Analysis of xx-top500-394-base.sdk
Contents
Original Sudoku
level: medium
position: ..74..5..6....2...............71.8..2.....1..3........5......3..4.9............26 initial
Autosolve
position: .2743.56.6....23...3....2....67138.22.....1.33..2..6..562...93..439267..7..3..426 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F9: 1 => CTR => F9: 5,8 * CNT 1 HDP CHAINS / 35 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F9: 1 => CTR => F9: 5,8 * DIS F9: 5,8 # C2: 8,9 => CTR => C2: 4 * PRF F9: 5,8 + C2: 4 => SOL * STA F9: 5,8 + C2: 4 * CNT 3 HDP CHAINS / 27 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..74..5..6....2...............71.8..2.....1..3........5......3..4.9............26 | initial |
| .2743.56.6....23...3....2....67138.22.....1.33..2..6..562...93..439267..7..3..426 | autosolve |
| 127438569684592371935671284456713892279864153318259647562147938843926715791385426 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) A4: 4,9 B4: 5,9 A8: 1,8 D7: 1,8 E7: 4,7 F7: 4,7 E9: 5,8 I7: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B6,C6: 1.. / B6 = 1 => 10 pairs (_) / C6 = 1 => 9 pairs (_) D7,F9: 1.. / D7 = 1 => 16 pairs (_) / F9 = 1 => 0 pairs (X) D7,I7: 1.. / D7 = 1 => 16 pairs (_) / I7 = 1 => 0 pairs (X) E7,F7: 4.. / E7 = 4 => 6 pairs (_) / F7 = 4 => 6 pairs (_) A4,H4: 4.. / A4 = 4 => 8 pairs (_) / H4 = 4 => 9 pairs (_) A3,A4: 4.. / A3 = 4 => 9 pairs (_) / A4 = 4 => 8 pairs (_) E9,F9: 5.. / E9 = 5 => 8 pairs (_) / F9 = 5 => 16 pairs (_) H8,I8: 5.. / H8 = 5 => 16 pairs (_) / I8 = 5 => 9 pairs (_) B4,H4: 5.. / B4 = 5 => 8 pairs (_) / H4 = 5 => 9 pairs (_) I6,I8: 5.. / I6 = 5 => 16 pairs (_) / I8 = 5 => 9 pairs (_) D3,E3: 6.. / D3 = 6 => 9 pairs (_) / E3 = 6 => 8 pairs (_) D5,E5: 6.. / D5 = 6 => 8 pairs (_) / E5 = 6 => 9 pairs (_) D3,D5: 6.. / D3 = 6 => 9 pairs (_) / D5 = 6 => 8 pairs (_) E3,E5: 6.. / E3 = 6 => 8 pairs (_) / E5 = 6 => 9 pairs (_) B5,B6: 7.. / B5 = 7 => 8 pairs (_) / B6 = 7 => 10 pairs (_) E7,F7: 7.. / E7 = 7 => 6 pairs (_) / F7 = 7 => 6 pairs (_) B5,H5: 7.. / B5 = 7 => 8 pairs (_) / H5 = 7 => 10 pairs (_) F3,F7: 7.. / F3 = 7 => 6 pairs (_) / F7 = 7 => 6 pairs (_) D7,I7: 8.. / D7 = 8 => 0 pairs (X) / I7 = 8 => 16 pairs (_) B9,C9: 9.. / B9 = 9 => 11 pairs (_) / C9 = 9 => 9 pairs (_) * DURATION: 0:00:28.247227 START: 16:18:06.841965 END: 16:18:35.089192 2017-05-04 * CP COUNT: (20) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A8,B4,D7,E7,E9,F7,I7) * .2743.56.6....23...3....2....67138.22.....1.33..2..6..562...93..439267..7..3..426 * PAIR A4: 4,9 BLK 4 C5: 4,9,5,8 # reduction candidate for 4,9 C5: 4,9 # 11 pairs C6: 4,9,1,5,8 # reduction candidate for 4,9 C6: 4,9 # 13 pairs * PAIR A4: 4,9 ROW 4 H4: 4,9,5 # reduction candidate for 4,9 H4: 5 # 9 pairs H4: 4,9 # 8 pairs * PAIR A4: 4,9 COL A A3: 4,9,1,8 # reduction candidate for 4,9 A3: 1,8 # 12 pairs A3: 4,9 # 10 pairs * PAIR B4: 5,9 BLK 4 B5: 5,9,7,8 # reduction candidate for 5,9 B5: 5,9 # 14 pairs C5: 5,9,4,8 # reduction candidate for 5,9 C5: 5,9 # 11 pairs B6: 5,9,1,7,8 # reduction candidate for 5,9 B6: 5,9 # 14 pairs C6: 5,9,1,4,8 # reduction candidate for 5,9 C6: 5,9 # 13 pairs * PAIR B4: 5,9 ROW 4 H4: 5,9,4 # reduction candidate for 5,9 H4: 4 # 9 pairs H4: 5,9 # 8 pairs * PAIR B4: 5,9 COL B B2: 5,9,1,8 # reduction candidate for 5,9 B2: 5,9 # 12 pairs B2: 1,8 # 9 pairs * PAIR A8: 1,8 BLK 7 B9: 1,8,9 # reduction candidate for 1,8 B9: 1,8 # 9 pairs C9: 1,8,9 # reduction candidate for 1,8 C9: 1,8 # 11 pairs * PAIR A8: 1,8 ROW 8 H8: 1,8,5 # reduction candidate for 1,8 H8: 1,8 # 9 pairs I8: 1,8,5 # reduction candidate for 1,8 I8: 1,8 # 16 pairs * PAIR A8: 1,8 COL A A1: 1,8,9 # reduction candidate for 1,8 A1: 1,8 # 10 pairs A3: 1,8,4,9 # reduction candidate for 1,8 A3: 1,8 # 12 pairs * PAIR D7: 1,8 BLK 8 F9: 1,8,5 # reduction candidate for 1,8 F9: 5 # 16 pairs F9: 1,8 # 8 pairs * PAIR D7: 1,8 COL D D2: 1,8,5 # reduction candidate for 1,8 D2: 1,8 # 11 pairs D3: 1,8,5,6 # reduction candidate for 1,8 D3: 1,8 # 9 pairs * PAIR E9: 5,8 BLK 8 F9: 5,8,1 # reduction candidate for 5,8 F9: 1 => CTR * .2743.56.6....23...3....2....67138.22.....1.33..2..6..5628..9311439267..7..351426 F9: 5,8 # 16 pairs * PAIR E9: 5,8 COL E E2: 5,8,7,9 # reduction candidate for 5,8 E2: 5,8 # 10 pairs E3: 5,8,6,7,9 # reduction candidate for 5,8 E3: 5,8 # 12 pairs E5: 5,8,4,6,9 # reduction candidate for 5,8 E5: 5,8 # 11 pairs E6: 5,8,4,9 # reduction candidate for 5,8 E6: 5,8 # 10 pairs * PAIR I7: 1,8 BLK 9 H8: 1,8,5 # reduction candidate for 1,8 H8: 1,8 # 9 pairs I8: 1,8,5 # reduction candidate for 1,8 I8: 1,8 # 16 pairs * PAIR I7: 1,8 COL I I1: 1,8,9 # reduction candidate for 1,8 I1: 1,8 # 10 pairs I2: 1,8,4,7,9 # reduction candidate for 1,8 I2: 1,8 # 15 pairs I3: 1,8,4,7,9 # reduction candidate for 1,8 I3: 1,8 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-394-base-pr-000.dot * REASONING * DIS # F9: 1 => CTR => F9: 5,8 * CNT 1 HDP CHAINS / 35 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A8,B4,D7,E7,E9,F7,I7) * .2743.56.6....23...3....2....67138.22.....1.33..2..6..562...93..439267..7..3..426 * PAIR A4: 4,9 BLK 4 C5: 4,9,5,8 # reduction candidate for 4,9 C5: 4,9 # 11 pairs C6: 4,9,1,5,8 # reduction candidate for 4,9 C6: 4,9 # 13 pairs * PAIR A4: 4,9 ROW 4 H4: 4,9,5 # reduction candidate for 4,9 H4: 5 # 9 pairs H4: 4,9 # 8 pairs * PAIR A4: 4,9 COL A A3: 4,9,1,8 # reduction candidate for 4,9 A3: 1,8 # 12 pairs A3: 4,9 # 10 pairs * PAIR B4: 5,9 BLK 4 B5: 5,9,7,8 # reduction candidate for 5,9 B5: 5,9 # 14 pairs C5: 5,9,4,8 # reduction candidate for 5,9 C5: 5,9 # 11 pairs B6: 5,9,1,7,8 # reduction candidate for 5,9 B6: 5,9 # 14 pairs C6: 5,9,1,4,8 # reduction candidate for 5,9 C6: 5,9 # 13 pairs * PAIR B4: 5,9 ROW 4 H4: 5,9,4 # reduction candidate for 5,9 H4: 4 # 9 pairs H4: 5,9 # 8 pairs * PAIR B4: 5,9 COL B B2: 5,9,1,8 # reduction candidate for 5,9 B2: 5,9 # 12 pairs B2: 1,8 # 9 pairs * PAIR A8: 1,8 BLK 7 B9: 1,8,9 # reduction candidate for 1,8 B9: 1,8 # 9 pairs C9: 1,8,9 # reduction candidate for 1,8 C9: 1,8 # 11 pairs * PAIR A8: 1,8 ROW 8 H8: 1,8,5 # reduction candidate for 1,8 H8: 1,8 # 9 pairs I8: 1,8,5 # reduction candidate for 1,8 I8: 1,8 # 16 pairs * PAIR A8: 1,8 COL A A1: 1,8,9 # reduction candidate for 1,8 A1: 1,8 # 10 pairs A3: 1,8,4,9 # reduction candidate for 1,8 A3: 1,8 # 12 pairs * PAIR D7: 1,8 BLK 8 F9: 1,8,5 # reduction candidate for 1,8 F9: 5 # 16 pairs F9: 1,8 # 8 pairs * PAIR D7: 1,8 COL D D2: 1,8,5 # reduction candidate for 1,8 D2: 1,8 # 11 pairs D3: 1,8,5,6 # reduction candidate for 1,8 D3: 1,8 # 9 pairs * PAIR E9: 5,8 BLK 8 F9: 5,8,1 # reduction candidate for 5,8 F9: 1 => CTR * .2743.56.6....23...3....2....67138.22.....1.33..2..6..5628..9311439267..7..351426 * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A3,A4,B2,B6,B9,C5,C6,C9,E2,E3,F5,F6,H2,H4,I3,I6) * 1274385696..5.23.1.356.128..567138.227.86.1533..25.6..5621479388439267157..385426 * PAIR B2: 8,9 BLK 1 C2: 8,9,4 # reduction candidate for 8,9 C2: 8,9 => CTR * 1274385696..5.23414356912879567138.227.86.1533..25.6..5621479388439267157..385426 C2: 4 => SOLVED * 127438569684592371935671284456713892279864153318259647562147938843926715791385426 * DURATION: 0:00:23.919471 START: 16:19:02.845720 END: 16:19:26.765191 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-394-base-pr-001.dot * REASONING * DIS # F9: 1 => CTR => F9: 5,8 * DIS F9: 5,8 # C2: 8,9 => CTR => C2: 4 * PRF F9: 5,8 + C2: 4 => SOL * STA F9: 5,8 + C2: 4 * CNT 3 HDP CHAINS / 27 HYP OPENED
Header Info
Top 500 Minimum 17 394 solution: 127438569684592371935671284456713892279864153318259647562147938843926715791385426 info: 58674 FNBTXK S8.f 14405 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 127438569684592371935671284456713892279864153318259647562147938843926715791385426 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 # C5: 4,9 => UNS * INC # C6: 4,9 => UNS * INC # H4: 4,9 => UNS * INC # H4: 5 => UNS * INC # A3: 4,9 => UNS * INC # A3: 1,8 => UNS * INC # B5: 5,9 => UNS * INC # C5: 5,9 => UNS * INC # B6: 5,9 => UNS * INC # C6: 5,9 => UNS * INC # H4: 5,9 => UNS * INC # H4: 4 => UNS * INC # B2: 5,9 => UNS * INC # B2: 1,8 => UNS * INC # B9: 1,8 => UNS * INC # C9: 1,8 => UNS * INC # H8: 1,8 => UNS * INC # I8: 1,8 => UNS * INC # A1: 1,8 => UNS * INC # A3: 1,8 => UNS * INC # F9: 1,8 => UNS * INC # F9: 5 => UNS * INC # D2: 1,8 => UNS * INC # D3: 1,8 => UNS * INC # F9: 5,8 => UNS * DIS # F9: 1 => CTR => F9: 5,8 * INC # E2: 5,8 => UNS * INC # E3: 5,8 => UNS * INC # E5: 5,8 => UNS * INC # E6: 5,8 => UNS * INC # H8: 1,8 => UNS * INC # I8: 1,8 => UNS * INC # I1: 1,8 => UNS * INC # I2: 1,8 => UNS * INC # I3: 1,8 => UNS * CNT 35 HDP CHAINS / 35 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C5: 4,9 => UNS * INC # C6: 4,9 => UNS * INC # H4: 4,9 => UNS * INC # H4: 5 => UNS * INC # A3: 4,9 => UNS * INC # A3: 1,8 => UNS * INC # B5: 5,9 => UNS * INC # C5: 5,9 => UNS * INC # B6: 5,9 => UNS * INC # C6: 5,9 => UNS * INC # H4: 5,9 => UNS * INC # H4: 4 => UNS * INC # B2: 5,9 => UNS * INC # B2: 1,8 => UNS * INC # B9: 1,8 => UNS * INC # C9: 1,8 => UNS * INC # H8: 1,8 => UNS * INC # I8: 1,8 => UNS * INC # A1: 1,8 => UNS * INC # A3: 1,8 => UNS * INC # F9: 1,8 => UNS * INC # F9: 5 => UNS * INC # D2: 1,8 => UNS * INC # D3: 1,8 => UNS * INC # F9: 5,8 => UNS * DIS # F9: 1 => CTR => F9: 5,8 * DIS F9: 5,8 # C2: 8,9 => CTR => C2: 4 * PRF F9: 5,8 + C2: 4 => SOL * STA F9: 5,8 + C2: 4 * CNT 28 HDP CHAINS / 27 HYP OPENED