Analysis of xx-top95-014-base.sdk
Contents
Original Sudoku
level: medium
position: 3.6.7...........518.........1.4.5...7.....6.....2......2.....4.....8.3.....5..... initial
Autosolve
position: 356.7.294....4.8518419527...1.4.59..7.4...625...2.741..2....54.....8.3.2...52.1.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 7 => CTR => C2: 2,9 * DIS # C2: 7,9 => CTR => C2: 2 * DIS # B8: 7,9 => CTR => B8: 6 * PRF # B8: 6 => SOL * DIS # B9: 7,9 => CTR => B9: 3,6,8 * DIS # D5: 1,8 => CTR => D5: 3 * PRF # D5: 3 => SOL * DIS # F5: 3,9 => CTR => F5: 1,8 * DIS # D7: 3,6 => CTR => D7: 1,7 * DIS # B6: 3,9 => CTR => B6: 6,8 * DIS # E5: 3,9 => CTR => E5: 1 * DIS # F5: 3,9 => CTR => F5: 1,8 * PRF # B9: 3,9 => SOL * DIS # E6: 3,6 => CTR => E6: 9 * PRF # E6: 9 => SOL * DIS # I4: 3,8 => CTR => I4: 7 * DIS # C6: 3,8 => CTR => C6: 5,9 * DIS # I7: 6,7 => CTR => I7: 8,9 * DIS # I9: 6,7 => CTR => I9: 8,9 * PRF # B8: 6,7 => SOL * DIS # B8: 9 => CTR => B8: 6,7 * DIS # D8: 6,7 => CTR => D8: 1 * PRF # D8: 1 => SOL * CNT 23 HDP CHAINS / 42 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C2: 7 => CTR => C2: 2,9 * DIS C2: 2,9 # D5: 1,8 => CTR => D5: 3 * PRF C2: 2,9 + D5: 3 => SOL * STA C2: 2,9 + D5: 3 * CNT 3 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 3.6.7...........518.........1.4.5...7.....6.....2......2.....4.....8.3.....5..... | initial |
| 356.7.294....4.8518419527...1.4.59..7.4...625...2.741..2....54.....8.3.2...52.1.. | autosolve |
| 356871294972643851841952736213465987794318625685297413128736549569184372437529168 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) A2: 2,9 B2: 7,9 D1: 1,8 F1: 1,8 D2: 3,6 F2: 3,6 H3: 3,6 I3: 3,6 A4: 2,6 B5: 3,9 E4: 3,6 I6: 3,8 H8: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,F1: 1.. / D1 = 1 => 0 pairs (X) / F1 = 1 => 13 pairs (_) A7,A8: 1.. / A7 = 1 => 15 pairs (_) / A8 = 1 => 0 pairs (X) E5,E7: 1.. / E5 = 1 => 15 pairs (_) / E7 = 1 => 0 pairs (X) A2,C2: 2.. / A2 = 2 => 0 pairs (X) / C2 = 2 => 15 pairs (_) A4,C4: 2.. / A4 = 2 => 15 pairs (_) / C4 = 2 => 0 pairs (X) A2,A4: 2.. / A2 = 2 => 0 pairs (X) / A4 = 2 => 15 pairs (_) C2,C4: 2.. / C2 = 2 => 15 pairs (_) / C4 = 2 => 0 pairs (X) D2,F2: 3.. / D2 = 3 => 0 pairs (X) / F2 = 3 => 12 pairs (_) H3,I3: 3.. / H3 = 3 => 12 pairs (_) / I3 = 3 => 0 pairs (X) H3,H4: 3.. / H3 = 3 => 12 pairs (_) / H4 = 3 => 0 pairs (X) A8,A9: 4.. / A8 = 4 => 16 pairs (_) / A9 = 4 => 14 pairs (_) F8,F9: 4.. / F8 = 4 => 14 pairs (_) / F9 = 4 => 16 pairs (_) A8,F8: 4.. / A8 = 4 => 16 pairs (_) / F8 = 4 => 14 pairs (_) A9,F9: 4.. / A9 = 4 => 14 pairs (_) / F9 = 4 => 16 pairs (_) A6,C6: 5.. / A6 = 5 => 13 pairs (_) / C6 = 5 => 0 pairs (*) A8,C8: 5.. / A8 = 5 => 0 pairs (*) / C8 = 5 => 0 pairs (X) A6,A8: 5.. / A6 = 5 => 13 pairs (_) / A8 = 5 => 0 pairs (*) C6,C8: 5.. / C6 = 5 => 0 pairs (*) / C8 = 5 => 0 pairs (X) D2,F2: 6.. / D2 = 6 => 12 pairs (_) / F2 = 6 => 0 pairs (X) H3,I3: 6.. / H3 = 6 => 0 pairs (X) / I3 = 6 => 12 pairs (_) E4,E6: 6.. / E4 = 6 => 15 pairs (_) / E6 = 6 => 0 pairs (X) A4,E4: 6.. / A4 = 6 => 0 pairs (X) / E4 = 6 => 15 pairs (_) B2,C2: 7.. / B2 = 7 => 14 pairs (_) / C2 = 7 => 0 pairs (X) H4,I4: 7.. / H4 = 7 => 0 pairs (X) / I4 = 7 => 14 pairs (_) D7,D8: 7.. / D7 = 7 => 14 pairs (_) / D8 = 7 => 0 pairs (X) D1,F1: 8.. / D1 = 8 => 13 pairs (_) / F1 = 8 => 0 pairs (X) D5,F5: 8.. / D5 = 8 => 0 pairs (X) / F5 = 8 => 13 pairs (_) C7,I7: 8.. / C7 = 8 => 0 pairs (*) / I7 = 8 => 0 pairs (X) B6,B9: 8.. / B6 = 8 => 18 pairs (_) / B9 = 8 => 0 pairs (X) D1,D5: 8.. / D1 = 8 => 13 pairs (_) / D5 = 8 => 0 pairs (X) F1,F5: 8.. / F1 = 8 => 0 pairs (X) / F5 = 8 => 13 pairs (_) H4,H9: 8.. / H4 = 8 => 15 pairs (_) / H9 = 8 => 0 pairs (X) I7,I9: 9.. / I7 = 9 => 0 pairs (*) / I9 = 9 => 0 pairs (X) * DURATION: 0:01:01.810366 START: 23:08:39.652601 END: 23:09:41.462967 2017-05-03 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,B2,B5,D1,D2,E4,F1,F2,H3,H8,I3,I6) * 356.7.294....4.8518419527...1.4.59..7.4...625...2.741..2....54.....8.3.2...52.1.. * PAIR A2: 2,9 BLK 1 C2: 2,9,7 # reduction candidate for 2,9 C2: 7 => CTR * 356.7.294297.4.8518419527366124359..734...625.8.267413.2....54.....8.3.2...52.1.. C2: 2,9 # 14 pairs * PAIR B2: 7,9 BLK 1 C2: 7,9,2 # reduction candidate for 7,9 C2: 7,9 => CTR * 356.7.2942...4.8518419527366124359..734...625...267413.2....54....78.362.6352.1.. C2: 2 # 15 pairs * PAIR B2: 7,9 COL B B8: 7,9,6 # reduction candidate for 7,9 B8: 7,9 => CTR * 356.7.294972.4.8518419527..2184659..734...625569237418.2....54..95.8.3.2.8.52.1.. B8: 6 => SOLVED * 356871294972643851841952736213465987794318625685297413128736549569184372437529168 B9: 7,9,3,6,8 # reduction candidate for 7,9 B9: 7,9 => CTR * 356.7.294....4.851841952736.1.4.5987734...625.8.2.7413.2.7.654..6.18.372...52.1.. B9: 3,6,8 # 13 pairs * PAIR D1: 1,8 COL D D5: 1,8,3 # reduction candidate for 1,8 D5: 1,8 => CTR * 356.7.294972.4.8518419527..2184659..734...625569237418.2....54..95.8.3.2.8.52.1.. D5: 3 => SOLVED * 356871294972643851841952736213465987794318625685297413128736549569184372437529168 * PAIR F1: 1,8 COL F F5: 1,8,3,9 # reduction candidate for 1,8 F5: 3,9 => CTR * 356178294972.4.8518419527..2184659..734819625569237418.2..9.54..95.8.3.2.8.52.1.9 F5: 1,8 # 15 pairs * PAIR D2: 3,6 COL D D7: 3,6,1,7 # reduction candidate for 3,6 D7: 3,6 => CTR * 356.7.294972.4.851841952736218465973734...625569237418.2....54..9578.362.8.52.1.. D7: 1,7 # 14 pairs * PAIR F2: 3,6 COL F F7: 3,6,1,9 # reduction candidate for 3,6 F7: 3,6 # 15 pairs F9: 3,6,4,9 # reduction candidate for 3,6 F9: 3,6 # 16 pairs * PAIR B5: 3,9 BLK 4 B6: 3,9,6,8 # reduction candidate for 3,9 B6: 3,9 => CTR * 356.7.294.7.346851841952736.1.4.5987734...625598267413.23...548.65.8.372.87523169 B6: 6,8 # 14 pairs C6: 3,9,5,8 # reduction candidate for 3,9 C6: 3,9 # 16 pairs * PAIR B5: 3,9 ROW 5 E5: 3,9,1 # reduction candidate for 3,9 E5: 3,9 => CTR * 356.7.294972.4.8518419527..21.4659..734.9.625569237418628.1.54.195.843.24..52.1.. E5: 1 # 15 pairs F5: 3,9,1,8 # reduction candidate for 3,9 F5: 3,9 => CTR * 356178294972.4.8518419527..2184659..734819625569237418.2..9.54..95.8.3.2.8.52.1.9 F5: 1,8 # 15 pairs * PAIR B5: 3,9 COL B B9: 3,9,6,7,8 # reduction candidate for 3,9 B9: 3,9 => SOLVED * 356871294972643851841952736213465987794318625685297413128736549569184372437529168 B9: 6,7,8 # 14 pairs * PAIR E4: 3,6 BLK 5 E6: 3,6,9 # reduction candidate for 3,6 E6: 3,6 => CTR * 356.7.294972.4.8518419527..2184659..734...625569237418.2....54..95.8.3.2.8.52.1.. E6: 9 => SOLVED * 356871294972643851841952736213465987794318625685297413128736549569184372437529168 * PAIR I6: 3,8 BLK 6 H4: 3,8,7 # reduction candidate for 3,8 H4: 3,8 # 14 pairs I4: 3,8,7 # reduction candidate for 3,8 I4: 3,8 => CTR * 356.7.294....4.851841952736.12435978734...625.8.267413.287..54.....8.362.6352.187 I4: 7 # 14 pairs * PAIR I6: 3,8 ROW 6 B6: 3,8,6,9 # reduction candidate for 3,8 B6: 3,8 # 18 pairs C6: 3,8,5,9 # reduction candidate for 3,8 C6: 3,8 => CTR * 356.7.294.7..4.8518419527..612435987734...625598267413.237..548.6518.372..752.1.. C6: 5,9 # 14 pairs * PAIR H8: 6,7 BLK 9 I7: 6,7,8,9 # reduction candidate for 6,7 I7: 6,7 => CTR * 356.7.294....4.851841952736.1.4.59787.4...625.8.2.7413.28...547...78.362.6.52.189 I7: 8,9 # 14 pairs H9: 6,7,8 # reduction candidate for 6,7 H9: 6,7 # 15 pairs I9: 6,7,8,9 # reduction candidate for 6,7 I9: 6,7 => CTR * 356.7.294...643851841952736.12435978734...625.8.2674131287..549....8.362.6352.187 I9: 8,9 # 14 pairs * PAIR H8: 6,7 ROW 8 B8: 6,7,9 # reduction candidate for 6,7 B8: 6,7 => SOLVED * 356871294972643851841952736213465987794318625685297413128736549569184372437529168 B8: 9 => CTR * 356.7.294.7..4.8518419527...184.59..734...625569237418.2....54..95.8.3.2.8.52.1.. D8: 6,7,1 # reduction candidate for 6,7 D8: 6,7 => CTR * 356.7.294972.4.8518419527..2184659..734...625569237418.2....54..95.8.3.2.8.52.1.. D8: 1 => SOLVED * 356871294972643851841952736213465987794318625685297413128736549569184372437529168 * INCONCLUSIVE * SAVE PR GRAPH xx-top95-014-base-pr-000.dot * REASONING * DIS # C2: 7 => CTR => C2: 2,9 * DIS # C2: 7,9 => CTR => C2: 2 * DIS # B8: 7,9 => CTR => B8: 6 * PRF # B8: 6 => SOL * DIS # B9: 7,9 => CTR => B9: 3,6,8 * DIS # D5: 1,8 => CTR => D5: 3 * PRF # D5: 3 => SOL * DIS # F5: 3,9 => CTR => F5: 1,8 * DIS # D7: 3,6 => CTR => D7: 1,7 * DIS # B6: 3,9 => CTR => B6: 6,8 * DIS # E5: 3,9 => CTR => E5: 1 * DIS # F5: 3,9 => CTR => F5: 1,8 * PRF # B9: 3,9 => SOL * DIS # E6: 3,6 => CTR => E6: 9 * PRF # E6: 9 => SOL * DIS # I4: 3,8 => CTR => I4: 7 * DIS # C6: 3,8 => CTR => C6: 5,9 * DIS # I7: 6,7 => CTR => I7: 8,9 * DIS # I9: 6,7 => CTR => I9: 8,9 * PRF # B8: 6,7 => SOL * DIS # B8: 9 => CTR => B8: 6,7 * DIS # D8: 6,7 => CTR => D8: 1 * PRF # D8: 1 => SOL * CNT 23 HDP CHAINS / 42 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,B2,B5,D1,D2,E4,F1,F2,H3,H8,I3,I6) * 356.7.294....4.8518419527...1.4.59..7.4...625...2.741..2....54.....8.3.2...52.1.. * PAIR A2: 2,9 BLK 1 C2: 2,9,7 # reduction candidate for 2,9 C2: 7 => CTR * 356.7.294297.4.8518419527366124359..734...625.8.267413.2....54.....8.3.2...52.1.. * PAIR D1: 1,8 COL D D5: 1,8,3 # reduction candidate for 1,8 D5: 1,8 => CTR * 356.7.294972.4.8518419527..2184659..734...625569237418.2....54..95.8.3.2.8.52.1.. D5: 3 => SOLVED * 356871294972643851841952736213465987794318625685297413128736549569184372437529168 * DURATION: 0:00:05.599317 START: 23:10:27.741258 END: 23:10:33.340575 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-014-base-pr-001.dot * REASONING * DIS # C2: 7 => CTR => C2: 2,9 * DIS C2: 2,9 # D5: 1,8 => CTR => D5: 3 * PRF C2: 2,9 + D5: 3 => SOL * STA C2: 2,9 + D5: 3 * CNT 3 HDP CHAINS / 3 HYP OPENED
Header Info
Top 95 Sudokus 014 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 356871294972643851841952736213465987794318625685297413128736549569184372437529168 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 # C2: 2,9 => UNS * DIS # C2: 7 => CTR => C2: 2,9 * DIS # C2: 7,9 => CTR => C2: 2 * INC # C2: 2 => UNS * DIS # B8: 7,9 => CTR => B8: 6 * PRF # B8: 6 => SOL * DIS # B9: 7,9 => CTR => B9: 3,6,8 * INC # B9: 3,6,8 => UNS * DIS # D5: 1,8 => CTR => D5: 3 * PRF # D5: 3 => SOL * INC # F5: 1,8 => UNS * DIS # F5: 3,9 => CTR => F5: 1,8 * DIS # D7: 3,6 => CTR => D7: 1,7 * INC # D7: 1,7 => UNS * INC # F7: 3,6 => UNS * INC # F9: 3,6 => UNS * DIS # B6: 3,9 => CTR => B6: 6,8 * INC # B6: 6,8 => UNS * INC # C6: 3,9 => UNS * DIS # E5: 3,9 => CTR => E5: 1 * INC # E5: 1 => UNS * DIS # F5: 3,9 => CTR => F5: 1,8 * INC # F5: 1,8 => UNS * PRF # B9: 3,9 => SOL * INC # B9: 6,7,8 => UNS * DIS # E6: 3,6 => CTR => E6: 9 * PRF # E6: 9 => SOL * INC # H4: 3,8 => UNS * DIS # I4: 3,8 => CTR => I4: 7 * INC # I4: 7 => UNS * INC # B6: 3,8 => UNS * DIS # C6: 3,8 => CTR => C6: 5,9 * INC # C6: 5,9 => UNS * DIS # I7: 6,7 => CTR => I7: 8,9 * INC # I7: 8,9 => UNS * INC # H9: 6,7 => UNS * DIS # I9: 6,7 => CTR => I9: 8,9 * INC # I9: 8,9 => UNS * PRF # B8: 6,7 => SOL * DIS # B8: 9 => CTR => B8: 6,7 * DIS # D8: 6,7 => CTR => D8: 1 * PRF # D8: 1 => SOL * CNT 42 HDP CHAINS / 42 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C2: 2,9 => UNS * DIS # C2: 7 => CTR => C2: 2,9 * DIS C2: 2,9 # D5: 1,8 => CTR => D5: 3 * PRF C2: 2,9 + D5: 3 => SOL * STA C2: 2,9 + D5: 3 * CNT 4 HDP CHAINS / 3 HYP OPENED