Analysis of xx-top500-436-base.sdk
Contents
Original Sudoku
level: medium
position: ......8.1...7........6........5...6..9.....5..2..3....4...8.1..6.....3..5.7...... initial
Autosolve
position: 763.5.8.1.5.7..6...4.6..5.73745.1.681968...53825.3671.43..8517668.1..3.551736..8. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E2: 2,9 => CTR => E2: 1,4 * DIS # H2: 2,9 => CTR => H2: 3,4 * DIS # E2: 2,9 => CTR => E2: 1,4 * DIS # E8: 2,9 => CTR => E8: 4,7 * PRF # D1: 2 => SOL * PRF # I9: 4,9 => SOL * DIS # E8: 2,9 => CTR => E8: 4,7 * DIS # F8: 2,9 => CTR => F8: 4,7 * DIS # E8: 2,9 => CTR => E8: 4,7 * DIS # F8: 2,9 => CTR => F8: 4,7 * DIS # D1: 4 => CTR => D1: 2,9 * PRF # I9: 4,9 => SOL * PRF # F9: 2 => SOL * CNT 13 HDP CHAINS / 36 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E2: 2,9 => CTR => E2: 1,4 * DIS E2: 1,4 # H2: 2,9 => CTR => H2: 3,4 * PRF E2: 1,4 + H2: 3,4 # H3: 2,9 => SOL * STA E2: 1,4 + H2: 3,4 + H3: 2,9 * CNT 3 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ......8.1...7........6........5...6..9.....5..2..3....4...8.1..6.....3..5.7...... | initial |
| 763.5.8.1.5.7..6...4.6..5.73745.1.681968...53825.3671.43..8517668.1..3.551736..8. | autosolve |
| 763259841951748632248613597374591268196827453825436719432985176689174325517362984 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) A2: 2,9 C2: 1,8 A3: 2,9 C3: 1,8 F2: 3,8 F3: 3,8 E4: 2,9 D6: 4,9 G4: 2,9 G5: 2,4 I6: 4,9 C7: 2,9 C8: 2,9 D7: 2,9 G9: 4,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,C3: 1.. / C2 = 1 => 12 pairs (_) / C3 = 1 => 15 pairs (_) E2,E3: 1.. / E2 = 1 => 15 pairs (_) / E3 = 1 => 12 pairs (_) C2,E2: 1.. / C2 = 1 => 12 pairs (_) / E2 = 1 => 15 pairs (_) C3,E3: 1.. / C3 = 1 => 15 pairs (_) / E3 = 1 => 12 pairs (_) A2,A3: 2.. / A2 = 2 => 18 pairs (_) / A3 = 2 => 18 pairs (_) G4,G5: 2.. / G4 = 2 => 20 pairs (_) / G5 = 2 => 0 pairs (X) C7,C8: 2.. / C7 = 2 => 0 pairs (*) / C8 = 2 => 0 pairs (X) H8,I9: 2.. / H8 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) E4,G4: 2.. / E4 = 2 => 0 pairs (X) / G4 = 2 => 20 pairs (_) C7,D7: 2.. / C7 = 2 => 0 pairs (*) / D7 = 2 => 0 pairs (X) F9,I9: 2.. / F9 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) D1,D7: 2.. / D1 = 2 => 0 pairs (*) / D7 = 2 => 0 pairs (X) I2,I9: 2.. / I2 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) F2,F3: 3.. / F2 = 3 => 15 pairs (_) / F3 = 3 => 12 pairs (_) H2,H3: 3.. / H2 = 3 => 12 pairs (_) / H3 = 3 => 15 pairs (_) F2,H2: 3.. / F2 = 3 => 15 pairs (_) / H2 = 3 => 12 pairs (_) F3,H3: 3.. / F3 = 3 => 12 pairs (_) / H3 = 3 => 15 pairs (_) G5,I6: 4.. / G5 = 4 => 20 pairs (_) / I6 = 4 => 0 pairs (X) D6,I6: 4.. / D6 = 4 => 20 pairs (_) / I6 = 4 => 0 pairs (X) D1,D6: 4.. / D1 = 4 => 0 pairs (X) / D6 = 4 => 20 pairs (_) G5,G9: 4.. / G5 = 4 => 20 pairs (_) / G9 = 4 => 0 pairs (X) E5,F5: 7.. / E5 = 7 => 16 pairs (_) / F5 = 7 => 19 pairs (_) E8,F8: 7.. / E8 = 7 => 19 pairs (_) / F8 = 7 => 16 pairs (_) E5,E8: 7.. / E5 = 7 => 16 pairs (_) / E8 = 7 => 19 pairs (_) F5,F8: 7.. / F5 = 7 => 19 pairs (_) / F8 = 7 => 16 pairs (_) C2,C3: 8.. / C2 = 8 => 15 pairs (_) / C3 = 8 => 12 pairs (_) F2,F3: 8.. / F2 = 8 => 12 pairs (_) / F3 = 8 => 15 pairs (_) C2,F2: 8.. / C2 = 8 => 15 pairs (_) / F2 = 8 => 12 pairs (_) C3,F3: 8.. / C3 = 8 => 12 pairs (_) / F3 = 8 => 15 pairs (_) A2,A3: 9.. / A2 = 9 => 18 pairs (_) / A3 = 9 => 18 pairs (_) E4,D6: 9.. / E4 = 9 => 20 pairs (_) / D6 = 9 => 0 pairs (X) G4,I6: 9.. / G4 = 9 => 0 pairs (X) / I6 = 9 => 20 pairs (_) C7,C8: 9.. / C7 = 9 => 16 pairs (_) / C8 = 9 => 0 pairs (*) E4,G4: 9.. / E4 = 9 => 20 pairs (_) / G4 = 9 => 0 pairs (X) D6,I6: 9.. / D6 = 9 => 0 pairs (X) / I6 = 9 => 20 pairs (_) C7,D7: 9.. / C7 = 9 => 16 pairs (_) / D7 = 9 => 0 pairs (*) G4,G9: 9.. / G4 = 9 => 0 pairs (X) / G9 = 9 => 20 pairs (_) * DURATION: 0:01:17.052500 START: 17:39:41.291119 END: 17:40:58.343619 2017-05-04 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,C2,C3,C7,C8,D6,D7,E4,F2,F3,G4,G5,G9,I6) * 763.5.8.1.5.7..6...4.6..5.73745.1.681968...53825.3671.43..8517668.1..3.551736..8. * PAIR A2: 2,9 ROW 2 E2: 2,9,1,4 # reduction candidate for 2,9 E2: 2,9 => CTR * 763.5.8.1.517.8634.486135.73745.1.681968..45382543671943..8517668.1473.551736.982 E2: 1,4 # 16 pairs H2: 2,9,3,4 # reduction candidate for 2,9 H2: 2,9 => CTR * 763.5.8.1.587136.4.416.85373745.1.681968..45382543671943..8517668.1473.551736.982 H2: 3,4 # 16 pairs I2: 2,9,4 # reduction candidate for 2,9 I2: 2,9 # 22 pairs * PAIR A3: 2,9 ROW 3 E3: 2,9,1 # reduction candidate for 2,9 E3: 2,9 # 15 pairs H3: 2,9,3 # reduction candidate for 2,9 H3: 2,9 # 12 pairs * PAIR E4: 2,9 COL E E2: 2,9,1,4 # reduction candidate for 2,9 E2: 2,9 => CTR * 763.5.8.1.517.8634.486135.73745.1.681968..45382543671943..8517668.1473.551736.982 E2: 1,4 # 16 pairs E3: 2,9,1 # reduction candidate for 2,9 E3: 2,9 # 15 pairs E8: 2,9,4,7 # reduction candidate for 2,9 E8: 2,9 => CTR * 763459821.5.7..6.4.4.6..5.73745.1.6819687..53825.3671.43..8517668.1.7345517364982 E8: 4,7 # 16 pairs * PAIR D6: 4,9 COL D D1: 4,9,2 # reduction candidate for 4,9 D1: 2 => SOLVED * 763259841951748632248613597374591268196827453825436719432985176689174325517362984 D1: 4,9 # 16 pairs * PAIR G5: 2,4 ROW 5 E5: 2,4,7 # reduction candidate for 2,4 E5: 2,4 # 19 pairs F5: 2,4,7 # reduction candidate for 2,4 F5: 2,4 # 16 pairs * PAIR I6: 4,9 COL I I2: 4,9,2 # reduction candidate for 4,9 I2: 4,9 # 18 pairs I9: 4,9,2 # reduction candidate for 4,9 I9: 4,9 => SOLVED * 763259841951748632248613597374591268196827453825436719432985176689174325517362984 I9: 2 # 18 pairs * PAIR C8: 2,9 ROW 8 E8: 2,9,4,7 # reduction candidate for 2,9 E8: 2,9 => CTR * 763459821.5.7..6.4.4.6..5.73745.1.6819687..53825.3671.43..8517668.1.7345517364982 E8: 4,7 # 16 pairs F8: 2,9,4,7 # reduction candidate for 2,9 F8: 2,9 => CTR * 76345.8.1.5.7..6.4.4.6..5.73745.1.681968.7.53825.3671.43..8517668.17.345517364982 F8: 4,7 # 16 pairs H8: 2,9,4 # reduction candidate for 2,9 H8: 2,9 # 22 pairs * PAIR D7: 2,9 BLK 8 E8: 2,9,4,7 # reduction candidate for 2,9 E8: 2,9 => CTR * 763459821.5.7..6.4.4.6..5.73745.1.6819687..53825.3671.43..8517668.1.7345517364982 E8: 4,7 # 16 pairs F8: 2,9,4,7 # reduction candidate for 2,9 F8: 2,9 => CTR * 76345.8.1.5.7..6.4.4.6..5.73745.1.681968.7.53825.3671.43..8517668.17.345517364982 F8: 4,7 # 16 pairs F9: 2,9,4 # reduction candidate for 2,9 F9: 2,9 # 22 pairs * PAIR D7: 2,9 COL D D1: 2,9,4 # reduction candidate for 2,9 D1: 4 => CTR * 76345.8.1.5.7..64994.6..5373745219681968..25382593671443928517668219.3.551736.482 D1: 2,9 # 20 pairs * PAIR G9: 4,9 BLK 9 H8: 4,9,2 # reduction candidate for 4,9 H8: 4,9 # 18 pairs I9: 4,9,2 # reduction candidate for 4,9 I9: 4,9 => SOLVED * 763259841951748632248613597374591268196827453825436719432985176689174325517362984 I9: 2 # 18 pairs * PAIR G9: 4,9 ROW 9 F9: 4,9,2 # reduction candidate for 4,9 F9: 2 => SOLVED * 763259841951748632248613597374591268196827453825436719432985176689174325517362984 F9: 4,9 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-436-base-pr-000.dot * REASONING * DIS # E2: 2,9 => CTR => E2: 1,4 * DIS # H2: 2,9 => CTR => H2: 3,4 * DIS # E2: 2,9 => CTR => E2: 1,4 * DIS # E8: 2,9 => CTR => E8: 4,7 * PRF # D1: 2 => SOL * PRF # I9: 4,9 => SOL * DIS # E8: 2,9 => CTR => E8: 4,7 * DIS # F8: 2,9 => CTR => F8: 4,7 * DIS # E8: 2,9 => CTR => E8: 4,7 * DIS # F8: 2,9 => CTR => F8: 4,7 * DIS # D1: 4 => CTR => D1: 2,9 * PRF # I9: 4,9 => SOL * PRF # F9: 2 => SOL * CNT 13 HDP CHAINS / 36 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,C2,C3,C7,C8,D6,D7,E4,F2,F3,G4,G5,G9,I6) * 763.5.8.1.5.7..6...4.6..5.73745.1.681968...53825.3671.43..8517668.1..3.551736..8. * PAIR A2: 2,9 ROW 2 E2: 2,9,1,4 # reduction candidate for 2,9 E2: 2,9 => CTR * 763.5.8.1.517.8634.486135.73745.1.681968..45382543671943..8517668.1473.551736.982 H2: 2,9,3,4 # reduction candidate for 2,9 H2: 2,9 => CTR * 763.5.8.1.587136.4.416.85373745.1.681968..45382543671943..8517668.1473.551736.982 * RESTART * PAIR RESTART * PAIR A3: 2,9 ROW 3 E3: 2,9,1 # reduction candidate for 2,9 E3: 2,9 # 19 pairs H3: 2,9,3 # reduction candidate for 2,9 H3: 2,9 => SOLVED * 763259841951748632248613597374591268196827453825436719432985176689174325517362984 * DURATION: 0:00:06.745998 START: 17:41:40.195254 END: 17:41:46.941252 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-436-base-pr-001.dot * REASONING * DIS # E2: 2,9 => CTR => E2: 1,4 * DIS E2: 1,4 # H2: 2,9 => CTR => H2: 3,4 * PRF E2: 1,4 + H2: 3,4 # H3: 2,9 => SOL * STA E2: 1,4 + H2: 3,4 + H3: 2,9 * CNT 3 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 436 solution: 763259841951748632248613597374591268196827453825436719432985176689174325517362984 info: 95230 FNBTHWXK S8.f 1621 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 763259841951748632248613597374591268196827453825436719432985176689174325517362984 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:
* DIS # E2: 2,9 => CTR => E2: 1,4 * INC # E2: 1,4 => UNS * DIS # H2: 2,9 => CTR => H2: 3,4 * INC # H2: 3,4 => UNS * INC # I2: 2,9 => UNS * INC # E3: 2,9 => UNS * INC # H3: 2,9 => UNS * DIS # E2: 2,9 => CTR => E2: 1,4 * INC # E2: 1,4 => UNS * INC # E3: 2,9 => UNS * DIS # E8: 2,9 => CTR => E8: 4,7 * INC # E8: 4,7 => UNS * INC # D1: 4,9 => UNS * PRF # D1: 2 => SOL * INC # E5: 2,4 => UNS * INC # F5: 2,4 => UNS * INC # I2: 4,9 => UNS * PRF # I9: 4,9 => SOL * INC # I9: 2 => UNS * DIS # E8: 2,9 => CTR => E8: 4,7 * INC # E8: 4,7 => UNS * DIS # F8: 2,9 => CTR => F8: 4,7 * INC # F8: 4,7 => UNS * INC # H8: 2,9 => UNS * DIS # E8: 2,9 => CTR => E8: 4,7 * INC # E8: 4,7 => UNS * DIS # F8: 2,9 => CTR => F8: 4,7 * INC # F8: 4,7 => UNS * INC # F9: 2,9 => UNS * INC # D1: 2,9 => UNS * DIS # D1: 4 => CTR => D1: 2,9 * INC # H8: 4,9 => UNS * PRF # I9: 4,9 => SOL * INC # I9: 2 => UNS * INC # F9: 4,9 => UNS * PRF # F9: 2 => SOL * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # E2: 2,9 => CTR => E2: 1,4 * DIS E2: 1,4 # H2: 2,9 => CTR => H2: 3,4 * INC E2: 1,4 + H2: 3,4 # E3: 2,9 => UNS * PRF E2: 1,4 + H2: 3,4 # H3: 2,9 => SOL * STA E2: 1,4 + H2: 3,4 + H3: 2,9 * CNT 4 HDP CHAINS / 4 HYP OPENED