Analysis of xx-top500-045-base.sdk
Contents
Original Sudoku
level: medium
position: 8.....4........6.7...35.....3.2...5.6....7.............1..3..2.7....6...4........ initial
Autosolve
position: 8.....4353....26.7...354....3.2...5.6....7...2....3...51..3..2.7....65..4....5... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 1 => CTR => C1: 2,9 * DIS # B6: 4,5 => CTR => B6: 7,8,9 * DIS # H5: 1,9 => CTR => H5: 4,8 * DIS # C4: 1,9 => CTR => C4: 4,7,8 * DIS # E4: 1,9 => CTR => E4: 4,6,8 * DIS # G4: 1,9 => CTR => G4: 7,8 * PRF # I4: 1,9 => SOL * DIS # D7: 8,9 => CTR => D7: 4,7 * DIS # C7: 8,9 => CTR => C7: 6 * DIS # I7: 8,9 => CTR => I7: 4,6 * DIS # F4: 1 => CTR => F4: 8,9 * CNT 11 HDP CHAINS / 52 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 1 => CTR => C1: 2,9 * PRF C1: 2,9 # B9: 2,9 => SOL * STA C1: 2,9 + B9: 2,9 * CNT 2 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 8.....4........6.7...35.....3.2...5.6....7.............1..3..2.7....6...4........ | initial |
| 8.....4353....26.7...354....3.2...5.6....7...2....3...51..3..2.7....65..4....5... | autosolve |
| 829671435345982617167354289934268751658197342271543968516739824782416593493825176 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) B1: 2,9 B2: 4,5 C2: 4,5 A3: 1,9 B3: 6,7 C3: 6,7 D1: 6,7 E1: 6,7 F1: 1,9 H2: 1,9 A4: 1,9 G5: 2,3 I5: 2,3 H6: 6,7 F7: 8,9 H9: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,A3: 1.. / C1 = 1 => 0 pairs (X) / A3 = 1 => 18 pairs (_) C1,F1: 1.. / C1 = 1 => 0 pairs (X) / F1 = 1 => 18 pairs (_) A3,A4: 1.. / A3 = 1 => 18 pairs (_) / A4 = 1 => 0 pairs (X) F1,F4: 1.. / F1 = 1 => 18 pairs (_) / F4 = 1 => 0 pairs (X) B1,C1: 2.. / B1 = 2 => 19 pairs (_) / C1 = 2 => 19 pairs (_) G3,I3: 2.. / G3 = 2 => 14 pairs (_) / I3 = 2 => 14 pairs (_) G5,I5: 2.. / G5 = 2 => 14 pairs (_) / I5 = 2 => 14 pairs (_) E8,E9: 2.. / E8 = 2 => 17 pairs (_) / E9 = 2 => 14 pairs (_) G3,G5: 2.. / G3 = 2 => 14 pairs (_) / G5 = 2 => 14 pairs (_) I3,I5: 2.. / I3 = 2 => 14 pairs (_) / I5 = 2 => 14 pairs (_) G5,I5: 3.. / G5 = 3 => 14 pairs (_) / I5 = 3 => 14 pairs (_) C8,C9: 3.. / C8 = 3 => 16 pairs (_) / C9 = 3 => 14 pairs (_) C8,I8: 3.. / C8 = 3 => 16 pairs (_) / I8 = 3 => 14 pairs (_) G5,G9: 3.. / G5 = 3 => 14 pairs (_) / G9 = 3 => 14 pairs (_) B2,C2: 4.. / B2 = 4 => 14 pairs (_) / C2 = 4 => 16 pairs (_) D7,I7: 4.. / D7 = 4 => 0 pairs (X) / I7 = 4 => 9 pairs (_) H5,H8: 4.. / H5 = 4 => 16 pairs (_) / H8 = 4 => 0 pairs (X) B2,C2: 5.. / B2 = 5 => 16 pairs (_) / C2 = 5 => 14 pairs (_) D5,D6: 5.. / D5 = 5 => 16 pairs (_) / D6 = 5 => 14 pairs (_) B3,C3: 6.. / B3 = 6 => 9 pairs (_) / C3 = 6 => 0 pairs (X) D1,E1: 6.. / D1 = 6 => 14 pairs (_) / E1 = 6 => 0 pairs (X) E4,I4: 6.. / E4 = 6 => 14 pairs (_) / I4 = 6 => 0 pairs (X) C7,I7: 6.. / C7 = 6 => 9 pairs (_) / I7 = 6 => 0 pairs (X) B3,B9: 6.. / B3 = 6 => 9 pairs (_) / B9 = 6 => 0 pairs (X) D1,D6: 6.. / D1 = 6 => 14 pairs (_) / D6 = 6 => 0 pairs (X) H6,H9: 6.. / H6 = 6 => 9 pairs (_) / H9 = 6 => 0 pairs (X) B3,C3: 7.. / B3 = 7 => 0 pairs (X) / C3 = 7 => 9 pairs (_) D1,E1: 7.. / D1 = 7 => 0 pairs (X) / E1 = 7 => 14 pairs (_) C4,G4: 7.. / C4 = 7 => 0 pairs (X) / G4 = 7 => 9 pairs (_) D7,G7: 7.. / D7 = 7 => 9 pairs (_) / G7 = 7 => 0 pairs (X) B3,B6: 7.. / B3 = 7 => 0 pairs (X) / B6 = 7 => 9 pairs (_) E1,E9: 7.. / E1 = 7 => 14 pairs (_) / E9 = 7 => 0 pairs (X) H6,H9: 7.. / H6 = 7 => 0 pairs (X) / H9 = 7 => 9 pairs (_) D2,E2: 8.. / D2 = 8 => 17 pairs (_) / E2 = 8 => 17 pairs (_) F4,F7: 8.. / F4 = 8 => 18 pairs (_) / F7 = 8 => 19 pairs (_) A3,A4: 9.. / A3 = 9 => 0 pairs (X) / A4 = 9 => 18 pairs (_) * DURATION: 0:01:05.553290 START: 04:11:45.570345 END: 04:12:51.123635 2017-05-04 * CP COUNT: (36) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B1,B2,B3,C2,C3,D1,E1,F1,F7,G5,H2,H6,H9,I5) * 8.....4353....26.7...354....3.2...5.6....7...2....3...51..3..2.7....65..4....5... * PAIR B1: 2,9 BLK 1 C1: 2,9,1 # reduction candidate for 2,9 C1: 1 => CTR * 821..94353....26979..354...13.2.8.5.6....7...2....3...51..3..2.7....65..4....5... C1: 2,9 # 18 pairs * PAIR B1: 2,9 COL B B8: 2,9,8 # reduction candidate for 2,9 B8: 2,9 # 18 pairs B9: 2,9,6,8 # reduction candidate for 2,9 B9: 2,9 # 12 pairs * PAIR B2: 4,5 COL B B5: 4,5,8,9 # reduction candidate for 4,5 B5: 4,5 # 17 pairs B6: 4,5,7,8,9 # reduction candidate for 4,5 B6: 4,5 => CTR * 8.....4353....26.7.76354....3.2...5.6....7...2....3...51..3..267....65..46...5.7. B6: 7,8,9 # 17 pairs * PAIR C2: 4,5 COL C C5: 4,5,1,8,9 # reduction candidate for 4,5 C5: 4,5 # 19 pairs C6: 4,5,1,7,8,9 # reduction candidate for 4,5 C6: 4,5 # 19 pairs * PAIR A3: 1,9 BLK 1 C1: 1,9,2 # reduction candidate for 1,9 C1: 2 # 19 pairs C1: 1,9 # 19 pairs * PAIR A3: 1,9 ROW 3 G3: 1,9,2,8 # reduction candidate for 1,9 G3: 1,9 # 15 pairs H3: 1,9,8 # reduction candidate for 1,9 H3: 1,9 # 21 pairs I3: 1,9,2,8 # reduction candidate for 1,9 I3: 1,9 # 15 pairs * PAIR F1: 1,9 BLK 2 D2: 1,9,8 # reduction candidate for 1,9 D2: 1,9 # 17 pairs E2: 1,9,8 # reduction candidate for 1,9 E2: 1,9 # 17 pairs * PAIR F1: 1,9 ROW 1 C1: 1,9,2 # reduction candidate for 1,9 C1: 2 # 19 pairs C1: 1,9 # 19 pairs * PAIR F1: 1,9 COL F F4: 1,9,8 # reduction candidate for 1,9 F4: 1,9 # 19 pairs F4: 8 # 18 pairs * PAIR H2: 1,9 BLK 3 G3: 1,9,2,8 # reduction candidate for 1,9 G3: 1,9 # 15 pairs H3: 1,9,8 # reduction candidate for 1,9 H3: 1,9 # 21 pairs I3: 1,9,2,8 # reduction candidate for 1,9 I3: 1,9 # 15 pairs * PAIR H2: 1,9 ROW 2 D2: 1,9,8 # reduction candidate for 1,9 D2: 1,9 # 17 pairs E2: 1,9,8 # reduction candidate for 1,9 E2: 1,9 # 17 pairs * PAIR H2: 1,9 COL H H5: 1,9,4,8 # reduction candidate for 1,9 H5: 1,9 => CTR * 8.....4353....26.7.67354.8..3.2...5.6....7...27...3...51.43.72.7....654.4....5.6. H5: 4,8 # 17 pairs H8: 1,9,4,8 # reduction candidate for 1,9 H8: 1,9 # 17 pairs * PAIR A4: 1,9 BLK 4 C4: 1,9,4,7,8 # reduction candidate for 1,9 C4: 1,9 => CTR * 8.....4353....26.7...354....3.2..75.6....7...2....3.6.51.73..247....65..4....5.76 C4: 4,7,8 # 16 pairs C5: 1,9,4,5,8 # reduction candidate for 1,9 C5: 1,9 # 17 pairs C6: 1,9,4,5,7,8 # reduction candidate for 1,9 C6: 1,9 # 17 pairs * PAIR A4: 1,9 ROW 4 E4: 1,9,4,6,8 # reduction candidate for 1,9 E4: 1,9 => CTR * 8.....4353....26.7...354....3.2...566....7...2....3.7.516.3..2.7....65..4....5... E4: 4,6,8 # 16 pairs F4: 1,9,8 # reduction candidate for 1,9 F4: 1,9 # 19 pairs G4: 1,9,7,8 # reduction candidate for 1,9 G4: 1,9 => CTR * 8.....4353....26.7.76354....372...5.6....7...2....3...51..3..267....65..46...5.7. G4: 7,8 # 17 pairs I4: 1,9,4,6,8 # reduction candidate for 1,9 I4: 1,9 => SOLVED * 829671435345982617167354289934268751658197342271543968516739824782416593493825176 I4: 4,6,8 # 16 pairs * PAIR F7: 8,9 BLK 8 D7: 8,9,4,7 # reduction candidate for 8,9 D7: 8,9 => CTR * 8.....4353....26.7.67354....3.2...5.6....7.4.27...3...51..3.7247....65..4....5.6. D7: 4,7 # 17 pairs D8: 8,9,1,4 # reduction candidate for 8,9 D8: 8,9 # 19 pairs E8: 8,9,1,2,4 # reduction candidate for 8,9 E8: 8,9 # 19 pairs D9: 8,9,1,7 # reduction candidate for 8,9 D9: 8,9 # 19 pairs E9: 8,9,1,2,7 # reduction candidate for 8,9 E9: 8,9 # 20 pairs * PAIR F7: 8,9 ROW 7 C7: 8,9,6 # reduction candidate for 8,9 C7: 8,9 => CTR * 8.....4353....26.7...354....3.2...5.6....7...2....3...51..3..267....65..4....5.7. C7: 6 # 9 pairs G7: 8,9,7 # reduction candidate for 8,9 G7: 8,9 # 9 pairs I7: 8,9,4,6 # reduction candidate for 8,9 I7: 8,9 => CTR * 8.....4353....26.7.67354....3.2...5.6....7...27...3...51643.72.7....65..4....5.6. I7: 4,6 # 17 pairs * PAIR F7: 8,9 COL F F4: 8,9,1 # reduction candidate for 8,9 F4: 1 => CTR * 8.1..94353....26979..354....3.2.1.5.6....7...2....3...51..38.2.7....65..4....5... F4: 8,9 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-045-base-pr-000.dot * REASONING * DIS # C1: 1 => CTR => C1: 2,9 * DIS # B6: 4,5 => CTR => B6: 7,8,9 * DIS # H5: 1,9 => CTR => H5: 4,8 * DIS # C4: 1,9 => CTR => C4: 4,7,8 * DIS # E4: 1,9 => CTR => E4: 4,6,8 * DIS # G4: 1,9 => CTR => G4: 7,8 * PRF # I4: 1,9 => SOL * DIS # D7: 8,9 => CTR => D7: 4,7 * DIS # C7: 8,9 => CTR => C7: 6 * DIS # I7: 8,9 => CTR => I7: 4,6 * DIS # F4: 1 => CTR => F4: 8,9 * CNT 11 HDP CHAINS / 52 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B1,B2,B3,C2,C3,D1,E1,F1,F7,G5,H2,H6,H9,I5) * 8.....4353....26.7...354....3.2...5.6....7...2....3...51..3..2.7....65..4....5... * PAIR B1: 2,9 BLK 1 C1: 2,9,1 # reduction candidate for 2,9 C1: 1 => CTR * 821..94353....26979..354...13.2.8.5.6....7...2....3...51..3..2.7....65..4....5... * PAIR B1: 2,9 COL B B8: 2,9,8 # reduction candidate for 2,9 B8: 2,9 # 20 pairs B9: 2,9,6,8 # reduction candidate for 2,9 B9: 2,9 => SOLVED * 829671435345982617167354289934268751658197342271543968516739824782416593493825176 * DURATION: 0:00:05.743893 START: 04:13:41.855480 END: 04:13:47.599373 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-045-base-pr-001.dot * REASONING * DIS # C1: 1 => CTR => C1: 2,9 * PRF C1: 2,9 # B9: 2,9 => SOL * STA C1: 2,9 + B9: 2,9 * CNT 2 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 045 solution: 829671435345982617167354289934268751658197342271543968516739824782416593493825176 info: 1377 FNBHXY S8.f 41710 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 829671435345982617167354289934268751658197342271543968516739824782416593493825176 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 # C1: 2,9 => UNS * DIS # C1: 1 => CTR => C1: 2,9 * INC # B8: 2,9 => UNS * INC # B9: 2,9 => UNS * INC # B5: 4,5 => UNS * DIS # B6: 4,5 => CTR => B6: 7,8,9 * INC # B6: 7,8,9 => UNS * INC # C5: 4,5 => UNS * INC # C6: 4,5 => UNS * INC # C1: 1,9 => UNS * INC # C1: 2 => UNS * INC # G3: 1,9 => UNS * INC # H3: 1,9 => UNS * INC # I3: 1,9 => UNS * INC # D2: 1,9 => UNS * INC # E2: 1,9 => UNS * INC # C1: 1,9 => UNS * INC # C1: 2 => UNS * INC # F4: 1,9 => UNS * INC # F4: 8 => UNS * INC # G3: 1,9 => UNS * INC # H3: 1,9 => UNS * INC # I3: 1,9 => UNS * INC # D2: 1,9 => UNS * INC # E2: 1,9 => UNS * DIS # H5: 1,9 => CTR => H5: 4,8 * INC # H5: 4,8 => UNS * INC # H8: 1,9 => UNS * DIS # C4: 1,9 => CTR => C4: 4,7,8 * INC # C4: 4,7,8 => UNS * INC # C5: 1,9 => UNS * INC # C6: 1,9 => UNS * DIS # E4: 1,9 => CTR => E4: 4,6,8 * INC # E4: 4,6,8 => UNS * INC # F4: 1,9 => UNS * DIS # G4: 1,9 => CTR => G4: 7,8 * INC # G4: 7,8 => UNS * PRF # I4: 1,9 => SOL * INC # I4: 4,6,8 => UNS * DIS # D7: 8,9 => CTR => D7: 4,7 * INC # D7: 4,7 => UNS * INC # D8: 8,9 => UNS * INC # E8: 8,9 => UNS * INC # D9: 8,9 => UNS * INC # E9: 8,9 => UNS * DIS # C7: 8,9 => CTR => C7: 6 * INC # C7: 6 => UNS * INC # G7: 8,9 => UNS * DIS # I7: 8,9 => CTR => I7: 4,6 * INC # I7: 4,6 => UNS * INC # F4: 8,9 => UNS * DIS # F4: 1 => CTR => F4: 8,9 * CNT 52 HDP CHAINS / 52 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 2,9 => UNS * DIS # C1: 1 => CTR => C1: 2,9 * INC C1: 2,9 # B8: 2,9 => UNS * PRF C1: 2,9 # B9: 2,9 => SOL * STA C1: 2,9 + B9: 2,9 * CNT 4 HDP CHAINS / 4 HYP OPENED