Analysis of xx-top500-432-base.sdk
Contents
Original Sudoku
level: medium
position: ......2.8....2.5...4..6.....2.....9....5.1......8.....8.31.....5.....7.........4. initial
Autosolve
position: ....1.2.8....2.5.424..6.....2.....9....5.1......8.2...8.31.....5.42..7....2....4. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C4: 1,7 => CTR => C4: 5,8 * DIS # D1: 3,7 => CTR => D1: 4,9 * DIS # F1: 3,7 => CTR => F1: 4,5,9 * DIS # F2: 3,7 => CTR => F2: 8,9 * DIS # E9: 5,7 => CTR => E9: 3,8 * DIS # H8: 1 => CTR => H8: 3,8 * DIS # I8: 6,9 => CTR => I8: 1,3 * DIS # G9: 6,9 => CTR => G9: 1,3,8 * DIS # I9: 6,9 => CTR => I9: 1,3,5 * DIS # B7: 6,9 => CTR => B7: 7 * DIS # F7: 6,9 => CTR => F7: 4,7 * DIS # I7: 2,5 => CTR => I7: 6,9 * CNT 12 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C4: 1,7 => CTR => C4: 5,8 * DIS C4: 5,8 # D1: 3,7 => CTR => D1: 4,9 * DIS C4: 5,8 + D1: 4,9 # F1: 3,7 => CTR => F1: 4,5,9 * DIS C4: 5,8 + D1: 4,9 + F1: 4,5,9 # F2: 3,7 => CTR => F2: 8,9 * PRF C4: 5,8 + D1: 4,9 + F1: 4,5,9 + F2: 8,9 # E9: 3,8 => SOL * STA C4: 5,8 + D1: 4,9 + F1: 4,5,9 + F2: 8,9 + E9: 3,8 * CNT 5 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ......2.8....2.5...4..6.....2.....9....5.1......8.....8.31.....5.....7.........4. | initial |
| ....1.2.8....2.5.424..6.....2.....9....5.1......8.2...8.31.....5.42..7....2....4. | autosolve |
| 357419268961328574248765913125643897786591432439872156873154629594236781612987345 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) C3: 5,8 D3: 3,7 F3: 5,8 E8: 3,8 G7: 6,9 H7: 2,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H5,I5: 2.. / H5 = 2 => 0 pairs (X) / I5 = 2 => 14 pairs (_) H7,I7: 2.. / H7 = 2 => 14 pairs (_) / I7 = 2 => 0 pairs (X) H5,H7: 2.. / H5 = 2 => 0 pairs (X) / H7 = 2 => 14 pairs (_) I5,I7: 2.. / I5 = 2 => 14 pairs (_) / I7 = 2 => 0 pairs (X) D1,F1: 4.. / D1 = 4 => 6 pairs (_) / F1 = 4 => 0 pairs (X) E7,F7: 4.. / E7 = 4 => 0 pairs (X) / F7 = 4 => 7 pairs (_) D1,D4: 4.. / D1 = 4 => 6 pairs (_) / D4 = 4 => 0 pairs (X) F1,F3: 5.. / F1 = 5 => 0 pairs (X) / F3 = 5 => 14 pairs (_) E7,E9: 5.. / E7 = 5 => 14 pairs (_) / E9 = 5 => 0 pairs (X) C3,F3: 5.. / C3 = 5 => 0 pairs (X) / F3 = 5 => 14 pairs (_) C4,I4: 5.. / C4 = 5 => 14 pairs (_) / I4 = 5 => 0 pairs (X) E9,I9: 5.. / E9 = 5 => 0 pairs (X) / I9 = 5 => 14 pairs (_) B1,B6: 5.. / B1 = 5 => 14 pairs (_) / B6 = 5 => 0 pairs (X) H6,H7: 5.. / H6 = 5 => 14 pairs (_) / H7 = 5 => 0 pairs (X) H1,H2: 6.. / H1 = 6 => 7 pairs (_) / H2 = 6 => 7 pairs (_) D4,F4: 6.. / D4 = 6 => 6 pairs (_) / F4 = 6 => 7 pairs (_) D4,D9: 6.. / D4 = 6 => 6 pairs (_) / D9 = 6 => 7 pairs (_) F2,F3: 8.. / F2 = 8 => 14 pairs (_) / F3 = 8 => 0 pairs (X) E8,E9: 8.. / E8 = 8 => 0 pairs (X) / E9 = 8 => 14 pairs (_) H8,G9: 8.. / H8 = 8 => 14 pairs (_) / G9 = 8 => 0 pairs (X) C3,F3: 8.. / C3 = 8 => 14 pairs (_) / F3 = 8 => 0 pairs (X) C4,G4: 8.. / C4 = 8 => 0 pairs (X) / G4 = 8 => 14 pairs (_) E8,H8: 8.. / E8 = 8 => 0 pairs (X) / H8 = 8 => 14 pairs (_) E9,G9: 8.. / E9 = 8 => 14 pairs (_) / G9 = 8 => 0 pairs (X) B2,B5: 8.. / B2 = 8 => 0 pairs (X) / B5 = 8 => 14 pairs (_) H5,H8: 8.. / H5 = 8 => 0 pairs (X) / H8 = 8 => 14 pairs (_) G3,I3: 9.. / G3 = 9 => 6 pairs (_) / I3 = 9 => 7 pairs (_) E5,E6: 9.. / E5 = 9 => 6 pairs (_) / E6 = 9 => 6 pairs (_) * DURATION: 0:00:50.096042 START: 17:31:48.560371 END: 17:32:38.656413 2017-05-04 * CP COUNT: (28) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C3,D3,E8,F3,G7,H7) * ....1.2.8....2.5.424..6.....2.....9....5.1......8.2...8.31.....5.42..7....2....4. * PAIR C3: 5,8 COL C C4: 5,8,1,7 # reduction candidate for 5,8 C4: 1,7 => CTR * ....1.2.8....2.5.424..6.....2....895...5.1......8.2...8.31...525.42..78...2....4. C4: 5,8 # 7 pairs * PAIR D3: 3,7 BLK 2 D1: 3,7,4,9 # reduction candidate for 3,7 D1: 3,7 => CTR * ....142.8...9285.4248.65....2.4.6.9..8.5.1......8.2...8.314....5.428.7....265.84. D1: 4,9 # 7 pairs F1: 3,7,4,5,9 # reduction candidate for 3,7 F1: 3,7 => CTR * .5.4172.8761928534248.6591.125.4.89..8.5.14.243.8.2156873154629594236781612789345 F1: 4,5,9 # 6 pairs D2: 3,7,9 # reduction candidate for 3,7 D2: 3,7 # 11 pairs F2: 3,7,8,9 # reduction candidate for 3,7 F2: 3,7 => CTR * ....152.8....2.5.4245.68....2.....95...5.1....5.8.2...8.31...525.42..7....2.5.84. F2: 8,9 # 7 pairs * PAIR D3: 3,7 ROW 3 H3: 3,7,1 # reduction candidate for 3,7 H3: 3,7 # 12 pairs I3: 3,7,1,9 # reduction candidate for 3,7 I3: 3,7 # 10 pairs * PAIR D3: 3,7 COL D D4: 3,7,4,6 # reduction candidate for 3,7 D4: 3,7 # 9 pairs D9: 3,7,6,9 # reduction candidate for 3,7 D9: 3,7 # 7 pairs * PAIR E8: 3,8 BLK 8 E9: 3,8,5,7 # reduction candidate for 3,8 E9: 5,7 => CTR * ....1.2.8....2.5.424..6.....28....95...5.1.82...8.2...8.31.....5.428.7....2...84. E9: 3,8 # 14 pairs * PAIR E8: 3,8 ROW 8 H8: 3,8,1 # reduction candidate for 3,8 H8: 1 => CTR * ....1.2.8.8..2.5.4245.68....28....95...5.1.82.5.8.2...8.3154.2.5.428.71..12...84. H8: 3,8 # 8 pairs * PAIR G7: 6,9 BLK 9 I7: 6,9,2,5 # reduction candidate for 6,9 I7: 6,9 # 14 pairs I8: 6,9,1,3 # reduction candidate for 6,9 I8: 6,9 => CTR * ....1.2.8....2.5.424..6.....28....95...5.1.82...8.2...8.31.....5.42..7....2.5.84. I8: 1,3 # 9 pairs G9: 6,9,1,3,8 # reduction candidate for 6,9 G9: 6,9 => CTR * ....1.2.8....2.5.424..6.....2.....9....5.1......8.2...8.31.....5.42..78...2.8..45 G9: 1,3,8 # 6 pairs I9: 6,9,1,3,5 # reduction candidate for 6,9 I9: 6,9 => CTR * ....1.2.8....2.5.424..6.....28....95...5.1.82...8.2...8.31.....5.42..7....2.5.84. I9: 1,3,5 # 6 pairs * PAIR G7: 6,9 ROW 7 B7: 6,9,7 # reduction candidate for 6,9 B7: 6,9 => CTR * ....1.2.8....2.5.424..6.....28....95...5.1.82...8.2...8.31.....5.428.7....2.5.84. B7: 7 # 7 pairs F7: 6,9,4,7 # reduction candidate for 6,9 F7: 6,9 => CTR * ....1.2.8....2.5.424..6.....28....95...5.1.82...8.2...8.314....5.42..7....2.5.84. F7: 4,7 # 7 pairs * PAIR H7: 2,5 BLK 9 I7: 2,5,6,9 # reduction candidate for 2,5 I7: 2,5 => CTR * ....1.2.8....2.5.424..6.....28....95...5.1.82...8.2...8.31.....5.42..7....2.5.84. I7: 6,9 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-432-base-pr-000.dot * REASONING * DIS # C4: 1,7 => CTR => C4: 5,8 * DIS # D1: 3,7 => CTR => D1: 4,9 * DIS # F1: 3,7 => CTR => F1: 4,5,9 * DIS # F2: 3,7 => CTR => F2: 8,9 * DIS # E9: 5,7 => CTR => E9: 3,8 * DIS # H8: 1 => CTR => H8: 3,8 * DIS # I8: 6,9 => CTR => I8: 1,3 * DIS # G9: 6,9 => CTR => G9: 1,3,8 * DIS # I9: 6,9 => CTR => I9: 1,3,5 * DIS # B7: 6,9 => CTR => B7: 7 * DIS # F7: 6,9 => CTR => F7: 4,7 * DIS # I7: 2,5 => CTR => I7: 6,9 * CNT 12 HDP CHAINS / 30 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C3,D3,E8,F3,G7,H7) * ....1.2.8....2.5.424..6.....2.....9....5.1......8.2...8.31.....5.42..7....2....4. * PAIR C3: 5,8 COL C C4: 5,8,1,7 # reduction candidate for 5,8 C4: 1,7 => CTR * ....1.2.8....2.5.424..6.....2....895...5.1......8.2...8.31...525.42..78...2....4. * PAIR RESTART * PAIR D3: 3,7 BLK 2 D1: 3,7,4,9 # reduction candidate for 3,7 D1: 3,7 => CTR * ....142.8....2.5.424..65....254.689..8.5.1......8.2...8.314....5.42..78...26...4. F1: 3,7,4,5,9 # reduction candidate for 3,7 F1: 3,7 => CTR * .5.4172.8761928534248.6591.125.4.89..8.5.14.243.8.2156873154629594236781612789345 D2: 3,7,9 # reduction candidate for 3,7 D2: 3,7 # 12 pairs F2: 3,7,8,9 # reduction candidate for 3,7 F2: 3,7 => CTR * ....1.2.8.8..2.5.4245.68....28....95...5.1....5.8.2...8.31...525.42..7....2.5.84. * RESTART * PAIR D3: 3,7 ROW 3 H3: 3,7,1 # reduction candidate for 3,7 H3: 3,7 # 18 pairs I3: 3,7,1,9 # reduction candidate for 3,7 I3: 3,7 # 18 pairs * PAIR E8: 3,8 BLK 8 E9: 3,8,5,7 # reduction candidate for 3,8 E9: 3,8 => SOLVED * 357419268961328574248765913125643897786591432439872156873154629594236781612987345 * DURATION: 0:00:10.571144 START: 17:33:03.649714 END: 17:33:14.220858 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-432-base-pr-001.dot * REASONING * DIS # C4: 1,7 => CTR => C4: 5,8 * DIS C4: 5,8 # D1: 3,7 => CTR => D1: 4,9 * DIS C4: 5,8 + D1: 4,9 # F1: 3,7 => CTR => F1: 4,5,9 * DIS C4: 5,8 + D1: 4,9 + F1: 4,5,9 # F2: 3,7 => CTR => F2: 8,9 * PRF C4: 5,8 + D1: 4,9 + F1: 4,5,9 + F2: 8,9 # E9: 3,8 => SOL * STA C4: 5,8 + D1: 4,9 + F1: 4,5,9 + F2: 8,9 + E9: 3,8 * CNT 5 HDP CHAINS / 9 HYP OPENED
Header Info
Top 500 Minimum 17 432 solution: 357419268961328574248765913125643897786591432439872156873154629594236781612987345 info: 95204 FNBHXYK S8.f 41753 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 357419268961328574248765913125643897786591432439872156873154629594236781612987345 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 # C4: 5,8 => UNS * DIS # C4: 1,7 => CTR => C4: 5,8 * DIS # D1: 3,7 => CTR => D1: 4,9 * INC # D1: 4,9 => UNS * DIS # F1: 3,7 => CTR => F1: 4,5,9 * INC # F1: 4,5,9 => UNS * INC # D2: 3,7 => UNS * DIS # F2: 3,7 => CTR => F2: 8,9 * INC # F2: 8,9 => UNS * INC # H3: 3,7 => UNS * INC # I3: 3,7 => UNS * INC # D4: 3,7 => UNS * INC # D9: 3,7 => UNS * INC # E9: 3,8 => UNS * DIS # E9: 5,7 => CTR => E9: 3,8 * INC # H8: 3,8 => UNS * DIS # H8: 1 => CTR => H8: 3,8 * INC # I7: 6,9 => UNS * DIS # I8: 6,9 => CTR => I8: 1,3 * INC # I8: 1,3 => UNS * DIS # G9: 6,9 => CTR => G9: 1,3,8 * INC # G9: 1,3,8 => UNS * DIS # I9: 6,9 => CTR => I9: 1,3,5 * INC # I9: 1,3,5 => UNS * DIS # B7: 6,9 => CTR => B7: 7 * INC # B7: 7 => UNS * DIS # F7: 6,9 => CTR => F7: 4,7 * INC # F7: 4,7 => UNS * DIS # I7: 2,5 => CTR => I7: 6,9 * INC # I7: 6,9 => UNS * CNT 30 HDP CHAINS / 30 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C4: 5,8 => UNS * DIS # C4: 1,7 => CTR => C4: 5,8 * DIS C4: 5,8 # D1: 3,7 => CTR => D1: 4,9 * DIS C4: 5,8 + D1: 4,9 # F1: 3,7 => CTR => F1: 4,5,9 * INC C4: 5,8 + D1: 4,9 + F1: 4,5,9 # D2: 3,7 => UNS * DIS C4: 5,8 + D1: 4,9 + F1: 4,5,9 # F2: 3,7 => CTR => F2: 8,9 * INC C4: 5,8 + D1: 4,9 + F1: 4,5,9 + F2: 8,9 # H3: 3,7 => UNS * INC C4: 5,8 + D1: 4,9 + F1: 4,5,9 + F2: 8,9 # I3: 3,7 => UNS * PRF C4: 5,8 + D1: 4,9 + F1: 4,5,9 + F2: 8,9 # E9: 3,8 => SOL * STA C4: 5,8 + D1: 4,9 + F1: 4,5,9 + F2: 8,9 + E9: 3,8 * CNT 9 HDP CHAINS / 9 HYP OPENED