Analysis of xx-top95-025-base.sdk
Contents
Original Sudoku
level: medium
position: 1.....7.9.4...72..8.........7..1..6.3.......5.6..4..2.........8..53...7.7.2....46 initial
Autosolve
position: 1.....7.9.4...72.18.7...6.427..1..633.......556..43.27........8..53...727.2....46 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C2: 9 => SOL * DIS # C6: 8 => CTR => C6: 1,9 * PRF # B7: 1,9 => SOL * DIS # C4: 9 => CTR => C4: 4,8 * DIS # C6: 8,9 => CTR => C6: 1 * PRF # C6: 1 => SOL * PRF # G6: 8,9 => SOL * DIS # G6: 1 => CTR => G6: 8,9 * PRF # G4: 9 => SOL * PRF # G6: 8 => SOL * PRF # B7: 1,9 => SOL * DIS # D7: 1,9 => CTR => D7: 2,4,5,6,7 * DIS # F7: 1,9 => CTR => F7: 2,4,5,6 * PRF # G6: 8 => SOL * CNT 14 HDP CHAINS / 53 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C2: 9 => SOL * STA C2: 9 * CNT 1 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1.....7.9.4...72..8.........7..1..6.3.......5.6..4..2.........8..53...7.7.2....46 | initial |
| 1.....7.9.4...72.18.7...6.427..1..633.......556..43.27........8..53...727.2....46 | autosolve |
| 123456789649837251857291634274518963398672415561943827416725398985364172732189546 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) B1: 2,5 C1: 3,6 A2: 6,9 B3: 2,5 H3: 3,5 B5: 1,9 C5: 4,8 F5: 2,6 D6: 8,9 G5: 4,8 H5: 1,9 G7: 3,5 H7: 1,9 G8: 1,9 G9: 3,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D3,F3: 1.. / D3 = 1 => 18 pairs (_) / F3 = 1 => 15 pairs (_) B5,C6: 1.. / B5 = 1 => 0 pairs (X) / C6 = 1 => 0 pairs (_) H5,G6: 1.. / H5 = 1 => 0 pairs (*) / G6 = 1 => 0 pairs (X) H7,G8: 1.. / H7 = 1 => 0 pairs (X) / G8 = 1 => 0 pairs (_) B5,H5: 1.. / B5 = 1 => 0 pairs (X) / H5 = 1 => 0 pairs (_) C6,G6: 1.. / C6 = 1 => 0 pairs (*) / G6 = 1 => 0 pairs (X) C6,C7: 1.. / C6 = 1 => 0 pairs (*) / C7 = 1 => 0 pairs (X) G6,G8: 1.. / G6 = 1 => 0 pairs (X) / G8 = 1 => 0 pairs (_) H5,H7: 1.. / H5 = 1 => 0 pairs (*) / H7 = 1 => 0 pairs (X) B1,B3: 2.. / B1 = 2 => 15 pairs (_) / B3 = 2 => 17 pairs (_) C1,C2: 3.. / C1 = 3 => 22 pairs (_) / C2 = 3 => 15 pairs (_) B7,B9: 3.. / B7 = 3 => 13 pairs (_) / B9 = 3 => 0 pairs (*) G7,G9: 3.. / G7 = 3 => 0 pairs (*) / G9 = 3 => 0 pairs (X) E3,H3: 3.. / E3 = 3 => 17 pairs (_) / H3 = 3 => 16 pairs (_) B7,G7: 3.. / B7 = 3 => 13 pairs (_) / G7 = 3 => 0 pairs (*) B9,G9: 3.. / B9 = 3 => 0 pairs (*) / G9 = 3 => 0 pairs (X) D1,F1: 4.. / D1 = 4 => 15 pairs (_) / F1 = 4 => 13 pairs (_) C4,C5: 4.. / C4 = 4 => 15 pairs (_) / C5 = 4 => 15 pairs (_) G4,G5: 4.. / G4 = 4 => 15 pairs (_) / G5 = 4 => 15 pairs (_) A7,A8: 4.. / A7 = 4 => 16 pairs (_) / A8 = 4 => 16 pairs (_) C4,G4: 4.. / C4 = 4 => 15 pairs (_) / G4 = 4 => 15 pairs (_) C5,G5: 4.. / C5 = 4 => 15 pairs (_) / G5 = 4 => 15 pairs (_) A8,F8: 4.. / A8 = 4 => 16 pairs (_) / F8 = 4 => 16 pairs (_) D1,D7: 4.. / D1 = 4 => 15 pairs (_) / D7 = 4 => 13 pairs (_) B1,B3: 5.. / B1 = 5 => 17 pairs (_) / B3 = 5 => 15 pairs (_) D4,F4: 5.. / D4 = 5 => 17 pairs (_) / F4 = 5 => 18 pairs (_) G7,G9: 5.. / G7 = 5 => 13 pairs (_) / G9 = 5 => 0 pairs (*) D5,E5: 7.. / D5 = 7 => 16 pairs (_) / E5 = 7 => 16 pairs (_) D7,E7: 7.. / D7 = 7 => 16 pairs (_) / E7 = 7 => 16 pairs (_) D5,D7: 7.. / D5 = 7 => 16 pairs (_) / D7 = 7 => 16 pairs (_) E5,E7: 7.. / E5 = 7 => 16 pairs (_) / E7 = 7 => 16 pairs (_) H1,H2: 8.. / H1 = 8 => 16 pairs (_) / H2 = 8 => 17 pairs (_) B8,B9: 8.. / B8 = 8 => 16 pairs (_) / B9 = 8 => 17 pairs (_) C5,G5: 8.. / C5 = 8 => 15 pairs (_) / G5 = 8 => 15 pairs (_) A2,C2: 9.. / A2 = 9 => 16 pairs (_) / C2 = 9 => 0 pairs (*) H7,G8: 9.. / H7 = 9 => 0 pairs (*) / G8 = 9 => 0 pairs (X) B5,H5: 9.. / B5 = 9 => 0 pairs (*) / H5 = 9 => 0 pairs (X) H5,H7: 9.. / H5 = 9 => 0 pairs (X) / H7 = 9 => 0 pairs (_) * DURATION: 0:01:04.666226 START: 23:21:16.390848 END: 23:22:21.057074 2017-05-03 * CP COUNT: (38) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B1,B3,B5,C1,C5,D6,F5,G5,G7,G8,G9,H3,H5,H7) * 1.....7.9.4...72.18.7...6.427..1..633.......556..43.27........8..53...727.2....46 * PAIR B1: 2,5 ROW 1 D1: 2,5,4,6,8 # reduction candidate for 2,5 D1: 2,5 # 17 pairs E1: 2,5,3,6,8 # reduction candidate for 2,5 E1: 2,5 # 17 pairs F1: 2,5,4,6,8 # reduction candidate for 2,5 F1: 2,5 # 17 pairs * PAIR C1: 3,6 BLK 1 C2: 3,6,9 # reduction candidate for 3,6 C2: 9 => SOLVED * 123456789649837251857291634274518963398672415561943827416725398985364172732189546 C2: 3,6 # 16 pairs * PAIR C1: 3,6 ROW 1 E1: 3,6,2,5,8 # reduction candidate for 3,6 E1: 3,6 # 17 pairs E1: 2,5,8 # 15 pairs * PAIR A2: 6,9 BLK 1 C2: 6,9,3 # reduction candidate for 6,9 C2: 6,9 # 22 pairs C2: 3 # 15 pairs * PAIR A2: 6,9 COL A A7: 6,9,4 # reduction candidate for 6,9 A7: 6,9 # 16 pairs A8: 6,9,4 # reduction candidate for 6,9 A8: 6,9 # 16 pairs * PAIR B3: 2,5 ROW 3 D3: 2,5,1,9 # reduction candidate for 2,5 D3: 2,5 # 19 pairs E3: 2,5,3,9 # reduction candidate for 2,5 E3: 2,5 # 21 pairs F3: 2,5,1,9 # reduction candidate for 2,5 F3: 2,5 # 20 pairs * PAIR H3: 3,5 BLK 3 H1: 3,5,8 # reduction candidate for 3,5 H1: 3,5 # 17 pairs H2: 3,5,8 # reduction candidate for 3,5 H2: 3,5 # 16 pairs * PAIR H3: 3,5 ROW 3 E3: 3,5,2,9 # reduction candidate for 3,5 E3: 3,5 # 21 pairs E3: 2,9 # 17 pairs * PAIR B5: 1,9 BLK 4 C6: 1,9,8 # reduction candidate for 1,9 C6: 8 => CTR * 1.....7.9.4...72.18.7...6.427..1..6331.....95568943127..1.....8..53...727.2....46 C6: 1,9 # 17 pairs * PAIR B5: 1,9 COL B B7: 1,9,3 # reduction candidate for 1,9 B7: 1,9 => SOLVED * 123456789649837251857291634274518963398672415561943827416725398985364172732189546 B7: 3 # 13 pairs B8: 1,9,8 # reduction candidate for 1,9 B8: 1,9 # 17 pairs B9: 1,9,3,8 # reduction candidate for 1,9 B9: 1,9 # 15 pairs * PAIR C5: 4,8 BLK 4 C4: 4,8,9 # reduction candidate for 4,8 C4: 9 => CTR * 1.....7.9.4...72.18.7...6.4279.1.463314...895568943127..1.....8..53...727.2....46 C4: 4,8 # 17 pairs * PAIR F5: 2,6 BLK 5 D5: 2,6,7 # reduction candidate for 2,6 D5: 2,6 # 16 pairs E5: 2,6,7 # reduction candidate for 2,6 E5: 2,6 # 16 pairs * PAIR F5: 2,6 COL F F1: 2,6,4,5,8 # reduction candidate for 2,6 F1: 2,6 # 20 pairs F7: 2,6,1,4,5,9 # reduction candidate for 2,6 F7: 2,6 # 16 pairs * PAIR D6: 8,9 BLK 5 D4: 8,9,5 # reduction candidate for 8,9 D4: 8,9 # 18 pairs F4: 8,9,5 # reduction candidate for 8,9 F4: 8,9 # 17 pairs * PAIR D6: 8,9 ROW 6 C6: 8,9,1 # reduction candidate for 8,9 C6: 8,9 => CTR * 1.....7.9.4...72.18.7...6.427..1..6331.....9556..43127..1.....8..53...727.2....46 C6: 1 => SOLVED * 123456789649837251857291634274518963398672415561943827416725398985364172732189546 G6: 8,9,1 # reduction candidate for 8,9 G6: 8,9 => SOLVED * 123456789649837251857291634274518963398672415561943827416725398985364172732189546 G6: 1 => CTR * 1.....7.9.4...72.18.7...6.427..1..633.......556..43127..1....98..53...727.2....46 * PAIR D6: 8,9 COL D D9: 8,9,1,5 # reduction candidate for 8,9 D9: 8,9 # 20 pairs D9: 1,5 # 16 pairs * PAIR G5: 4,8 BLK 6 G4: 4,8,9 # reduction candidate for 4,8 G4: 9 => SOLVED * 123456789649837251857291634274518963398672415561943827416725398985364172732189546 G4: 4,8 # 17 pairs * PAIR H5: 1,9 BLK 6 G6: 1,9,8 # reduction candidate for 1,9 G6: 8 => SOLVED * 123456789649837251857291634274518963398672415561943827416725398985364172732189546 G6: 1,9 # 17 pairs * PAIR H7: 1,9 ROW 7 B7: 1,9,3 # reduction candidate for 1,9 B7: 1,9 => SOLVED * 123456789649837251857291634274518963398672415561943827416725398985364172732189546 B7: 3 # 13 pairs C7: 1,9,6 # reduction candidate for 1,9 C7: 1,9 # 16 pairs D7: 1,9,2,4,5,6,7 # reduction candidate for 1,9 D7: 1,9 => CTR * 1..4..7.9.4.6.72.18.72.16.427..1..633..726..556..43.27436.725.89.53.4.727.2...346 D7: 2,4,5,6,7 # 15 pairs F7: 1,9,2,4,5,6 # reduction candidate for 1,9 F7: 1,9 => CTR * 1.34.67.9649..72.18.71..6.427..1..6339.672.15561.43.27436...5.8985364172712...346 F7: 2,4,5,6 # 15 pairs * PAIR G8: 1,9 ROW 8 B8: 1,9,8 # reduction candidate for 1,9 B8: 1,9 # 17 pairs F8: 1,9,4,6,8 # reduction candidate for 1,9 F8: 1,9 # 19 pairs * PAIR G8: 1,9 COL G G6: 1,9,8 # reduction candidate for 1,9 G6: 8 => SOLVED * 123456789649837251857291634274518963398672415561943827416725398985364172732189546 G6: 1,9 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-025-base-pr-000.dot * REASONING * PRF # C2: 9 => SOL * DIS # C6: 8 => CTR => C6: 1,9 * PRF # B7: 1,9 => SOL * DIS # C4: 9 => CTR => C4: 4,8 * DIS # C6: 8,9 => CTR => C6: 1 * PRF # C6: 1 => SOL * PRF # G6: 8,9 => SOL * DIS # G6: 1 => CTR => G6: 8,9 * PRF # G4: 9 => SOL * PRF # G6: 8 => SOL * PRF # B7: 1,9 => SOL * DIS # D7: 1,9 => CTR => D7: 2,4,5,6,7 * DIS # F7: 1,9 => CTR => F7: 2,4,5,6 * PRF # G6: 8 => SOL * CNT 14 HDP CHAINS / 53 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B1,B3,B5,C1,C5,D6,F5,G5,G7,G8,G9,H3,H5,H7) * 1.....7.9.4...72.18.7...6.427..1..633.......556..43.27........8..53...727.2....46 * PAIR B1: 2,5 ROW 1 D1: 2,5,4,6,8 # reduction candidate for 2,5 D1: 2,5 # 17 pairs E1: 2,5,3,6,8 # reduction candidate for 2,5 E1: 2,5 # 17 pairs F1: 2,5,4,6,8 # reduction candidate for 2,5 F1: 2,5 # 17 pairs * PAIR C1: 3,6 BLK 1 C2: 3,6,9 # reduction candidate for 3,6 C2: 9 => SOLVED * 123456789649837251857291634274518963398672415561943827416725398985364172732189546 * DURATION: 0:00:06.181960 START: 23:23:12.450814 END: 23:23:18.632774 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-025-base-pr-001.dot * REASONING * PRF # C2: 9 => SOL * STA C2: 9 * CNT 1 HDP CHAINS / 5 HYP OPENED
Header Info
Top 95 Sudokus 025 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 123456789649837251857291634274518963398672415561943827416725398985364172732189546 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 # D1: 2,5 => UNS * INC # E1: 2,5 => UNS * INC # F1: 2,5 => UNS * INC # C2: 3,6 => UNS * PRF # C2: 9 => SOL * INC # E1: 3,6 => UNS * INC # E1: 2,5,8 => UNS * INC # C2: 6,9 => UNS * INC # C2: 3 => UNS * INC # A7: 6,9 => UNS * INC # A8: 6,9 => UNS * INC # D3: 2,5 => UNS * INC # E3: 2,5 => UNS * INC # F3: 2,5 => UNS * INC # H1: 3,5 => UNS * INC # H2: 3,5 => UNS * INC # E3: 3,5 => UNS * INC # E3: 2,9 => UNS * INC # C6: 1,9 => UNS * DIS # C6: 8 => CTR => C6: 1,9 * PRF # B7: 1,9 => SOL * INC # B7: 3 => UNS * INC # B8: 1,9 => UNS * INC # B9: 1,9 => UNS * INC # C4: 4,8 => UNS * DIS # C4: 9 => CTR => C4: 4,8 * INC # D5: 2,6 => UNS * INC # E5: 2,6 => UNS * INC # F1: 2,6 => UNS * INC # F7: 2,6 => UNS * INC # D4: 8,9 => UNS * INC # F4: 8,9 => UNS * DIS # C6: 8,9 => CTR => C6: 1 * PRF # C6: 1 => SOL * PRF # G6: 8,9 => SOL * DIS # G6: 1 => CTR => G6: 8,9 * INC # D9: 8,9 => UNS * INC # D9: 1,5 => UNS * INC # G4: 4,8 => UNS * PRF # G4: 9 => SOL * INC # G6: 1,9 => UNS * PRF # G6: 8 => SOL * PRF # B7: 1,9 => SOL * INC # B7: 3 => UNS * INC # C7: 1,9 => UNS * DIS # D7: 1,9 => CTR => D7: 2,4,5,6,7 * INC # D7: 2,4,5,6,7 => UNS * DIS # F7: 1,9 => CTR => F7: 2,4,5,6 * INC # F7: 2,4,5,6 => UNS * INC # B8: 1,9 => UNS * INC # F8: 1,9 => UNS * INC # G6: 1,9 => UNS * PRF # G6: 8 => SOL * CNT 53 HDP CHAINS / 53 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D1: 2,5 => UNS * INC # E1: 2,5 => UNS * INC # F1: 2,5 => UNS * INC # C2: 3,6 => UNS * PRF # C2: 9 => SOL * STA C2: 9 * CNT 5 HDP CHAINS / 5 HYP OPENED