Analysis of xx-top500-306-base.sdk
Contents
Original Sudoku
level: medium
position: .16....4.3..2..5............4.....182..3......6...........18...7.....2......4.... initial
Autosolve
position: .168...423..2..5............4..2..182..3......6.....2.....18...7.....2......42... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C3: 4,8 => CTR => C3: 2,5,7,9 * DIS # F3: 1,4 => CTR => F3: 3,5,6,7,9 * DIS # C6: 1,8 => CTR => C6: 3,5,7,9 * DIS # A9: 6 => CTR => A9: 1,8 * DIS # F6: 1,4 => CTR => F6: 5,7,9 * DIS # C9: 1,8 => CTR => C9: 5,9 * CNT 6 HDP CHAINS / 29 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C3: 4,8 => CTR => C3: 2,5,7,9 * DIS C3: 2,5,7,9 # F3: 1,4 => CTR => F3: 3,5,6,7,9 * DIS C3: 2,5,7,9 + F3: 3,5,6,7,9 # C6: 1,8 => CTR => C6: 3,5,7,9 * DIS C3: 2,5,7,9 + F3: 3,5,6,7,9 + C6: 3,5,7,9 # A9: 6 => CTR => A9: 1,8 * PRF C3: 2,5,7,9 + F3: 3,5,6,7,9 + C6: 3,5,7,9 + A9: 1,8 # B3: 7 => SOL * STA C3: 2,5,7,9 + F3: 3,5,6,7,9 + C6: 3,5,7,9 + A9: 1,8 + B3: 7 * CNT 5 HDP CHAINS / 24 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .16....4.3..2..5............4.....182..3......6...........18...7.....2......4.... | initial |
| .168...423..2..5............4..2..182..3......6.....2.....18...7.....2......42... | autosolve |
| 516893742389274561472156839943527618258361497167489325624718953791635284835942176 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) A1: 5,9 A3: 4,8 D3: 1,4 G3: 1,8 A4: 5,9 A6: 1,8 D6: 1,4 A7: 4,6 C8: 1,4 I8: 1,4 G9: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F2,I2: 1.. / F2 = 1 => 0 pairs (X) / I2 = 1 => 7 pairs (_) C5,F5: 1.. / C5 = 1 => 0 pairs (X) / F5 = 1 => 7 pairs (_) C8,I8: 1.. / C8 = 1 => 7 pairs (_) / I8 = 1 => 0 pairs (X) A6,A9: 1.. / A6 = 1 => 7 pairs (_) / A9 = 1 => 0 pairs (X) D3,D6: 1.. / D3 = 1 => 7 pairs (_) / D6 = 1 => 0 pairs (X) G3,G9: 1.. / G3 = 1 => 0 pairs (X) / G9 = 1 => 7 pairs (_) B3,C3: 2.. / B3 = 2 => 11 pairs (_) / C3 = 2 => 11 pairs (_) B7,C7: 2.. / B7 = 2 => 11 pairs (_) / C7 = 2 => 11 pairs (_) B3,B7: 2.. / B3 = 2 => 11 pairs (_) / B7 = 2 => 11 pairs (_) C3,C7: 2.. / C3 = 2 => 11 pairs (_) / C7 = 2 => 11 pairs (_) C4,C6: 3.. / C4 = 3 => 11 pairs (_) / C6 = 3 => 12 pairs (_) B7,B9: 3.. / B7 = 3 => 11 pairs (_) / B9 = 3 => 11 pairs (_) E8,F8: 3.. / E8 = 3 => 11 pairs (_) / F8 = 3 => 11 pairs (_) C4,G4: 3.. / C4 = 3 => 11 pairs (_) / G4 = 3 => 12 pairs (_) C2,F2: 4.. / C2 = 4 => 0 pairs (X) / F2 = 4 => 7 pairs (_) C8,I8: 4.. / C8 = 4 => 0 pairs (X) / I8 = 4 => 7 pairs (_) A3,A7: 4.. / A3 = 4 => 7 pairs (_) / A7 = 4 => 0 pairs (X) D3,D6: 4.. / D3 = 4 => 0 pairs (X) / D6 = 4 => 7 pairs (_) A1,A4: 5.. / A1 = 5 => 10 pairs (_) / A4 = 5 => 15 pairs (_) A7,A9: 6.. / A7 = 6 => 7 pairs (_) / A9 = 6 => 0 pairs (X) D7,D9: 7.. / D7 = 7 => 11 pairs (_) / D9 = 7 => 11 pairs (_) E5,E6: 8.. / E5 = 8 => 11 pairs (_) / E6 = 8 => 7 pairs (_) B8,H8: 8.. / B8 = 8 => 13 pairs (_) / H8 = 8 => 7 pairs (_) G3,G9: 8.. / G3 = 8 => 7 pairs (_) / G9 = 8 => 0 pairs (X) A1,A4: 9.. / A1 = 9 => 15 pairs (_) / A4 = 9 => 10 pairs (_) * DURATION: 0:00:40.825205 START: 13:26:28.439861 END: 13:27:09.265066 2017-05-04 * CP COUNT: (25) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,A4,A6,A7,C8,D3,D6,G3,G9,I8) * .168...423..2..5............4..2..182..3......6.....2.....18...7.....2......42... * PAIR A1: 5,9 BLK 1 B3: 5,9,2,7,8 # reduction candidate for 5,9 B3: 5,9 # 14 pairs C3: 5,9,2,4,7,8 # reduction candidate for 5,9 C3: 5,9 # 14 pairs * PAIR A1: 5,9 ROW 1 E1: 5,9,3,7 # reduction candidate for 5,9 E1: 5,9 # 14 pairs F1: 5,9,3,7 # reduction candidate for 5,9 F1: 5,9 # 14 pairs * PAIR A3: 4,8 BLK 1 C2: 4,8,7,9 # reduction candidate for 4,8 C2: 4,8 # 13 pairs C3: 4,8,2,5,7,9 # reduction candidate for 4,8 C3: 4,8 => CTR * 5168...423..26.581.2.......94..2..182..3......6.....2...2.18...7.....2......42... C3: 2,5,7,9 # 11 pairs * PAIR D3: 1,4 BLK 2 F2: 1,4,6,7,9 # reduction candidate for 1,4 F2: 1,4 # 12 pairs F3: 1,4,3,5,6,7,9 # reduction candidate for 1,4 F3: 1,4 => CTR * .168...423..2..5............4..2..182..3......6.....2.....18...7.....2......42... F3: 3,5,6,7,9 # 12 pairs * PAIR A4: 5,9 BLK 4 C4: 5,9,3,7 # reduction candidate for 5,9 C4: 5,9 # 17 pairs B5: 5,9,7,8 # reduction candidate for 5,9 B5: 5,9 # 13 pairs C5: 5,9,1,7,8 # reduction candidate for 5,9 C5: 5,9 # 10 pairs C6: 5,9,1,3,7,8 # reduction candidate for 5,9 C6: 5,9 # 13 pairs * PAIR A4: 5,9 ROW 4 D4: 5,9,6 # reduction candidate for 5,9 D4: 5,9 # 14 pairs F4: 5,9,6,7 # reduction candidate for 5,9 F4: 5,9 # 17 pairs * PAIR A6: 1,8 BLK 4 C5: 1,8,5,7,9 # reduction candidate for 1,8 C5: 1,8 # 12 pairs C6: 1,8,3,5,7,9 # reduction candidate for 1,8 C6: 1,8 => CTR * .168...4238.2.45.14.21..8...43.2.6182..3814..1684...2.624.18...7.1...28483..421.. C6: 3,5,7,9 # 11 pairs * PAIR A6: 1,8 COL A A9: 1,8,6 # reduction candidate for 1,8 A9: 6 => CTR * .168...423..2..5..8..1......4..2..182..3.....16.4...2.....18...7.....2..6...42... A9: 1,8 # 7 pairs * PAIR D6: 1,4 BLK 5 F5: 1,4,5,6,7,9 # reduction candidate for 1,4 F5: 1,4 # 12 pairs F6: 1,4,5,7,9 # reduction candidate for 1,4 F6: 1,4 => CTR * .168...423..2..5............4..2..182.13.....86.....2.....18...7.4...2.11...428.. F6: 5,7,9 # 12 pairs * PAIR A7: 4,6 ROW 7 G7: 4,6,3,7,9 # reduction candidate for 4,6 G7: 4,6 # 12 pairs I7: 4,6,3,5,7,9 # reduction candidate for 4,6 I7: 4,6 # 12 pairs * PAIR G9: 1,8 ROW 9 A9: 1,8,6 # reduction candidate for 1,8 A9: 1,8 # 7 pairs C9: 1,8,5,9 # reduction candidate for 1,8 C9: 1,8 => CTR * .168...423..2..5..8..1......4..2..182..3.....16.4...2.....18...7.....2..6...42... C9: 5,9 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-306-base-pr-000.dot * REASONING * DIS # C3: 4,8 => CTR => C3: 2,5,7,9 * DIS # F3: 1,4 => CTR => F3: 3,5,6,7,9 * DIS # C6: 1,8 => CTR => C6: 3,5,7,9 * DIS # A9: 6 => CTR => A9: 1,8 * DIS # F6: 1,4 => CTR => F6: 5,7,9 * DIS # C9: 1,8 => CTR => C9: 5,9 * CNT 6 HDP CHAINS / 29 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,A4,A6,A7,C8,D3,D6,G3,G9,I8) * .168...423..2..5............4..2..182..3......6.....2.....18...7.....2......42... * PAIR A1: 5,9 BLK 1 B3: 5,9,2,7,8 # reduction candidate for 5,9 B3: 5,9 # 14 pairs C3: 5,9,2,4,7,8 # reduction candidate for 5,9 C3: 5,9 # 14 pairs * PAIR A1: 5,9 ROW 1 E1: 5,9,3,7 # reduction candidate for 5,9 E1: 5,9 # 14 pairs F1: 5,9,3,7 # reduction candidate for 5,9 F1: 5,9 # 14 pairs * PAIR A3: 4,8 BLK 1 C2: 4,8,7,9 # reduction candidate for 4,8 C2: 4,8 # 13 pairs C3: 4,8,2,5,7,9 # reduction candidate for 4,8 C3: 4,8 => CTR * 5168...423..26.581.2.......94..2..182..3......6.....2...2.18...7.....2......42... * RESTART * PAIR A3: 4,8 BLK 1 C2: 4,8,7,9 # reduction candidate for 4,8 C2: 4,8 # 13 pairs C2: 7,9 # 8 pairs * PAIR D3: 1,4 BLK 2 F2: 1,4,6,7,9 # reduction candidate for 1,4 F2: 1,4 # 12 pairs F3: 1,4,3,5,6,7,9 # reduction candidate for 1,4 F3: 1,4 => CTR * .168...423..2..5............4..2..182..3......6.....2.....18...7.....2......42... * RESTART * PAIR A4: 5,9 BLK 4 C4: 5,9,3,7 # reduction candidate for 5,9 C4: 5,9 # 18 pairs B5: 5,9,7,8 # reduction candidate for 5,9 B5: 5,9 # 14 pairs C5: 5,9,1,7,8 # reduction candidate for 5,9 C5: 5,9 # 10 pairs C6: 5,9,1,3,7,8 # reduction candidate for 5,9 C6: 5,9 # 14 pairs * PAIR A4: 5,9 ROW 4 D4: 5,9,6 # reduction candidate for 5,9 D4: 5,9 # 15 pairs F4: 5,9,6,7 # reduction candidate for 5,9 F4: 5,9 # 18 pairs * PAIR A6: 1,8 BLK 4 C5: 1,8,5,7,9 # reduction candidate for 1,8 C5: 1,8 # 13 pairs C6: 1,8,3,5,7,9 # reduction candidate for 1,8 C6: 1,8 => CTR * .168...4238.2.45.14.21..8...43.2.6182..3814..1684...2.624.18...7.1...28483..421.. * RESTART * PAIR A6: 1,8 BLK 4 C5: 1,8,5,7,9 # reduction candidate for 1,8 C5: 1,8 # 13 pairs C5: 5,7,9 # 8 pairs * PAIR A6: 1,8 COL A A9: 1,8,6 # reduction candidate for 1,8 A9: 6 => CTR * .168...423..2..5............4..2..182..3.....16.48..2.....18...7.....2..6...42... * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A1,A4,B8,C9,D4,E2,F6) * .168...423..2.45614.21.68...43.276182..3614..16.48..2.624.18...7.16..28483..421.6 * PAIR A1: 5,9 BLK 1 B3: 5,9,7 # reduction candidate for 5,9 B3: 7 => SOLVED * 516893742389274561472156839943527618258361497167489325624718953791635284835942176 * DURATION: 0:00:25.024291 START: 13:27:34.682544 END: 13:27:59.706835 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-306-base-pr-001.dot * REASONING * DIS # C3: 4,8 => CTR => C3: 2,5,7,9 * DIS C3: 2,5,7,9 # F3: 1,4 => CTR => F3: 3,5,6,7,9 * DIS C3: 2,5,7,9 + F3: 3,5,6,7,9 # C6: 1,8 => CTR => C6: 3,5,7,9 * DIS C3: 2,5,7,9 + F3: 3,5,6,7,9 + C6: 3,5,7,9 # A9: 6 => CTR => A9: 1,8 * PRF C3: 2,5,7,9 + F3: 3,5,6,7,9 + C6: 3,5,7,9 + A9: 1,8 # B3: 7 => SOL * STA C3: 2,5,7,9 + F3: 3,5,6,7,9 + C6: 3,5,7,9 + A9: 1,8 + B3: 7 * CNT 5 HDP CHAINS / 24 HYP OPENED
Header Info
Top 500 Minimum 17 306 solution: 516893742389274561472156839943527618258361497167489325624718953791635284835942176 info: 2623 FNBTHWXY S8.f 15995 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 516893742389274561472156839943527618258361497167489325624718953791635284835942176 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 # B3: 5,9 => UNS * INC # C3: 5,9 => UNS * INC # E1: 5,9 => UNS * INC # F1: 5,9 => UNS * INC # C2: 4,8 => UNS * DIS # C3: 4,8 => CTR => C3: 2,5,7,9 * INC # C3: 2,5,7,9 => UNS * INC # F2: 1,4 => UNS * DIS # F3: 1,4 => CTR => F3: 3,5,6,7,9 * INC # F3: 3,5,6,7,9 => UNS * INC # C4: 5,9 => UNS * INC # B5: 5,9 => UNS * INC # C5: 5,9 => UNS * INC # C6: 5,9 => UNS * INC # D4: 5,9 => UNS * INC # F4: 5,9 => UNS * INC # C5: 1,8 => UNS * DIS # C6: 1,8 => CTR => C6: 3,5,7,9 * INC # C6: 3,5,7,9 => UNS * INC # A9: 1,8 => UNS * DIS # A9: 6 => CTR => A9: 1,8 * INC # F5: 1,4 => UNS * DIS # F6: 1,4 => CTR => F6: 5,7,9 * INC # F6: 5,7,9 => UNS * INC # G7: 4,6 => UNS * INC # I7: 4,6 => UNS * INC # A9: 1,8 => UNS * DIS # C9: 1,8 => CTR => C9: 5,9 * INC # C9: 5,9 => UNS * CNT 29 HDP CHAINS / 29 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B3: 5,9 => UNS * INC # C3: 5,9 => UNS * INC # E1: 5,9 => UNS * INC # F1: 5,9 => UNS * INC # C2: 4,8 => UNS * DIS # C3: 4,8 => CTR => C3: 2,5,7,9 * INC C3: 2,5,7,9 # C2: 4,8 => UNS * INC C3: 2,5,7,9 # C2: 7,9 => UNS * INC C3: 2,5,7,9 # F2: 1,4 => UNS * DIS C3: 2,5,7,9 # F3: 1,4 => CTR => F3: 3,5,6,7,9 * INC C3: 2,5,7,9 + F3: 3,5,6,7,9 # C4: 5,9 => UNS * INC C3: 2,5,7,9 + F3: 3,5,6,7,9 # B5: 5,9 => UNS * INC C3: 2,5,7,9 + F3: 3,5,6,7,9 # C5: 5,9 => UNS * INC C3: 2,5,7,9 + F3: 3,5,6,7,9 # C6: 5,9 => UNS * INC C3: 2,5,7,9 + F3: 3,5,6,7,9 # D4: 5,9 => UNS * INC C3: 2,5,7,9 + F3: 3,5,6,7,9 # F4: 5,9 => UNS * INC C3: 2,5,7,9 + F3: 3,5,6,7,9 # C5: 1,8 => UNS * DIS C3: 2,5,7,9 + F3: 3,5,6,7,9 # C6: 1,8 => CTR => C6: 3,5,7,9 * INC C3: 2,5,7,9 + F3: 3,5,6,7,9 + C6: 3,5,7,9 # C5: 1,8 => UNS * INC C3: 2,5,7,9 + F3: 3,5,6,7,9 + C6: 3,5,7,9 # C5: 5,7,9 => UNS * INC C3: 2,5,7,9 + F3: 3,5,6,7,9 + C6: 3,5,7,9 # A9: 1,8 => UNS * DIS C3: 2,5,7,9 + F3: 3,5,6,7,9 + C6: 3,5,7,9 # A9: 6 => CTR => A9: 1,8 * INC C3: 2,5,7,9 + F3: 3,5,6,7,9 + C6: 3,5,7,9 + A9: 1,8 # B3: 5,9 => UNS * PRF C3: 2,5,7,9 + F3: 3,5,6,7,9 + C6: 3,5,7,9 + A9: 1,8 # B3: 7 => SOL * STA C3: 2,5,7,9 + F3: 3,5,6,7,9 + C6: 3,5,7,9 + A9: 1,8 + B3: 7 * CNT 24 HDP CHAINS / 24 HYP OPENED