Analysis of xx-top500-118-base.sdk
Contents
Original Sudoku
level: medium
position: ......63..7.5...........4..6.4...1.....82....3...........16...7.2.....5......4... initial
Autosolve
position: ......63..7.5...........47.6.4...1.....82.5..3.2...7.....16...7.2.....5......4... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B1: 1,9 => SOL * DIS # B1: 4 => CTR => B1: 1,9 * DIS # B3: 1,9 => CTR => B3: 3,6 * DIS # B9: 1,9 => CTR => B9: 3,6 * PRF # I5: 3,6 => SOL * DIS # I5: 4 => CTR => I5: 3,6 * DIS # F3: 3,6 => CTR => F3: 1,2,8,9 * DIS # I5: 3 => CTR => I5: 4,6 * PRF # I8: 1,4 => SOL * DIS # I8: 6 => CTR => I8: 1,4 * DIS # A1: 1,4 => CTR => A1: 2,5,8,9 * DIS # B9: 1,6 => CTR => B9: 3,9 * PRF # B9: 3,9 => SOL * DIS # C9: 1,6 => CTR => C9: 3,5,7,8,9 * DIS # I8: 1,6 => CTR => I8: 4 * PRF # I8: 4 => SOL * DIS # C3: 1,6 => CTR => C3: 3,5,8,9 * CNT 17 HDP CHAINS / 29 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B1: 1,9 => SOL * STA B1: 1,9 * CNT 1 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ......63..7.5...........4..6.4...1.....82....3...........16...7.2.....5......4... | initial |
| ......63..7.5...........47.6.4...1.....82.5..3.2...7.....16...7.2.....5......4... | autosolve |
| 218479635479536812563218479684795123791823546352641798945162387126387954837954261 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) B4: 5,8 B5: 1,9 B6: 5,8 F5: 3,6 H5: 4,6 A8: 1,4 C8: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E6,F6: 1.. / E6 = 1 => 0 pairs (X) / F6 = 1 => 7 pairs (_) H2,H9: 1.. / H2 = 1 => 7 pairs (_) / H9 = 1 => 10 pairs (_) H4,I4: 2.. / H4 = 2 => 7 pairs (_) / I4 = 2 => 0 pairs (X) F7,D9: 2.. / F7 = 2 => 12 pairs (_) / D9 = 2 => 7 pairs (_) I4,I5: 3.. / I4 = 3 => 11 pairs (_) / I5 = 3 => 0 pairs (X) F5,I5: 3.. / F5 = 3 => 11 pairs (_) / I5 = 3 => 0 pairs (X) D6,E6: 4.. / D6 = 4 => 0 pairs (X) / E6 = 4 => 0 pairs (_) H5,I5: 4.. / H5 = 4 => 0 pairs (*) / I5 = 4 => 0 pairs (X) H7,I8: 4.. / H7 = 4 => 0 pairs (X) / I8 = 4 => 0 pairs (_) A2,E2: 4.. / A2 = 4 => 0 pairs (*) / E2 = 4 => 0 pairs (X) A8,I8: 4.. / A8 = 4 => 0 pairs (X) / I8 = 4 => 0 pairs (_) B1,B7: 4.. / B1 = 4 => 0 pairs (X) / B7 = 4 => 0 pairs (_) D1,D6: 4.. / D1 = 4 => 0 pairs (*) / D6 = 4 => 0 pairs (X) H5,H7: 4.. / H5 = 4 => 0 pairs (*) / H7 = 4 => 0 pairs (X) I5,I8: 4.. / I5 = 4 => 0 pairs (X) / I8 = 4 => 0 pairs (_) I1,I3: 5.. / I1 = 5 => 7 pairs (_) / I3 = 5 => 7 pairs (_) B4,B6: 5.. / B4 = 5 => 0 pairs (X) / B6 = 5 => 6 pairs (_) F7,E9: 5.. / F7 = 5 => 9 pairs (_) / E9 = 5 => 7 pairs (_) C2,F2: 6.. / C2 = 6 => 0 pairs (X) / F2 = 6 => 0 pairs (_) C8,I8: 6.. / C8 = 6 => 0 pairs (*) / I8 = 6 => 0 pairs (X) B3,B9: 6.. / B3 = 6 => 0 pairs (*) / B9 = 6 => 0 pairs (X) D3,D6: 6.. / D3 = 6 => 0 pairs (X) / D6 = 6 => 0 pairs (_) A5,C5: 7.. / A5 = 7 => 8 pairs (_) / C5 = 7 => 8 pairs (_) A9,C9: 7.. / A9 = 7 => 8 pairs (_) / C9 = 7 => 8 pairs (_) A5,A9: 7.. / A5 = 7 => 8 pairs (_) / A9 = 7 => 8 pairs (_) C5,C9: 7.. / C5 = 7 => 8 pairs (_) / C9 = 7 => 8 pairs (_) B4,B6: 8.. / B4 = 8 => 6 pairs (_) / B6 = 8 => 0 pairs (X) * DURATION: 0:00:44.670604 START: 06:49:24.764615 END: 06:50:09.435219 2017-05-04 * CP COUNT: (27) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B4,B5,B6,C8,F5,H5) * ......63..7.5...........47.6.4...1.....82.5..3.2...7.....16...7.2.....5......4... * PAIR B5: 1,9 BLK 4 A5: 1,9,7 # reduction candidate for 1,9 A5: 1,9 # 8 pairs C5: 1,9,7 # reduction candidate for 1,9 C5: 1,9 # 8 pairs * PAIR B5: 1,9 COL B B1: 1,9,4 # reduction candidate for 1,9 B1: 1,9 => SOLVED * 218479635479536812563218479684795123791823546352641798945162387126387954837954261 B1: 4 => CTR * .4....63..76543......6..47.6.4...1.....8265433.24..7.....16...7.2.....5..6...4... B3: 1,9,3,6 # reduction candidate for 1,9 B3: 1,9 => CTR * .4....63..7.54.......6..47.6.4...1.3...8235643.24.67...3.16..47421....56.6...4... B3: 3,6 # 8 pairs B9: 1,9,3,6 # reduction candidate for 1,9 B9: 1,9 => CTR * .4....63..7.5.6....6....47.6.4...1.....8235..3526417...3.16...7.2.....5......4... B9: 3,6 # 8 pairs * PAIR F5: 3,6 ROW 5 I5: 3,6,4 # reduction candidate for 3,6 I5: 3,6 => SOLVED * 218479635479536812563218479684795123791823546352641798945162387126387954837954261 I5: 4 => CTR * .4....63..7.54..........47.6.4...123...8235643.24.67.....16..4742.....5......4... * PAIR F5: 3,6 COL F F2: 3,6,1,2,8,9 # reduction candidate for 3,6 F2: 3,6 # 8 pairs F3: 3,6,1,2,8,9 # reduction candidate for 3,6 F3: 3,6 => CTR * ...4..63.47653.........647.6.4...1.....8235..3.26417.....16...7.21....56.6...4... F3: 1,2,8,9 # 7 pairs * PAIR H5: 4,6 BLK 6 I5: 4,6,3 # reduction candidate for 4,6 I5: 3 => CTR * ......63..7.5...........47.6.4...1.....8265433.2...7.....16...7126....54.....4... I5: 4,6 # 11 pairs * PAIR A8: 1,4 ROW 8 I8: 1,4,6 # reduction candidate for 1,4 I8: 1,4 => SOLVED * 218479635479536812563218479684795123791823546352641798945162387126387954837954261 I8: 6 => CTR * .4....63..7.54..........47.6.4...1.3...8235643.24.67.....16..47421....56.....4... * PAIR A8: 1,4 COL A A1: 1,4,2,5,8,9 # reduction candidate for 1,4 A1: 1,4 => CTR * ......63..76543......6..47.6.4...1.....8265433.24..7.....16...7.2.....5..6...4... A1: 2,5,8,9 # 7 pairs A2: 1,4,2,8,9 # reduction candidate for 1,4 A2: 1,4 # 9 pairs * PAIR C8: 1,6 BLK 7 B9: 1,6,3,9 # reduction candidate for 1,6 B9: 1,6 => CTR * .4....63..7.54..........47.6.4...1.3...8235643.24.67.....16..4742.....5......4... B9: 3,9 => SOLVED * 218479635479536812563218479684795123791823546352641798945162387126387954837954261 C9: 1,6,3,5,7,8,9 # reduction candidate for 1,6 C9: 1,6 => CTR * ......63..7.5.6....6....47.6.4...1....78235.43.26417.....16..4742.....5.7...54... C9: 3,5,7,8,9 # 7 pairs * PAIR C8: 1,6 ROW 8 I8: 1,6,4 # reduction candidate for 1,6 I8: 1,6 => CTR * .4....63..7.54..........47.6.4...1.3...8235643.24.67.....16..4742.....5......4... I8: 4 => SOLVED * 218479635479536812563218479684795123791823546352641798945162387126387954837954261 * PAIR C8: 1,6 COL C C2: 1,6,3,8,9 # reduction candidate for 1,6 C2: 1,6 # 9 pairs C3: 1,6,3,5,8,9 # reduction candidate for 1,6 C3: 1,6 => CTR * 29.41763.473586912.6123.47.684...123.1.8235463526417...4.1623.712637..54.3.954261 C3: 3,5,8,9 # 7 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-118-base-pr-000.dot * REASONING * PRF # B1: 1,9 => SOL * DIS # B1: 4 => CTR => B1: 1,9 * DIS # B3: 1,9 => CTR => B3: 3,6 * DIS # B9: 1,9 => CTR => B9: 3,6 * PRF # I5: 3,6 => SOL * DIS # I5: 4 => CTR => I5: 3,6 * DIS # F3: 3,6 => CTR => F3: 1,2,8,9 * DIS # I5: 3 => CTR => I5: 4,6 * PRF # I8: 1,4 => SOL * DIS # I8: 6 => CTR => I8: 1,4 * DIS # A1: 1,4 => CTR => A1: 2,5,8,9 * DIS # B9: 1,6 => CTR => B9: 3,9 * PRF # B9: 3,9 => SOL * DIS # C9: 1,6 => CTR => C9: 3,5,7,8,9 * DIS # I8: 1,6 => CTR => I8: 4 * PRF # I8: 4 => SOL * DIS # C3: 1,6 => CTR => C3: 3,5,8,9 * CNT 17 HDP CHAINS / 29 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B4,B5,B6,C8,F5,H5) * ......63..7.5...........47.6.4...1.....82.5..3.2...7.....16...7.2.....5......4... * PAIR B5: 1,9 BLK 4 A5: 1,9,7 # reduction candidate for 1,9 A5: 1,9 # 8 pairs C5: 1,9,7 # reduction candidate for 1,9 C5: 1,9 # 8 pairs * PAIR B5: 1,9 COL B B1: 1,9,4 # reduction candidate for 1,9 B1: 1,9 => SOLVED * 218479635479536812563218479684795123791823546352641798945162387126387954837954261 * DURATION: 0:00:04.197627 START: 06:50:36.458914 END: 06:50:40.656541 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-118-base-pr-001.dot * REASONING * PRF # B1: 1,9 => SOL * STA B1: 1,9 * CNT 1 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 118 solution: 218479635479536812563218479684795123791823546352641798945162387126387954837954261 info: 1777 FNBTHXY S8.f 45999 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 218479635479536812563218479684795123791823546352641798945162387126387954837954261 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 # A5: 1,9 => UNS * INC # C5: 1,9 => UNS * PRF # B1: 1,9 => SOL * DIS # B1: 4 => CTR => B1: 1,9 * DIS # B3: 1,9 => CTR => B3: 3,6 * INC # B3: 3,6 => UNS * DIS # B9: 1,9 => CTR => B9: 3,6 * INC # B9: 3,6 => UNS * PRF # I5: 3,6 => SOL * DIS # I5: 4 => CTR => I5: 3,6 * INC # F2: 3,6 => UNS * DIS # F3: 3,6 => CTR => F3: 1,2,8,9 * INC # F3: 1,2,8,9 => UNS * INC # I5: 4,6 => UNS * DIS # I5: 3 => CTR => I5: 4,6 * PRF # I8: 1,4 => SOL * DIS # I8: 6 => CTR => I8: 1,4 * DIS # A1: 1,4 => CTR => A1: 2,5,8,9 * INC # A1: 2,5,8,9 => UNS * INC # A2: 1,4 => UNS * DIS # B9: 1,6 => CTR => B9: 3,9 * PRF # B9: 3,9 => SOL * DIS # C9: 1,6 => CTR => C9: 3,5,7,8,9 * INC # C9: 3,5,7,8,9 => UNS * DIS # I8: 1,6 => CTR => I8: 4 * PRF # I8: 4 => SOL * INC # C2: 1,6 => UNS * DIS # C3: 1,6 => CTR => C3: 3,5,8,9 * INC # C3: 3,5,8,9 => UNS * CNT 29 HDP CHAINS / 29 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A5: 1,9 => UNS * INC # C5: 1,9 => UNS * PRF # B1: 1,9 => SOL * STA B1: 1,9 * CNT 3 HDP CHAINS / 3 HYP OPENED