 4 * PRF # I5: 4 => SOL * PRF # I6: 2,9 => SOL * DIS # I6: 4 => CTR => I6: 2,9 * CNT 10 HDP CHAINS / 10 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,B3,B5,C2,C6,D1,D6,E2,E4,F1,F5,H1,H3,I4) * 138.5.7.6.5.7.34187.41683.53418.657.5.731.68..8..7513.879541263463287951215639847 * PAIR B5: 2,9 ROW 5 I5: 2,9,4 # reduction candidate for 2,9 I5: 2,9 => CTR * 13845279695.7.34187.41683.53418.657.5.731468..8.975134879541263463287951215639847 I5: 4 => SOLVED * 138954726956723418724168395341896572597312684682475139879541263463287951215639847 * DURATION: 0:00:03.144498 START: 06:57:51.292948 END: 06:57:54.437446 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-122-base-pr-001.dot * REASONING * DIS # I5: 2,9 => CTR => I5: 4 * PRF I5: 4 => SOL * STA I5: 4 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 122 solution: 138954726956723418724168395341896572597312684682475139879541263463287951215639847 info: 1805 FNWX S8.f 26234 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 138954726956723418724168395341896572597312684682475139879541263463287951215639847 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 # I5: 2,9 => CTR => I5: 4 * PRF # I5: 4 => SOL * PRF # I5: 2,4 => SOL * DIS # I5: 9 => CTR => I5: 2,4 * PRF # I6: 4,9 => SOL * DIS # I6: 2 => CTR => I6: 4,9 * DIS # I5: 2,9 => CTR => I5: 4 * PRF # I5: 4 => SOL * PRF # I6: 2,9 => SOL * DIS # I6: 4 => CTR => I6: 2,9 * CNT 10 HDP CHAINS / 10 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # I5: 2,9 => CTR => I5: 4 * PRF I5: 4 => SOL * STA I5: 4 * CNT 2 HDP CHAINS / 1 HYP OPENED