Analysis of xx-top95-013-base.sdk
Contents
Original Sudoku
level: medium
position: ..5...987.4..5...1..7......2...48....9.1.....6..2.....3..6..2.......9.7.......5.. initial
Autosolve
position: 1.5...987.4..57..1..7......2...48....9.1.....6..2.....3..6..2.......9.7.......5.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D8: 3,4 => CTR => D8: 5,8 * DIS # D9: 3,4 => CTR => D9: 7,8 * DIS # D4: 3,5 => CTR => D4: 7,9 * PRF # D4: 7,9 => SOL * PRF # F5: 3,5 => SOL * DIS # D8: 3,8 => CTR => D8: 4,5 * PRF # A5: 4,5 => SOL * DIS # A5: 7 => CTR => A5: 4,5 * PRF # D9: 3,8 => SOL * DIS # A5: 4,7 => CTR => A5: 5 * PRF # A5: 5 => SOL * CNT 11 HDP CHAINS / 38 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D8: 3,4 => CTR => D8: 5,8 * DIS D8: 5,8 # D9: 3,4 => CTR => D9: 7,8 * DIS D8: 5,8 + D9: 7,8 # D3: 8,9 => CTR => D3: 3 * PRF D8: 5,8 + D9: 7,8 + D3: 3 # F5: 3,5 => SOL * STA D8: 5,8 + D9: 7,8 + D3: 3 + F5: 3,5 * CNT 4 HDP CHAINS / 16 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..5...987.4..5...1..7......2...48....9.1.....6..2.....3..6..2.......9.7.......5.. | initial |
| 1.5...987.4..57..1..7......2...48....9.1.....6..2.....3..6..2.......9.7.......5.. | autosolve |
| 135426987846957321927381465213748659598163742674295813351674298482539176769812534 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) A2: 8,9 A3: 8,9 D1: 3,4 D2: 8,9 G2: 3,6 C4: 1,3 F6: 3,5 A8: 4,5 A9: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E3,F3: 1.. / E3 = 1 => 11 pairs (_) / F3 = 1 => 10 pairs (_) H5,I5: 2.. / H5 = 2 => 12 pairs (_) / I5 = 2 => 9 pairs (_) C2,H2: 2.. / C2 = 2 => 14 pairs (_) / H2 = 2 => 10 pairs (_) I3,I5: 2.. / I3 = 2 => 12 pairs (_) / I5 = 2 => 9 pairs (_) D1,F1: 4.. / D1 = 4 => 8 pairs (_) / F1 = 4 => 17 pairs (_) H3,I3: 5.. / H3 = 5 => 9 pairs (_) / I3 = 5 => 9 pairs (_) F7,D8: 5.. / F7 = 5 => 0 pairs (X) / D8 = 5 => 0 pairs (_) B7,F7: 5.. / B7 = 5 => 0 pairs (*) / F7 = 5 => 0 pairs (X) A5,A8: 5.. / A5 = 5 => 0 pairs (*) / A8 = 5 => 0 pairs (X) D4,D8: 5.. / D4 = 5 => 0 pairs (X) / D8 = 5 => 0 pairs (_) E5,F5: 6.. / E5 = 6 => 0 pairs (*) / F5 = 6 => 0 pairs (X) B7,E7: 7.. / B7 = 7 => 0 pairs (X) / E7 = 7 => 0 pairs (_) A5,A9: 7.. / A5 = 7 => 0 pairs (X) / A9 = 7 => 0 pairs (_) D4,D9: 7.. / D4 = 7 => 0 pairs (*) / D9 = 7 => 0 pairs (X) A2,A3: 8.. / A2 = 8 => 7 pairs (_) / A3 = 8 => 7 pairs (_) A2,D2: 8.. / A2 = 8 => 7 pairs (_) / D2 = 8 => 7 pairs (_) A2,A3: 9.. / A2 = 9 => 7 pairs (_) / A3 = 9 => 7 pairs (_) D4,E6: 9.. / D4 = 9 => 0 pairs (X) / E6 = 9 => 9 pairs (_) C7,C9: 9.. / C7 = 9 => 11 pairs (_) / C9 = 9 => 12 pairs (_) A2,D2: 9.. / A2 = 9 => 7 pairs (_) / D2 = 9 => 7 pairs (_) E3,E6: 9.. / E3 = 9 => 0 pairs (X) / E6 = 9 => 9 pairs (_) * DURATION: 0:00:28.399232 START: 23:07:13.037106 END: 23:07:41.436338 2017-05-03 * CP COUNT: (21) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A8,A9,C4,D1,D2,F6,G2) * 1.5...987.4..57..1..7......2...48....9.1.....6..2.....3..6..2.......9.7.......5.. * PAIR A3: 8,9 ROW 3 D3: 8,9,3 # reduction candidate for 8,9 D3: 8,9 # 10 pairs E3: 8,9,1,2,3,6 # reduction candidate for 8,9 E3: 8,9 # 17 pairs * PAIR D1: 3,4 BLK 2 F1: 3,4,2,6 # reduction candidate for 3,4 F1: 3,4 # 13 pairs F1: 2,6 # 9 pairs * PAIR D1: 3,4 COL D D8: 3,4,5,8 # reduction candidate for 3,4 D8: 3,4 => CTR * 1.5...987.4..57..1..7......2..548...79.16....6..293...3..6.52.......9.7....7..5.. D8: 5,8 # 10 pairs D9: 3,4,7,8 # reduction candidate for 3,4 D9: 3,4 => CTR * 1.53.4987.4..57321.37...4..2..7486..5981..7..67429581335.67.2.84.25391767..482539 D9: 7,8 # 10 pairs * PAIR D2: 8,9 BLK 2 D3: 8,9,3 # reduction candidate for 8,9 D3: 8,9 # 10 pairs E3: 8,9,1,2,3,6 # reduction candidate for 8,9 E3: 8,9 # 17 pairs * PAIR G2: 3,6 BLK 3 H2: 3,6,2 # reduction candidate for 3,6 H2: 3,6 # 14 pairs G3: 3,6,4 # reduction candidate for 3,6 G3: 3,6 # 14 pairs H3: 3,6,2,4,5 # reduction candidate for 3,6 H3: 3,6 # 11 pairs I3: 3,6,2,4,5 # reduction candidate for 3,6 I3: 3,6 # 12 pairs * PAIR G2: 3,6 ROW 2 C2: 3,6,2 # reduction candidate for 3,6 C2: 2 # 14 pairs C2: 3,6 # 10 pairs * PAIR G2: 3,6 COL G G4: 3,6,1,7 # reduction candidate for 3,6 G4: 3,6 # 12 pairs G8: 3,6,1,4,8 # reduction candidate for 3,6 G8: 3,6 # 12 pairs * PAIR C4: 1,3 BLK 4 B4: 1,3,5,7 # reduction candidate for 1,3 B4: 1,3 # 16 pairs B6: 1,3,5,7,8 # reduction candidate for 1,3 B6: 1,3 # 15 pairs C6: 1,3,4,8 # reduction candidate for 1,3 C6: 1,3 # 14 pairs * PAIR C4: 1,3 ROW 4 G4: 1,3,6,7 # reduction candidate for 1,3 G4: 1,3 # 11 pairs H4: 1,3,5,6,9 # reduction candidate for 1,3 H4: 1,3 # 12 pairs * PAIR F6: 3,5 BLK 5 D4: 3,5,7,9 # reduction candidate for 3,5 D4: 3,5 => CTR * 1.5...987.4..57..1..7......2...48...79.1.....6..29.7..37.6.52..5....9.7.4..7..5.. D4: 7,9 => SOLVED * 135426987846957321927381465213748659598163742674295813351674298482539176769812534 F5: 3,5,6 # reduction candidate for 3,5 F5: 3,5 => SOLVED * 135426987846957321927381465213748659598163742674295813351674298482539176769812534 F5: 6 # 10 pairs * PAIR F6: 3,5 ROW 6 B6: 3,5,1,7,8 # reduction candidate for 3,5 B6: 3,5 # 11 pairs H6: 3,5,1,4,9 # reduction candidate for 3,5 H6: 3,5 # 11 pairs I6: 3,5,4,8,9 # reduction candidate for 3,5 I6: 3,5 # 11 pairs * PAIR A8: 4,5 ROW 8 D8: 4,5,3,8 # reduction candidate for 4,5 D8: 3,8 => CTR * 1.5...987.4..57..1..7......2..548....9.1.....6..293...3..6.52.......9.7....7.45.. D8: 4,5 # 10 pairs * PAIR A8: 4,5 COL A A5: 4,5,7 # reduction candidate for 4,5 A5: 4,5 => SOLVED * 135426987846957321927381465213748659598163742674295813351674298482539176769812534 A5: 7 => CTR * 1.5...987.4..57..1..7......2..5487..79.1.....65.2.....3..6..2..5....9.7.4.....5.. * PAIR A9: 4,7 ROW 9 D9: 4,7,3,8 # reduction candidate for 4,7 D9: 3,8 => SOLVED * 135426987846957321927381465213748659598163742674295813351674298482539176769812534 D9: 4,7 # 10 pairs * PAIR A9: 4,7 COL A A5: 4,7,5 # reduction candidate for 4,7 A5: 4,7 => CTR * 1.5...987.4..57..1..7......27.548...49.1.....65.2937..3..6.52..5....9.7....7..5.. A5: 5 => SOLVED * 135426987846957321927381465213748659598163742674295813351674298482539176769812534 * INCONCLUSIVE * SAVE PR GRAPH xx-top95-013-base-pr-000.dot * REASONING * DIS # D8: 3,4 => CTR => D8: 5,8 * DIS # D9: 3,4 => CTR => D9: 7,8 * DIS # D4: 3,5 => CTR => D4: 7,9 * PRF # D4: 7,9 => SOL * PRF # F5: 3,5 => SOL * DIS # D8: 3,8 => CTR => D8: 4,5 * PRF # A5: 4,5 => SOL * DIS # A5: 7 => CTR => A5: 4,5 * PRF # D9: 3,8 => SOL * DIS # A5: 4,7 => CTR => A5: 5 * PRF # A5: 5 => SOL * CNT 11 HDP CHAINS / 38 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A8,A9,C4,D1,D2,F6,G2) * 1.5...987.4..57..1..7......2...48....9.1.....6..2.....3..6..2.......9.7.......5.. * PAIR A3: 8,9 ROW 3 D3: 8,9,3 # reduction candidate for 8,9 D3: 8,9 # 10 pairs E3: 8,9,1,2,3,6 # reduction candidate for 8,9 E3: 8,9 # 17 pairs * PAIR D1: 3,4 BLK 2 F1: 3,4,2,6 # reduction candidate for 3,4 F1: 3,4 # 13 pairs F1: 2,6 # 9 pairs * PAIR D1: 3,4 COL D D8: 3,4,5,8 # reduction candidate for 3,4 D8: 3,4 => CTR * 1.5...987.4..57..1..7......2..548...79.16....6..293...3..6.52.......9.7....7..5.. D9: 3,4,7,8 # reduction candidate for 3,4 D9: 3,4 => CTR * 1.53.4987.4..57321.37...4..2..7486..5981..7..67429581335.67.2.84.25391767..482539 * PAIR RESTART * PAIR D2: 8,9 BLK 2 D3: 8,9,3 # reduction candidate for 8,9 D3: 8,9 => CTR * 1.54..987.4..57..1..7......2..348....9.1.....6..295...35.67.2..4..5.9.7.7..8..5.. * RESTART * PAIR G2: 3,6 BLK 3 H2: 3,6,2 # reduction candidate for 3,6 H2: 3,6 # 17 pairs H2: 2 # 14 pairs * PAIR G2: 3,6 COL G G4: 3,6,1,7 # reduction candidate for 3,6 G4: 3,6 # 19 pairs G8: 3,6,1,4,8 # reduction candidate for 3,6 G8: 3,6 # 19 pairs * PAIR C4: 1,3 BLK 4 C6: 1,3,4,8 # reduction candidate for 1,3 C6: 1,3 # 20 pairs C6: 4,8 # 18 pairs * PAIR C4: 1,3 ROW 4 G4: 1,3,6,7 # reduction candidate for 1,3 G4: 1,3 # 19 pairs H4: 1,3,5,6,9 # reduction candidate for 1,3 H4: 1,3 # 20 pairs * PAIR F6: 3,5 BLK 5 F5: 3,5,6 # reduction candidate for 3,5 F5: 3,5 => SOLVED * 135426987846957321927381465213748659598163742674295813351674298482539176769812534 * DURATION: 0:00:13.777384 START: 23:08:10.587814 END: 23:08:24.365198 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-013-base-pr-001.dot * REASONING * DIS # D8: 3,4 => CTR => D8: 5,8 * DIS D8: 5,8 # D9: 3,4 => CTR => D9: 7,8 * DIS D8: 5,8 + D9: 7,8 # D3: 8,9 => CTR => D3: 3 * PRF D8: 5,8 + D9: 7,8 + D3: 3 # F5: 3,5 => SOL * STA D8: 5,8 + D9: 7,8 + D3: 3 + F5: 3,5 * CNT 4 HDP CHAINS / 16 HYP OPENED
Header Info
Top 95 Sudokus 013 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 135426987846957321927381465213748659598163742674295813351674298482539176769812534 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 # D3: 8,9 => UNS * INC # E3: 8,9 => UNS * INC # F1: 3,4 => UNS * INC # F1: 2,6 => UNS * DIS # D8: 3,4 => CTR => D8: 5,8 * INC # D8: 5,8 => UNS * DIS # D9: 3,4 => CTR => D9: 7,8 * INC # D9: 7,8 => UNS * INC # D3: 8,9 => UNS * INC # E3: 8,9 => UNS * INC # H2: 3,6 => UNS * INC # G3: 3,6 => UNS * INC # H3: 3,6 => UNS * INC # I3: 3,6 => UNS * INC # C2: 3,6 => UNS * INC # C2: 2 => UNS * INC # G4: 3,6 => UNS * INC # G8: 3,6 => UNS * INC # B4: 1,3 => UNS * INC # B6: 1,3 => UNS * INC # C6: 1,3 => UNS * INC # G4: 1,3 => UNS * INC # H4: 1,3 => UNS * DIS # D4: 3,5 => CTR => D4: 7,9 * PRF # D4: 7,9 => SOL * PRF # F5: 3,5 => SOL * INC # F5: 6 => UNS * INC # B6: 3,5 => UNS * INC # H6: 3,5 => UNS * INC # I6: 3,5 => UNS * INC # D8: 4,5 => UNS * DIS # D8: 3,8 => CTR => D8: 4,5 * PRF # A5: 4,5 => SOL * DIS # A5: 7 => CTR => A5: 4,5 * INC # D9: 4,7 => UNS * PRF # D9: 3,8 => SOL * DIS # A5: 4,7 => CTR => A5: 5 * PRF # A5: 5 => SOL * CNT 38 HDP CHAINS / 38 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D3: 8,9 => UNS * INC # E3: 8,9 => UNS * INC # F1: 3,4 => UNS * INC # F1: 2,6 => UNS * DIS # D8: 3,4 => CTR => D8: 5,8 * DIS D8: 5,8 # D9: 3,4 => CTR => D9: 7,8 * DIS D8: 5,8 + D9: 7,8 # D3: 8,9 => CTR => D3: 3 * INC D8: 5,8 + D9: 7,8 + D3: 3 # H2: 3,6 => UNS * INC D8: 5,8 + D9: 7,8 + D3: 3 # H2: 2 => UNS * INC D8: 5,8 + D9: 7,8 + D3: 3 # G4: 3,6 => UNS * INC D8: 5,8 + D9: 7,8 + D3: 3 # G8: 3,6 => UNS * INC D8: 5,8 + D9: 7,8 + D3: 3 # C6: 1,3 => UNS * INC D8: 5,8 + D9: 7,8 + D3: 3 # C6: 4,8 => UNS * INC D8: 5,8 + D9: 7,8 + D3: 3 # G4: 1,3 => UNS * INC D8: 5,8 + D9: 7,8 + D3: 3 # H4: 1,3 => UNS * PRF D8: 5,8 + D9: 7,8 + D3: 3 # F5: 3,5 => SOL * STA D8: 5,8 + D9: 7,8 + D3: 3 + F5: 3,5 * CNT 16 HDP CHAINS / 16 HYP OPENED