Analysis of xx-top500-431-base.sdk
Contents
Original Sudoku
level: medium
position: 9.......4...3..6.............75.4.........71.....2..9....6..8..49.......2...1.... initial
Autosolve
position: 9.......4...3..6...........1275943..5498..712....2.495...6..8..49.......2...1.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F2: 7,8 => CTR => F2: 1,2,5,9 * DIS # D1: 1,7 => CTR => D1: 2 * DIS # F2: 1,7 => CTR => F2: 2,5,8,9 * DIS # E7: 3,7 => CTR => E7: 4,5 * DIS # F7: 3,7 => CTR => F7: 2,5,9 * DIS # I7: 3,7 => CTR => I7: 1,9 * DIS # F8: 2,7 => CTR => F8: 3,5,8 * DIS # D1: 1 => CTR => D1: 2,7 * DIS # F9: 5,9 => CTR => F9: 3,7,8 * DIS # G3: 1,2 => CTR => G3: 5,9 * CNT 10 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:
* DIS # F2: 7,8 => CTR => F2: 1,2,5,9 * DIS F2: 1,2,5,9 # D1: 1,7 => CTR => D1: 2 * DIS F2: 1,2,5,9 + D1: 2 # I7: 3,7 => CTR => I7: 1,9 * DIS F2: 1,2,5,9 + D1: 2 + I7: 1,9 # F9: 5,9 => CTR => F9: 3,8 * DIS F2: 1,2,5,9 + D1: 2 + I7: 1,9 + F9: 3,8 # G3: 1,2 => CTR => G3: 5,9 * PRF F2: 1,2,5,9 + D1: 2 + I7: 1,9 + F9: 3,8 + G3: 5,9 # B1: 7,8 => SOL * STA F2: 1,2,5,9 + D1: 2 + I7: 1,9 + F9: 3,8 + G3: 5,9 + B1: 7,8 * CNT 6 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 9.......4...3..6.............75.4.........71.....2..9....6..8..49.......2...1.... | initial |
| 9.......4...3..6...........1275943..5498..712....2.495...6..8..49.......2...1.... | autosolve |
| 985276134714359628632481957127594386549863712863127495351642879498735261276918543 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) A2: 7,8 D3: 4,9 E5: 3,6 F5: 3,6 D6: 1,7 F6: 1,7 H4: 6,8 I4: 6,8 A7: 3,7 D8: 2,7 D9: 4,9 G9: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D6,F6: 1.. / D6 = 1 => 11 pairs (_) / F6 = 1 => 0 pairs (X) D1,D6: 1.. / D1 = 1 => 0 pairs (X) / D6 = 1 => 11 pairs (_) F7,H7: 2.. / F7 = 2 => 12 pairs (_) / H7 = 2 => 0 pairs (X) D1,D8: 2.. / D1 = 2 => 12 pairs (_) / D8 = 2 => 0 pairs (X) E5,F5: 3.. / E5 = 3 => 10 pairs (_) / F5 = 3 => 10 pairs (_) C2,C3: 4.. / C2 = 4 => 12 pairs (_) / C3 = 4 => 0 pairs (X) E7,D9: 4.. / E7 = 4 => 12 pairs (_) / D9 = 4 => 0 pairs (X) H7,H9: 4.. / H7 = 4 => 0 pairs (X) / H9 = 4 => 12 pairs (_) C2,E2: 4.. / C2 = 4 => 12 pairs (_) / E2 = 4 => 0 pairs (X) E7,H7: 4.. / E7 = 4 => 12 pairs (_) / H7 = 4 => 0 pairs (X) D9,H9: 4.. / D9 = 4 => 0 pairs (X) / H9 = 4 => 12 pairs (_) D3,D9: 4.. / D3 = 4 => 12 pairs (_) / D9 = 4 => 0 pairs (X) E5,F5: 6.. / E5 = 6 => 10 pairs (_) / F5 = 6 => 10 pairs (_) H4,I4: 6.. / H4 = 6 => 10 pairs (_) / I4 = 6 => 10 pairs (_) A3,A6: 6.. / A3 = 6 => 13 pairs (_) / A6 = 6 => 14 pairs (_) D6,F6: 7.. / D6 = 7 => 0 pairs (X) / F6 = 7 => 11 pairs (_) H4,I4: 8.. / H4 = 8 => 10 pairs (_) / I4 = 8 => 10 pairs (_) F2,I2: 9.. / F2 = 9 => 12 pairs (_) / I2 = 9 => 0 pairs (X) F7,I7: 9.. / F7 = 9 => 0 pairs (X) / I7 = 9 => 12 pairs (_) D3,D9: 9.. / D3 = 9 => 0 pairs (X) / D9 = 9 => 12 pairs (_) G3,G9: 9.. / G3 = 9 => 12 pairs (_) / G9 = 9 => 0 pairs (X) * DURATION: 0:00:26.529006 START: 17:30:11.925906 END: 17:30:38.454912 2017-05-04 * CP COUNT: (21) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,D3,D6,D8,D9,E5,F5,F6,G9,H4,I4) * 9.......4...3..6...........1275943..5498..712....2.495...6..8..49.......2...1.... * PAIR A2: 7,8 BLK 1 B1: 7,8,1,3,5,6 # reduction candidate for 7,8 B1: 7,8 # 15 pairs B2: 7,8,1,5 # reduction candidate for 7,8 B2: 7,8 # 17 pairs A3: 7,8,3,6 # reduction candidate for 7,8 A3: 7,8 # 16 pairs B3: 7,8,1,3,5,6 # reduction candidate for 7,8 B3: 7,8 # 15 pairs * PAIR A2: 7,8 ROW 2 E2: 7,8,4,5 # reduction candidate for 7,8 E2: 7,8 # 16 pairs F2: 7,8,1,2,5,9 # reduction candidate for 7,8 F2: 7,8 => CTR * 9.......4...3..6.9.........1275943..5498..712....2.495...6.982.49.......2..41.9.. F2: 1,2,5,9 # 12 pairs H2: 7,8,2,5 # reduction candidate for 7,8 H2: 7,8 # 16 pairs I2: 7,8,1,9 # reduction candidate for 7,8 I2: 7,8 # 12 pairs * PAIR D6: 1,7 COL D D1: 1,7,2 # reduction candidate for 1,7 D1: 1,7 => CTR * 9.......4..43.26.9...4.9...1275943..5498..712....2.495...64.82.49.2..1..2..91.54. D1: 2 # 12 pairs * PAIR F6: 1,7 COL F F1: 1,7,2,5,6,8 # reduction candidate for 1,7 F1: 1,7 # 14 pairs F2: 1,7,2,5,8,9 # reduction candidate for 1,7 F2: 1,7 => CTR * 9.......4...3..6.9.........1275943..5498..712....2.495...6.982.49.......2..41.9.. F2: 2,5,8,9 # 12 pairs F3: 1,7,2,5,6,8,9 # reduction candidate for 1,7 F3: 1,7 # 13 pairs * PAIR A7: 3,7 BLK 7 B7: 3,7,1,5 # reduction candidate for 3,7 B7: 3,7 # 16 pairs B9: 3,7,5,6,8 # reduction candidate for 3,7 B9: 3,7 # 19 pairs * PAIR A7: 3,7 ROW 7 E7: 3,7,4,5 # reduction candidate for 3,7 E7: 3,7 => CTR * 9.......4...3..6.....9.....1275943..5498..712....2.495...6.284949.7.....2..4195.. E7: 4,5 # 13 pairs F7: 3,7,2,5,9 # reduction candidate for 3,7 F7: 3,7 => CTR * 9.......4...3.96.....4..9..1275943..5498..712....2.495...64.82949....1..2..91.54. F7: 2,5,9 # 12 pairs H7: 3,7,2,4,5 # reduction candidate for 3,7 H7: 3,7 # 12 pairs I7: 3,7,1,9 # reduction candidate for 3,7 I7: 3,7 => CTR * 9.......4...3..6...........1275943..5498..712....2.495...6.982.49.......2..41.... I7: 1,9 # 13 pairs * PAIR A7: 3,7 COL A A3: 3,7,6,8 # reduction candidate for 3,7 A3: 3,7 # 14 pairs A3: 6,8 # 13 pairs * PAIR D8: 2,7 BLK 8 F7: 2,7,3,5,9 # reduction candidate for 2,7 F7: 2,7 # 12 pairs F8: 2,7,3,5,8 # reduction candidate for 2,7 F8: 2,7 => CTR * 9.......4..43.26.9...4.9...1275943..5498..712....2.495...64.82.49.2.71..2..91.54. F8: 3,5,8 # 12 pairs * PAIR D8: 2,7 ROW 8 H8: 2,7,3,5,6 # reduction candidate for 2,7 H8: 2,7 # 14 pairs H8: 3,5,6 # 12 pairs * PAIR D8: 2,7 COL D D1: 2,7,1 # reduction candidate for 2,7 D1: 1 => CTR * 9..1..2.4..43.26.9..24.91..1275943..5498..712...721495...64.82.49.2.....2..91.54. D1: 2,7 # 11 pairs * PAIR G9: 5,9 ROW 9 F9: 5,9,3,7,8 # reduction candidate for 5,9 F9: 5,9 => CTR * 9.......4...3..6.....9.....1275943..5498..712....2.495...6..84.49.......2..41.9.. F9: 3,7,8 # 12 pairs * PAIR G9: 5,9 COL G G3: 5,9,1,2 # reduction candidate for 5,9 G3: 1,2 => CTR * 9.......4...3..6.....9.....1275943..5498..712....2.495...6.982.49.......2..41.9.. G3: 5,9 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-431-base-pr-000.dot * REASONING * DIS # F2: 7,8 => CTR => F2: 1,2,5,9 * DIS # D1: 1,7 => CTR => D1: 2 * DIS # F2: 1,7 => CTR => F2: 2,5,8,9 * DIS # E7: 3,7 => CTR => E7: 4,5 * DIS # F7: 3,7 => CTR => F7: 2,5,9 * DIS # I7: 3,7 => CTR => I7: 1,9 * DIS # F8: 2,7 => CTR => F8: 3,5,8 * DIS # D1: 1 => CTR => D1: 2,7 * DIS # F9: 5,9 => CTR => F9: 3,7,8 * DIS # G3: 1,2 => CTR => G3: 5,9 * CNT 10 HDP CHAINS / 37 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,D3,D6,D8,D9,E5,F5,F6,G9,H4,I4) * 9.......4...3..6...........1275943..5498..712....2.495...6..8..49.......2...1.... * PAIR A2: 7,8 BLK 1 B1: 7,8,1,3,5,6 # reduction candidate for 7,8 B1: 7,8 # 15 pairs B2: 7,8,1,5 # reduction candidate for 7,8 B2: 7,8 # 17 pairs A3: 7,8,3,6 # reduction candidate for 7,8 A3: 7,8 # 16 pairs B3: 7,8,1,3,5,6 # reduction candidate for 7,8 B3: 7,8 # 15 pairs * PAIR A2: 7,8 ROW 2 E2: 7,8,4,5 # reduction candidate for 7,8 E2: 7,8 # 16 pairs F2: 7,8,1,2,5,9 # reduction candidate for 7,8 F2: 7,8 => CTR * 9.......4...3..6.9.........1275943..5498..712....2.495...6.982.49.......2..41.9.. H2: 7,8,2,5 # reduction candidate for 7,8 H2: 7,8 # 16 pairs I2: 7,8,1,9 # reduction candidate for 7,8 I2: 7,8 # 12 pairs * PAIR RESTART * PAIR A2: 7,8 BLK 1 B1: 7,8,1,3,5,6 # reduction candidate for 7,8 B1: 7,8 # 15 pairs B2: 7,8,1,5 # reduction candidate for 7,8 B2: 7,8 # 17 pairs A3: 7,8,3,6 # reduction candidate for 7,8 A3: 7,8 # 16 pairs B3: 7,8,1,3,5,6 # reduction candidate for 7,8 B3: 7,8 # 15 pairs * PAIR A2: 7,8 ROW 2 E2: 7,8,4,5 # reduction candidate for 7,8 E2: 7,8 # 16 pairs H2: 7,8,2,5 # reduction candidate for 7,8 H2: 7,8 # 16 pairs I2: 7,8,1,9 # reduction candidate for 7,8 I2: 7,8 # 12 pairs * PAIR D6: 1,7 COL D D1: 1,7,2 # reduction candidate for 1,7 D1: 1,7 => CTR * 9.......4..43.26.9...4.9...1275943..5498..712....2.495...64.82.49.2..1..2..91.54. * PAIR RESTART * PAIR A7: 3,7 BLK 7 B7: 3,7,1,5 # reduction candidate for 3,7 B7: 3,7 # 16 pairs B9: 3,7,5,6,8 # reduction candidate for 3,7 B9: 3,7 # 22 pairs * PAIR A7: 3,7 ROW 7 H7: 3,7,2,4,5 # reduction candidate for 3,7 H7: 3,7 # 12 pairs I7: 3,7,1,9 # reduction candidate for 3,7 I7: 3,7 => CTR * 9..2....4...3..6...........1275943..5498..712...127495...6.982.49.7.2...2..41.... * RESTART * PAIR A7: 3,7 ROW 7 H7: 3,7,2,4,5 # reduction candidate for 3,7 H7: 2,4,5 # 13 pairs H7: 3,7 # 12 pairs * PAIR A7: 3,7 COL A A3: 3,7,6,8 # reduction candidate for 3,7 A3: 3,7 # 15 pairs A3: 6,8 # 14 pairs * PAIR RESTART * PAIR A7: 3,7 BLK 7 B7: 3,7,1,5 # reduction candidate for 3,7 B7: 3,7 # 16 pairs B9: 3,7,5,6,8 # reduction candidate for 3,7 B9: 3,7 # 17 pairs * PAIR A7: 3,7 ROW 7 H7: 3,7,2,4,5 # reduction candidate for 3,7 H7: 2,4,5 # 13 pairs H7: 3,7 # 12 pairs * PAIR A7: 3,7 COL A A3: 3,7,6,8 # reduction candidate for 3,7 A3: 3,7 # 15 pairs A3: 6,8 # 14 pairs * PAIR G9: 5,9 ROW 9 F9: 5,9,3,8 # reduction candidate for 5,9 F9: 5,9 => CTR * 9..2....4...3..6.....9.....1275943..5498..712...127495...6..84.49.7.....2..41.9.. * PAIR G9: 5,9 COL G G3: 5,9,1,2 # reduction candidate for 5,9 G3: 1,2 => CTR * 9..2....4...3..6.....9.....1275943..5498..712...127495...6.98214917.25..2..41.9.. * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A2,A7,E5,E8,F1,F5,F9,H4,H7,H8,I2,I4) * 9.52..1.4.1435962...24.195.1275943..5498..712...127495.516428.949.7.52.12..91.54. * PAIR A2: 7,8 BLK 1 B1: 7,8,3,6 # reduction candidate for 7,8 B1: 7,8 => SOLVED * 985276134714359628632481957127594386549863712863127495351642879498735261276918543 * DURATION: 0:00:29.816593 START: 17:31:02.717430 END: 17:31:32.534023 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-431-base-pr-001.dot * REASONING * DIS # F2: 7,8 => CTR => F2: 1,2,5,9 * DIS F2: 1,2,5,9 # D1: 1,7 => CTR => D1: 2 * DIS F2: 1,2,5,9 + D1: 2 # I7: 3,7 => CTR => I7: 1,9 * DIS F2: 1,2,5,9 + D1: 2 + I7: 1,9 # F9: 5,9 => CTR => F9: 3,8 * DIS F2: 1,2,5,9 + D1: 2 + I7: 1,9 + F9: 3,8 # G3: 1,2 => CTR => G3: 5,9 * PRF F2: 1,2,5,9 + D1: 2 + I7: 1,9 + F9: 3,8 + G3: 5,9 # B1: 7,8 => SOL * STA F2: 1,2,5,9 + D1: 2 + I7: 1,9 + F9: 3,8 + G3: 5,9 + B1: 7,8 * CNT 6 HDP CHAINS / 34 HYP OPENED
Header Info
Top 500 Minimum 17 431 solution: 985276134714359628632481957127594386549863712863127495351642879498735261276918543 info: 95188 FNBHWXYK S8.f 41318 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 985276134714359628632481957127594386549863712863127495351642879498735261276918543 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 # B1: 7,8 => UNS * INC # B2: 7,8 => UNS * INC # A3: 7,8 => UNS * INC # B3: 7,8 => UNS * INC # E2: 7,8 => UNS * DIS # F2: 7,8 => CTR => F2: 1,2,5,9 * INC # F2: 1,2,5,9 => UNS * INC # H2: 7,8 => UNS * INC # I2: 7,8 => UNS * DIS # D1: 1,7 => CTR => D1: 2 * INC # D1: 2 => UNS * INC # F1: 1,7 => UNS * DIS # F2: 1,7 => CTR => F2: 2,5,8,9 * INC # F2: 2,5,8,9 => UNS * INC # F3: 1,7 => UNS * INC # B7: 3,7 => UNS * INC # B9: 3,7 => UNS * DIS # E7: 3,7 => CTR => E7: 4,5 * INC # E7: 4,5 => UNS * DIS # F7: 3,7 => CTR => F7: 2,5,9 * INC # F7: 2,5,9 => UNS * INC # H7: 3,7 => UNS * DIS # I7: 3,7 => CTR => I7: 1,9 * INC # I7: 1,9 => UNS * INC # A3: 3,7 => UNS * INC # A3: 6,8 => UNS * INC # F7: 2,7 => UNS * DIS # F8: 2,7 => CTR => F8: 3,5,8 * INC # F8: 3,5,8 => UNS * INC # H8: 2,7 => UNS * INC # H8: 3,5,6 => UNS * INC # D1: 2,7 => UNS * DIS # D1: 1 => CTR => D1: 2,7 * DIS # F9: 5,9 => CTR => F9: 3,7,8 * INC # F9: 3,7,8 => UNS * INC # G3: 5,9 => UNS * DIS # G3: 1,2 => CTR => G3: 5,9 * CNT 37 HDP CHAINS / 37 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 7,8 => UNS * INC # B2: 7,8 => UNS * INC # A3: 7,8 => UNS * INC # B3: 7,8 => UNS * INC # E2: 7,8 => UNS * DIS # F2: 7,8 => CTR => F2: 1,2,5,9 * INC F2: 1,2,5,9 # H2: 7,8 => UNS * INC F2: 1,2,5,9 # I2: 7,8 => UNS * INC F2: 1,2,5,9 # B1: 7,8 => UNS * INC F2: 1,2,5,9 # B2: 7,8 => UNS * INC F2: 1,2,5,9 # A3: 7,8 => UNS * INC F2: 1,2,5,9 # B3: 7,8 => UNS * INC F2: 1,2,5,9 # E2: 7,8 => UNS * INC F2: 1,2,5,9 # H2: 7,8 => UNS * INC F2: 1,2,5,9 # I2: 7,8 => UNS * DIS F2: 1,2,5,9 # D1: 1,7 => CTR => D1: 2 * INC F2: 1,2,5,9 + D1: 2 # B7: 3,7 => UNS * INC F2: 1,2,5,9 + D1: 2 # B9: 3,7 => UNS * INC F2: 1,2,5,9 + D1: 2 # H7: 3,7 => UNS * DIS F2: 1,2,5,9 + D1: 2 # I7: 3,7 => CTR => I7: 1,9 * INC F2: 1,2,5,9 + D1: 2 + I7: 1,9 # H7: 3,7 => UNS * INC F2: 1,2,5,9 + D1: 2 + I7: 1,9 # H7: 2,4,5 => UNS * INC F2: 1,2,5,9 + D1: 2 + I7: 1,9 # A3: 3,7 => UNS * INC F2: 1,2,5,9 + D1: 2 + I7: 1,9 # A3: 6,8 => UNS * INC F2: 1,2,5,9 + D1: 2 + I7: 1,9 # B7: 3,7 => UNS * INC F2: 1,2,5,9 + D1: 2 + I7: 1,9 # B9: 3,7 => UNS * INC F2: 1,2,5,9 + D1: 2 + I7: 1,9 # H7: 3,7 => UNS * INC F2: 1,2,5,9 + D1: 2 + I7: 1,9 # H7: 2,4,5 => UNS * INC F2: 1,2,5,9 + D1: 2 + I7: 1,9 # A3: 3,7 => UNS * INC F2: 1,2,5,9 + D1: 2 + I7: 1,9 # A3: 6,8 => UNS * DIS F2: 1,2,5,9 + D1: 2 + I7: 1,9 # F9: 5,9 => CTR => F9: 3,8 * INC F2: 1,2,5,9 + D1: 2 + I7: 1,9 + F9: 3,8 # G3: 5,9 => UNS * DIS F2: 1,2,5,9 + D1: 2 + I7: 1,9 + F9: 3,8 # G3: 1,2 => CTR => G3: 5,9 * PRF F2: 1,2,5,9 + D1: 2 + I7: 1,9 + F9: 3,8 + G3: 5,9 # B1: 7,8 => SOL * STA F2: 1,2,5,9 + D1: 2 + I7: 1,9 + F9: 3,8 + G3: 5,9 + B1: 7,8 * CNT 34 HDP CHAINS / 34 HYP OPENED