Analysis of xx-top500-279-base.sdk
Contents
Original Sudoku
level: medium
position: ....2..4.1.....5.......6....6..4..2.5..3..1..............1.8....2.....7....5..3.. initial
Autosolve
position: ....2.64.1764835922.4..6....6.84..2.54236.18....2..4.6...1.82...2.6.4.7....5.23.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A8: 8 => SOL * PRF # I9: 8 => SOL * DIS # I9: 4 => CTR => I9: 8,9 * CNT 3 HDP CHAINS / 26 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A8: 8 => SOL * STA A8: 8 * CNT 1 HDP CHAINS / 16 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....2..4.1.....5.......6....6..4..2.5..3..1..............1.8....2.....7....5..3.. | initial |
| ....2.64.1764835922.4..6....6.84..2.54236.18....2..4.6...1.82...2.6.4.7....5.23.. | autosolve |
| 958721643176483592234956817361849725542367189789215436693178254825634971417592368 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (22) D1: 7,9 F1: 1,5 D3: 7,9 E3: 1,5 G3: 7,8 H3: 1,3 F5: 7,9 E6: 1,5 G4: 7,9 I4: 3,5 I5: 7,9 H6: 3,5 A7: 4,6 C8: 1,5 A9: 4,6 E8: 3,9 E9: 7,9 H7: 5,6 I7: 4,9 G8: 8,9 I8: 1,5 H9: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F1,E3: 1.. / F1 = 1 => 16 pairs (_) / E3 = 1 => 0 pairs (X) I8,H9: 1.. / I8 = 1 => 16 pairs (_) / H9 = 1 => 0 pairs (X) F1,I1: 1.. / F1 = 1 => 16 pairs (_) / I1 = 1 => 0 pairs (X) C4,F4: 1.. / C4 = 1 => 16 pairs (_) / F4 = 1 => 0 pairs (X) C8,I8: 1.. / C8 = 1 => 0 pairs (X) / I8 = 1 => 16 pairs (_) B6,B9: 1.. / B6 = 1 => 0 pairs (X) / B9 = 1 => 16 pairs (_) E3,E6: 1.. / E3 = 1 => 0 pairs (X) / E6 = 1 => 16 pairs (_) H3,H9: 1.. / H3 = 1 => 16 pairs (_) / H9 = 1 => 0 pairs (X) I4,H6: 3.. / I4 = 3 => 0 pairs (X) / H6 = 3 => 16 pairs (_) E7,E8: 3.. / E7 = 3 => 19 pairs (_) / E8 = 3 => 23 pairs (_) A8,E8: 3.. / A8 = 3 => 19 pairs (_) / E8 = 3 => 23 pairs (_) H3,H6: 3.. / H3 = 3 => 0 pairs (X) / H6 = 3 => 16 pairs (_) A7,A9: 4.. / A7 = 4 => 0 pairs (X) / A9 = 4 => 16 pairs (_) I7,I9: 4.. / I7 = 4 => 16 pairs (_) / I9 = 4 => 0 pairs (X) A7,I7: 4.. / A7 = 4 => 0 pairs (X) / I7 = 4 => 16 pairs (_) A9,I9: 4.. / A9 = 4 => 16 pairs (_) / I9 = 4 => 0 pairs (X) F1,E3: 5.. / F1 = 5 => 0 pairs (X) / E3 = 5 => 16 pairs (_) I4,H6: 5.. / I4 = 5 => 16 pairs (_) / H6 = 5 => 0 pairs (X) H7,I8: 5.. / H7 = 5 => 16 pairs (_) / I8 = 5 => 0 pairs (X) B3,E3: 5.. / B3 = 5 => 0 pairs (X) / E3 = 5 => 16 pairs (_) F4,I4: 5.. / F4 = 5 => 0 pairs (X) / I4 = 5 => 16 pairs (_) C8,I8: 5.. / C8 = 5 => 16 pairs (_) / I8 = 5 => 0 pairs (X) E3,E6: 5.. / E3 = 5 => 16 pairs (_) / E6 = 5 => 0 pairs (X) H6,H7: 5.. / H6 = 5 => 0 pairs (X) / H7 = 5 => 16 pairs (_) I4,I8: 5.. / I4 = 5 => 16 pairs (_) / I8 = 5 => 0 pairs (X) A7,A9: 6.. / A7 = 6 => 16 pairs (_) / A9 = 6 => 0 pairs (X) H7,H9: 6.. / H7 = 6 => 0 pairs (X) / H9 = 6 => 16 pairs (_) A7,H7: 6.. / A7 = 6 => 16 pairs (_) / H7 = 6 => 0 pairs (X) A9,H9: 6.. / A9 = 6 => 0 pairs (X) / H9 = 6 => 16 pairs (_) D1,D3: 7.. / D1 = 7 => 20 pairs (_) / D3 = 7 => 0 pairs (X) A4,A6: 7.. / A4 = 7 => 19 pairs (_) / A6 = 7 => 23 pairs (_) G4,I5: 7.. / G4 = 7 => 0 pairs (*) / I5 = 7 => 0 pairs (X) C7,C9: 7.. / C7 = 7 => 22 pairs (_) / C9 = 7 => 23 pairs (_) E7,E9: 7.. / E7 = 7 => 23 pairs (_) / E9 = 7 => 22 pairs (_) D1,I1: 7.. / D1 = 7 => 20 pairs (_) / I1 = 7 => 0 pairs (X) F5,I5: 7.. / F5 = 7 => 0 pairs (*) / I5 = 7 => 0 pairs (X) A6,F6: 7.. / A6 = 7 => 23 pairs (_) / F6 = 7 => 19 pairs (_) C7,E7: 7.. / C7 = 7 => 22 pairs (_) / E7 = 7 => 23 pairs (_) C9,E9: 7.. / C9 = 7 => 23 pairs (_) / E9 = 7 => 22 pairs (_) G3,G4: 7.. / G3 = 7 => 19 pairs (_) / G4 = 7 => 0 pairs (*) G8,I9: 8.. / G8 = 8 => 19 pairs (_) / I9 = 8 => 0 pairs (*) A8,G8: 8.. / A8 = 8 => 0 pairs (*) / G8 = 8 => 0 pairs (X) G3,G8: 8.. / G3 = 8 => 0 pairs (*) / G8 = 8 => 0 pairs (X) D1,D3: 9.. / D1 = 9 => 0 pairs (X) / D3 = 9 => 20 pairs (_) G4,I5: 9.. / G4 = 9 => 19 pairs (_) / I5 = 9 => 0 pairs (*) B3,D3: 9.. / B3 = 9 => 0 pairs (X) / D3 = 9 => 20 pairs (_) F5,I5: 9.. / F5 = 9 => 19 pairs (_) / I5 = 9 => 0 pairs (*) G4,G8: 9.. / G4 = 9 => 19 pairs (_) / G8 = 9 => 0 pairs (*) * DURATION: 0:01:49.350304 START: 12:28:10.988344 END: 12:30:00.338648 2017-05-04 * CP COUNT: (48) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A9,C8,D1,D3,E3,E6,E8,E9,F1,F5,G3,G4,G8,H3,H6,H7,H9,I4,I5,I7,I8) * ....2.64.1764835922.4..6....6.84..2.54236.18....2..4.6...1.82...2.6.4.7....5.23.. * PAIR F1: 1,5 COL F F4: 1,5,7,9 # reduction candidate for 1,5 F4: 1,5 # 24 pairs F6: 1,5,7,9 # reduction candidate for 1,5 F6: 1,5 # 16 pairs * PAIR G3: 7,8 BLK 3 I1: 7,8,1,3 # reduction candidate for 7,8 I1: 7,8 # 18 pairs I3: 7,8,1,3 # reduction candidate for 7,8 I3: 7,8 # 23 pairs * PAIR H3: 1,3 BLK 3 I1: 1,3,7,8 # reduction candidate for 1,3 I1: 1,3 # 23 pairs I3: 1,3,7,8 # reduction candidate for 1,3 I3: 1,3 # 18 pairs * PAIR F5: 7,9 BLK 5 F4: 7,9,1,5 # reduction candidate for 7,9 F4: 7,9 # 16 pairs F6: 7,9,1,5 # reduction candidate for 7,9 F6: 7,9 # 24 pairs * PAIR E6: 1,5 BLK 5 F4: 1,5,7,9 # reduction candidate for 1,5 F4: 1,5 # 24 pairs F6: 1,5,7,9 # reduction candidate for 1,5 F6: 1,5 # 16 pairs * PAIR G4: 7,9 ROW 4 A4: 7,9,3 # reduction candidate for 7,9 A4: 7,9 # 26 pairs F4: 7,9,1,5 # reduction candidate for 7,9 F4: 7,9 # 16 pairs * PAIR E8: 3,9 BLK 8 E7: 3,9,7 # reduction candidate for 3,9 E7: 7 # 23 pairs E7: 3,9 # 22 pairs * PAIR E8: 3,9 ROW 8 A8: 3,9,8 # reduction candidate for 3,9 A8: 8 => SOLVED * 958721643176483592234956817361849725542367189789215436693178254825634971417592368 A8: 3,9 # 19 pairs * PAIR E9: 7,9 BLK 8 E7: 7,9,3 # reduction candidate for 7,9 E7: 7,9 # 23 pairs E7: 3 # 19 pairs * PAIR E9: 7,9 ROW 9 C9: 7,9,1,8 # reduction candidate for 7,9 C9: 7,9 # 25 pairs C9: 1,8 # 23 pairs * PAIR I7: 4,9 BLK 9 I9: 4,9,8 # reduction candidate for 4,9 I9: 8 => SOLVED * 958721643176483592234956817361849725542367189789215436693178254825634971417592368 I9: 4,9 # 19 pairs * PAIR G8: 8,9 BLK 9 I9: 8,9,4 # reduction candidate for 8,9 I9: 4 => CTR * ...72.64.1764835922.49.673..6.845923542369187.1.2..4.64..1.8269.2.6.48756..5.2314 I9: 8,9 # 16 pairs * PAIR G8: 8,9 ROW 8 A8: 8,9,3 # reduction candidate for 8,9 A8: 8,9 # 23 pairs A8: 3 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-279-base-pr-000.dot * REASONING * PRF # A8: 8 => SOL * PRF # I9: 8 => SOL * DIS # I9: 4 => CTR => I9: 8,9 * CNT 3 HDP CHAINS / 26 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A9,C8,D1,D3,E3,E6,E8,E9,F1,F5,G3,G4,G8,H3,H6,H7,H9,I4,I5,I7,I8) * ....2.64.1764835922.4..6....6.84..2.54236.18....2..4.6...1.82...2.6.4.7....5.23.. * PAIR F1: 1,5 COL F F4: 1,5,7,9 # reduction candidate for 1,5 F4: 1,5 # 24 pairs F6: 1,5,7,9 # reduction candidate for 1,5 F6: 1,5 # 16 pairs * PAIR G3: 7,8 BLK 3 I1: 7,8,1,3 # reduction candidate for 7,8 I1: 7,8 # 18 pairs I3: 7,8,1,3 # reduction candidate for 7,8 I3: 7,8 # 23 pairs * PAIR H3: 1,3 BLK 3 I1: 1,3,7,8 # reduction candidate for 1,3 I1: 1,3 # 23 pairs I3: 1,3,7,8 # reduction candidate for 1,3 I3: 1,3 # 18 pairs * PAIR F5: 7,9 BLK 5 F4: 7,9,1,5 # reduction candidate for 7,9 F4: 7,9 # 16 pairs F6: 7,9,1,5 # reduction candidate for 7,9 F6: 7,9 # 24 pairs * PAIR E6: 1,5 BLK 5 F4: 1,5,7,9 # reduction candidate for 1,5 F4: 1,5 # 24 pairs F6: 1,5,7,9 # reduction candidate for 1,5 F6: 1,5 # 16 pairs * PAIR G4: 7,9 ROW 4 A4: 7,9,3 # reduction candidate for 7,9 A4: 7,9 # 26 pairs F4: 7,9,1,5 # reduction candidate for 7,9 F4: 7,9 # 16 pairs * PAIR E8: 3,9 BLK 8 E7: 3,9,7 # reduction candidate for 3,9 E7: 7 # 23 pairs E7: 3,9 # 22 pairs * PAIR E8: 3,9 ROW 8 A8: 3,9,8 # reduction candidate for 3,9 A8: 8 => SOLVED * 958721643176483592234956817361849725542367189789215436693178254825634971417592368 * DURATION: 0:00:20.946129 START: 12:30:33.487170 END: 12:30:54.433299 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-279-base-pr-001.dot * REASONING * PRF # A8: 8 => SOL * STA A8: 8 * CNT 1 HDP CHAINS / 16 HYP OPENED
Header Info
Top 500 Minimum 17 279 solution: 958721643176483592234956817361849725542367189789215436693178254825634971417592368 info: 2253 FNBTHWXY S8.f 3212 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 958721643176483592234956817361849725542367189789215436693178254825634971417592368 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 # F4: 1,5 => UNS * INC # F6: 1,5 => UNS * INC # I1: 7,8 => UNS * INC # I3: 7,8 => UNS * INC # I1: 1,3 => UNS * INC # I3: 1,3 => UNS * INC # F4: 7,9 => UNS * INC # F6: 7,9 => UNS * INC # F4: 1,5 => UNS * INC # F6: 1,5 => UNS * INC # A4: 7,9 => UNS * INC # F4: 7,9 => UNS * INC # E7: 3,9 => UNS * INC # E7: 7 => UNS * INC # A8: 3,9 => UNS * PRF # A8: 8 => SOL * INC # E7: 7,9 => UNS * INC # E7: 3 => UNS * INC # C9: 7,9 => UNS * INC # C9: 1,8 => UNS * INC # I9: 4,9 => UNS * PRF # I9: 8 => SOL * INC # I9: 8,9 => UNS * DIS # I9: 4 => CTR => I9: 8,9 * INC # A8: 8,9 => UNS * INC # A8: 3 => UNS * CNT 26 HDP CHAINS / 26 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F4: 1,5 => UNS * INC # F6: 1,5 => UNS * INC # I1: 7,8 => UNS * INC # I3: 7,8 => UNS * INC # I1: 1,3 => UNS * INC # I3: 1,3 => UNS * INC # F4: 7,9 => UNS * INC # F6: 7,9 => UNS * INC # F4: 1,5 => UNS * INC # F6: 1,5 => UNS * INC # A4: 7,9 => UNS * INC # F4: 7,9 => UNS * INC # E7: 3,9 => UNS * INC # E7: 7 => UNS * INC # A8: 3,9 => UNS * PRF # A8: 8 => SOL * STA A8: 8 * CNT 16 HDP CHAINS / 16 HYP OPENED