Analysis of xx-top500-139-base.sdk
Contents
Original Sudoku
level: medium
position: 2......36.7.4............5.1..5........2..7..3.5..........36....4....8......1.... initial
Autosolve
position: 25.1.7.369734651...1632..5712754.36..6.2.37153.56712.47.2.36541641.528.353..146.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C5: 4,8 => SOL * DIS # C5: 9 => CTR => C5: 4,8 * PRF # C5: 4,8 => SOL * DIS # C5: 9 => CTR => C5: 4,8 * PRF # C5: 8,9 => SOL * DIS # C5: 4 => CTR => C5: 8,9 * PRF # C5: 8,9 => SOL * DIS # C5: 4 => CTR => C5: 8,9 * PRF # D9: 8,9 => SOL * DIS # D9: 7 => CTR => D9: 8,9 * PRF # C5: 8,9 => SOL * DIS # C5: 4 => CTR => C5: 8,9 * PRF # D9: 8,9 => SOL * DIS # D9: 7 => CTR => D9: 8,9 * DIS # D9: 7,9 => CTR => D9: 8 * PRF # D9: 8 => SOL * PRF # H9: 7,9 => SOL * DIS # H9: 2 => CTR => H9: 7,9 * DIS # H9: 2,9 => CTR => H9: 7 * PRF # H9: 7 => SOL * CNT 20 HDP CHAINS / 20 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C5: 4,8 => SOL * STA C5: 4,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 2......36.7.4............5.1..5........2..7..3.5..........36....4....8......1.... | initial |
| 25.1.7.369734651...1632..5712754.36..6.2.37153.56712.47.2.36541641.528.353..146.. | autosolve |
| 254187936973465128816329457127548369468293715395671284782936541641752893539814672 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) C1: 4,8 A3: 4,8 E1: 8,9 F3: 8,9 G1: 4,9 H2: 2,8 I2: 2,8 G3: 4,9 A5: 4,8 B6: 8,9 F4: 8,9 E5: 8,9 I4: 8,9 H6: 8,9 B7: 8,9 C9: 8,9 D7: 8,9 D8: 7,9 H8: 7,9 I9: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H2,I2: 2.. / H2 = 2 => 0 pairs (*) / I2 = 2 => 0 pairs (X) H9,I9: 2.. / H9 = 2 => 0 pairs (X) / I9 = 2 => 0 pairs (_) H2,H9: 2.. / H2 = 2 => 0 pairs (*) / H9 = 2 => 0 pairs (X) I2,I9: 2.. / I2 = 2 => 0 pairs (X) / I9 = 2 => 0 pairs (_) C1,A3: 4.. / C1 = 4 => 0 pairs (*) / A3 = 4 => 0 pairs (X) G1,G3: 4.. / G1 = 4 => 0 pairs (X) / G3 = 4 => 0 pairs (_) A5,C5: 4.. / A5 = 4 => 0 pairs (*) / C5 = 4 => 0 pairs (X) C1,G1: 4.. / C1 = 4 => 0 pairs (*) / G1 = 4 => 0 pairs (X) A3,G3: 4.. / A3 = 4 => 0 pairs (X) / G3 = 4 => 0 pairs (_) A3,A5: 4.. / A3 = 4 => 0 pairs (X) / A5 = 4 => 0 pairs (_) C1,C5: 4.. / C1 = 4 => 0 pairs (*) / C5 = 4 => 0 pairs (X) D8,D9: 7.. / D8 = 7 => 0 pairs (*) / D9 = 7 => 0 pairs (X) H8,H9: 7.. / H8 = 7 => 0 pairs (X) / H9 = 7 => 0 pairs (_) D8,H8: 7.. / D8 = 7 => 0 pairs (*) / H8 = 7 => 0 pairs (X) D9,H9: 7.. / D9 = 7 => 0 pairs (X) / H9 = 7 => 0 pairs (_) C1,A3: 8.. / C1 = 8 => 0 pairs (X) / A3 = 8 => 0 pairs (_) E1,F3: 8.. / E1 = 8 => 0 pairs (*) / F3 = 8 => 0 pairs (X) H2,I2: 8.. / H2 = 8 => 0 pairs (X) / I2 = 8 => 0 pairs (_) F4,E5: 8.. / F4 = 8 => 0 pairs (*) / E5 = 8 => 0 pairs (X) I4,H6: 8.. / I4 = 8 => 0 pairs (X) / H6 = 8 => 0 pairs (_) B7,C9: 8.. / B7 = 8 => 0 pairs (*) / C9 = 8 => 0 pairs (X) D7,D9: 8.. / D7 = 8 => 0 pairs (X) / D9 = 8 => 0 pairs (_) C1,E1: 8.. / C1 = 8 => 0 pairs (X) / E1 = 8 => 0 pairs (_) A3,F3: 8.. / A3 = 8 => 0 pairs (*) / F3 = 8 => 0 pairs (X) F4,I4: 8.. / F4 = 8 => 0 pairs (*) / I4 = 8 => 0 pairs (X) B6,H6: 8.. / B6 = 8 => 0 pairs (X) / H6 = 8 => 0 pairs (_) B7,D7: 8.. / B7 = 8 => 0 pairs (*) / D7 = 8 => 0 pairs (X) C9,D9: 8.. / C9 = 8 => 0 pairs (X) / D9 = 8 => 0 pairs (_) A3,A5: 8.. / A3 = 8 => 0 pairs (*) / A5 = 8 => 0 pairs (X) B6,B7: 8.. / B6 = 8 => 0 pairs (X) / B7 = 8 => 0 pairs (_) E1,E5: 8.. / E1 = 8 => 0 pairs (*) / E5 = 8 => 0 pairs (X) F3,F4: 8.. / F3 = 8 => 0 pairs (X) / F4 = 8 => 0 pairs (_) H2,H6: 8.. / H2 = 8 => 0 pairs (X) / H6 = 8 => 0 pairs (_) I2,I4: 8.. / I2 = 8 => 0 pairs (*) / I4 = 8 => 0 pairs (X) E1,F3: 9.. / E1 = 9 => 0 pairs (X) / F3 = 9 => 0 pairs (_) G1,G3: 9.. / G1 = 9 => 0 pairs (*) / G3 = 9 => 0 pairs (X) C5,B6: 9.. / C5 = 9 => 0 pairs (X) / B6 = 9 => 0 pairs (_) F4,E5: 9.. / F4 = 9 => 0 pairs (X) / E5 = 9 => 0 pairs (_) I4,H6: 9.. / I4 = 9 => 0 pairs (*) / H6 = 9 => 0 pairs (X) B7,C9: 9.. / B7 = 9 => 0 pairs (X) / C9 = 9 => 0 pairs (_) E1,G1: 9.. / E1 = 9 => 0 pairs (X) / G1 = 9 => 0 pairs (_) F3,G3: 9.. / F3 = 9 => 0 pairs (*) / G3 = 9 => 0 pairs (X) F4,I4: 9.. / F4 = 9 => 0 pairs (X) / I4 = 9 => 0 pairs (_) C5,E5: 9.. / C5 = 9 => 0 pairs (X) / E5 = 9 => 0 pairs (_) B6,H6: 9.. / B6 = 9 => 0 pairs (*) / H6 = 9 => 0 pairs (X) B7,D7: 9.. / B7 = 9 => 0 pairs (X) / D7 = 9 => 0 pairs (_) D8,H8: 9.. / D8 = 9 => 0 pairs (X) / H8 = 9 => 0 pairs (_) B6,B7: 9.. / B6 = 9 => 0 pairs (*) / B7 = 9 => 0 pairs (X) C5,C9: 9.. / C5 = 9 => 0 pairs (X) / C9 = 9 => 0 pairs (_) E1,E5: 9.. / E1 = 9 => 0 pairs (X) / E5 = 9 => 0 pairs (_) F3,F4: 9.. / F3 = 9 => 0 pairs (*) / F4 = 9 => 0 pairs (X) I4,I9: 9.. / I4 = 9 => 0 pairs (*) / I9 = 9 => 0 pairs (X) * DURATION: 0:01:28.309726 START: 07:29:26.878917 END: 07:30:55.188643 2017-05-04 * CP COUNT: (52) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,B6,B7,C1,C9,D7,D8,E1,E5,F3,F4,G1,G3,H2,H6,H8,I2,I4,I9) * 25.1.7.369734651...1632..5712754.36..6.2.37153.56712.47.2.36541641.528.353..146.. * PAIR C1: 4,8 COL C C5: 4,8,9 # reduction candidate for 4,8 C5: 4,8 => SOLVED * 254187936973465128816329457127548369468293715395671284782936541641752893539814672 C5: 9 => CTR * 2541879369734651..81632..5712754.36..6.2.37153.56712.47.2.36541641.528.353..146.. * PAIR A5: 4,8 BLK 4 C5: 4,8,9 # reduction candidate for 4,8 C5: 4,8 => SOLVED * 254187936973465128816329457127548369468293715395671284782936541641752893539814672 C5: 9 => CTR * 2541879369734651..81632..5712754.36..6.2.37153.56712.47.2.36541641.528.353..146.. * PAIR B6: 8,9 BLK 4 C5: 8,9,4 # reduction candidate for 8,9 C5: 8,9 => SOLVED * 254187936973465128816329457127548369468293715395671284782936541641752893539814672 C5: 4 => CTR * 25.1.7.369734651...1632..5712754.36..64293715395671284782936541641752893539814672 * PAIR E5: 8,9 ROW 5 C5: 8,9,4 # reduction candidate for 8,9 C5: 8,9 => SOLVED * 254187936973465128816329457127548369468293715395671284782936541641752893539814672 C5: 4 => CTR * 25.1.7.369734651...1632..5712754.36..64293715395671284782936541641752893539814672 * PAIR C9: 8,9 ROW 9 D9: 8,9,7 # reduction candidate for 8,9 D9: 8,9 => SOLVED * 254187936973465128816329457127548369468293715395671284782936541641752893539814672 D9: 7 => CTR * 2541879369734651..81632..5712754.36..6.2.37153.56712.47.28365416419528735387146.. * PAIR C9: 8,9 COL C C5: 8,9,4 # reduction candidate for 8,9 C5: 8,9 => SOLVED * 254187936973465128816329457127548369468293715395671284782936541641752893539814672 C5: 4 => CTR * 25.1.7.369734651...1632..5712754.36..64293715395671284782936541641752893539814672 * PAIR D7: 8,9 BLK 8 D9: 8,9,7 # reduction candidate for 8,9 D9: 8,9 => SOLVED * 254187936973465128816329457127548369468293715395671284782936541641752893539814672 D9: 7 => CTR * 2541879369734651..81632..5712754.36..6.2.37153.56712.47.28365416419528735387146.. * PAIR D8: 7,9 BLK 8 D9: 7,9,8 # reduction candidate for 7,9 D9: 7,9 => CTR * 2541879369734651..81632..5712754.36..6.2.37153.56712.47.2836541641.528.3538.146.. D9: 8 => SOLVED * 254187936973465128816329457127548369468293715395671284782936541641752893539814672 * PAIR H8: 7,9 BLK 9 H9: 7,9,2 # reduction candidate for 7,9 H9: 7,9 => SOLVED * 254187936973465128816329457127548369468293715395671284782936541641752893539814672 H9: 2 => CTR * 25.1.7.36973465182.1632..57127549368.69283715385671294792836541641952873538714629 * PAIR I9: 2,9 BLK 9 H9: 2,9,7 # reduction candidate for 2,9 H9: 2,9 => CTR * 2541879369734651..81632..5712754.36..6.2.37153.56712.47.28365416419528735387146.. H9: 7 => SOLVED * 254187936973465128816329457127548369468293715395671284782936541641752893539814672 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-139-base-pr-000.dot * REASONING * PRF # C5: 4,8 => SOL * DIS # C5: 9 => CTR => C5: 4,8 * PRF # C5: 4,8 => SOL * DIS # C5: 9 => CTR => C5: 4,8 * PRF # C5: 8,9 => SOL * DIS # C5: 4 => CTR => C5: 8,9 * PRF # C5: 8,9 => SOL * DIS # C5: 4 => CTR => C5: 8,9 * PRF # D9: 8,9 => SOL * DIS # D9: 7 => CTR => D9: 8,9 * PRF # C5: 8,9 => SOL * DIS # C5: 4 => CTR => C5: 8,9 * PRF # D9: 8,9 => SOL * DIS # D9: 7 => CTR => D9: 8,9 * DIS # D9: 7,9 => CTR => D9: 8 * PRF # D9: 8 => SOL * PRF # H9: 7,9 => SOL * DIS # H9: 2 => CTR => H9: 7,9 * DIS # H9: 2,9 => CTR => H9: 7 * PRF # H9: 7 => SOL * CNT 20 HDP CHAINS / 20 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,B6,B7,C1,C9,D7,D8,E1,E5,F3,F4,G1,G3,H2,H6,H8,I2,I4,I9) * 25.1.7.369734651...1632..5712754.36..6.2.37153.56712.47.2.36541641.528.353..146.. * PAIR C1: 4,8 COL C C5: 4,8,9 # reduction candidate for 4,8 C5: 4,8 => SOLVED * 254187936973465128816329457127548369468293715395671284782936541641752893539814672 * DURATION: 0:00:01.924636 START: 07:31:18.713514 END: 07:31:20.638150 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-139-base-pr-001.dot * REASONING * PRF # C5: 4,8 => SOL * STA C5: 4,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 139 solution: 254187936973465128816329457127548369468293715395671284782936541641752893539814672 info: 1813 FNBWX S8.f 26741 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 254187936973465128816329457127548369468293715395671284782936541641752893539814672 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:
* PRF # C5: 4,8 => SOL * DIS # C5: 9 => CTR => C5: 4,8 * PRF # C5: 4,8 => SOL * DIS # C5: 9 => CTR => C5: 4,8 * PRF # C5: 8,9 => SOL * DIS # C5: 4 => CTR => C5: 8,9 * PRF # C5: 8,9 => SOL * DIS # C5: 4 => CTR => C5: 8,9 * PRF # D9: 8,9 => SOL * DIS # D9: 7 => CTR => D9: 8,9 * PRF # C5: 8,9 => SOL * DIS # C5: 4 => CTR => C5: 8,9 * PRF # D9: 8,9 => SOL * DIS # D9: 7 => CTR => D9: 8,9 * DIS # D9: 7,9 => CTR => D9: 8 * PRF # D9: 8 => SOL * PRF # H9: 7,9 => SOL * DIS # H9: 2 => CTR => H9: 7,9 * DIS # H9: 2,9 => CTR => H9: 7 * PRF # H9: 7 => SOL * CNT 20 HDP CHAINS / 20 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C5: 4,8 => SOL * STA C5: 4,8 * CNT 1 HDP CHAINS / 1 HYP OPENED