Analysis of xx-top500-471-base.sdk
Contents
Original Sudoku
level: medium
position: ....41...2.....5...........5..7..3.....2...6.........1.61....4..4..8.......53.... initial
Autosolve
position: .5..41...2.....5...........5..7..3.....2...6....4...513619..845.45186......534... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G3: 6,7,9 => CTR => G3: 1,4 * DIS # F5: 8,9 => CTR => F5: 3,5 * DIS # F6: 8,9 => CTR => F6: 3 * DIS # B4: 8,9 => CTR => B4: 1,2 * DIS # I4: 8,9 => CTR => I4: 2,4 * DIS # E4: 1 => CTR => E4: 6,9 * DIS # C6: 6,9 => CTR => C6: 2,3,7,8 * DIS # A6: 7,9 => CTR => A6: 6,8 * CNT 8 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:
* DIS # G3: 6,7,9 => CTR => G3: 1,4 * DIS G3: 1,4 # F5: 8,9 => CTR => F5: 3,5 * DIS G3: 1,4 + F5: 3,5 # F6: 8,9 => CTR => F6: 3 * DIS G3: 1,4 + F5: 3,5 + F6: 3 # E4: 1 => CTR => E4: 6,9 * DIS G3: 1,4 + F5: 3,5 + F6: 3 + E4: 6,9 # C9: 7,9 => CTR => C9: 2 * PRF G3: 1,4 + F5: 3,5 + F6: 3 + E4: 6,9 + C9: 2 # B3: 3 => SOL * STA G3: 1,4 + F5: 3,5 + F6: 3 + E4: 6,9 + C9: 2 + B3: 3 * CNT 6 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....41...2.....5...........5..7..3.....2...6.........1.61....4..4..8.......53.... | initial |
| .5..41...2.....5...........5..7..3.....2...6....4...513619..845.45186......534... | autosolve |
| 957341682284679513136852497519768324473215968628493751361927845745186239892534176 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) A3: 1,4 E2: 7,9 F2: 7,9 E3: 2,5 F3: 2,5 A5: 1,4 F4: 8,9 E6: 6,9 A8: 7,9 E7: 2,7 F7: 2,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E4,E5: 1.. / E4 = 1 => 0 pairs (X) / E5 = 1 => 12 pairs (_) G9,H9: 1.. / G9 = 1 => 12 pairs (_) / H9 = 1 => 0 pairs (X) B2,H2: 1.. / B2 = 1 => 0 pairs (X) / H2 = 1 => 13 pairs (_) B4,E4: 1.. / B4 = 1 => 12 pairs (_) / E4 = 1 => 0 pairs (X) A3,A5: 1.. / A3 = 1 => 12 pairs (_) / A5 = 1 => 0 pairs (X) G3,G9: 1.. / G3 = 1 => 0 pairs (X) / G9 = 1 => 12 pairs (_) E3,F3: 2.. / E3 = 2 => 0 pairs (X) / F3 = 2 => 7 pairs (_) B9,C9: 2.. / B9 = 2 => 11 pairs (_) / C9 = 2 => 11 pairs (_) E7,F7: 2.. / E7 = 2 => 7 pairs (_) / F7 = 2 => 0 pairs (X) E3,E7: 2.. / E3 = 2 => 0 pairs (X) / E7 = 2 => 7 pairs (_) F3,F7: 2.. / F3 = 2 => 7 pairs (_) / F7 = 2 => 0 pairs (X) F5,F6: 3.. / F5 = 3 => 0 pairs (X) / F6 = 3 => 11 pairs (_) H8,I8: 3.. / H8 = 3 => 12 pairs (_) / I8 = 3 => 11 pairs (_) C2,I2: 4.. / C2 = 4 => 12 pairs (_) / I2 = 4 => 0 pairs (X) C4,I4: 4.. / C4 = 4 => 0 pairs (X) / I4 = 4 => 12 pairs (_) A3,A5: 4.. / A3 = 4 => 0 pairs (X) / A5 = 4 => 12 pairs (_) G3,G5: 4.. / G3 = 4 => 12 pairs (_) / G5 = 4 => 0 pairs (X) E3,F3: 5.. / E3 = 5 => 7 pairs (_) / F3 = 5 => 0 pairs (X) E5,F5: 5.. / E5 = 5 => 0 pairs (X) / F5 = 5 => 7 pairs (_) E3,E5: 5.. / E3 = 5 => 7 pairs (_) / E5 = 5 => 0 pairs (X) F3,F5: 5.. / F3 = 5 => 0 pairs (X) / F5 = 5 => 7 pairs (_) E4,E6: 6.. / E4 = 6 => 12 pairs (_) / E6 = 6 => 0 pairs (X) G9,I9: 6.. / G9 = 6 => 0 pairs (X) / I9 = 6 => 11 pairs (_) C4,E4: 6.. / C4 = 6 => 0 pairs (X) / E4 = 6 => 12 pairs (_) A1,A6: 6.. / A1 = 6 => 0 pairs (X) / A6 = 6 => 12 pairs (_) E2,F2: 7.. / E2 = 7 => 7 pairs (_) / F2 = 7 => 0 pairs (X) E7,F7: 7.. / E7 = 7 => 0 pairs (X) / F7 = 7 => 7 pairs (_) E2,E7: 7.. / E2 = 7 => 7 pairs (_) / E7 = 7 => 0 pairs (X) F2,F7: 7.. / F2 = 7 => 0 pairs (X) / F7 = 7 => 7 pairs (_) E2,F2: 9.. / E2 = 9 => 0 pairs (X) / F2 = 9 => 7 pairs (_) * DURATION: 0:00:54.552485 START: 18:46:41.327121 END: 18:47:35.879606 2017-05-04 * CP COUNT: (30) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,A8,E2,E3,E6,E7,F2,F3,F4,F7) * .5..41...2.....5...........5..7..3.....2...6....4...513619..845.45186......534... * PAIR A3: 1,4 ROW 3 G3: 1,4,6,7,9 # reduction candidate for 1,4 G3: 6,7,9 => CTR * .5..41...2.....5..4........5.476.3..1..2..46....49..513619..845.45186......5341.6 G3: 1,4 # 12 pairs * PAIR F4: 8,9 BLK 5 F5: 8,9,3,5 # reduction candidate for 8,9 F5: 8,9 => CTR * 65..41...2.4.975..1...254..5.671.3.441325..6....463.51361972845.45186......534... F5: 3,5 # 12 pairs F6: 8,9,3 # reduction candidate for 8,9 F6: 8,9 => CTR * 65..41...2.4.975..1...254..5.671.3.441.253.6....46..51361972845.45186......534... F6: 3 # 11 pairs * PAIR F4: 8,9 ROW 4 B4: 8,9,1,2 # reduction candidate for 8,9 B4: 8,9 => CTR * 65..41...2.4...5..1.....4..5.671.32441.2...68...46..513619..845.45186......534... B4: 1,2 # 12 pairs C4: 8,9,2,4,6 # reduction candidate for 8,9 C4: 8,9 # 11 pairs H4: 8,9,2 # reduction candidate for 8,9 H4: 8,9 # 15 pairs I4: 8,9,2,4 # reduction candidate for 8,9 I4: 8,9 => CTR * .5..41...2.....5...........5.476.3..1..2...6....49..513619..845.45186......534... I4: 2,4 # 12 pairs * PAIR E6: 6,9 BLK 5 E4: 6,9,1 # reduction candidate for 6,9 E4: 1 => CTR * 65..41...2.4...5..1.....4..5.671.3.441.2...6....46..513619..845.45186......534... E4: 6,9 # 12 pairs * PAIR E6: 6,9 ROW 6 A6: 6,9,7,8 # reduction candidate for 6,9 A6: 6,9 # 14 pairs C6: 6,9,2,3,7,8 # reduction candidate for 6,9 C6: 6,9 => CTR * 65..41...2.....5..4........5.476.3..1..2..46...649..513619..845.45186.....2534... C6: 2,3,7,8 # 11 pairs * PAIR A8: 7,9 BLK 7 A9: 7,9,8 # reduction candidate for 7,9 A9: 7,9 # 16 pairs B9: 7,9,2,8 # reduction candidate for 7,9 B9: 7,9 # 12 pairs C9: 7,9,2,8 # reduction candidate for 7,9 C9: 7,9 # 12 pairs * PAIR A8: 7,9 ROW 8 G8: 7,9,2 # reduction candidate for 7,9 G8: 7,9 # 14 pairs H8: 7,9,2,3 # reduction candidate for 7,9 H8: 7,9 # 13 pairs I8: 7,9,2,3 # reduction candidate for 7,9 I8: 7,9 # 14 pairs * PAIR A8: 7,9 COL A A1: 7,9,6,8 # reduction candidate for 7,9 A1: 7,9 # 12 pairs A6: 7,9,6,8 # reduction candidate for 7,9 A6: 7,9 => CTR * 65..41...2.....5..4........5.476.3..1..2..46...649..513619..845945186...8.2534... A6: 6,8 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-471-base-pr-000.dot * REASONING * DIS # G3: 6,7,9 => CTR => G3: 1,4 * DIS # F5: 8,9 => CTR => F5: 3,5 * DIS # F6: 8,9 => CTR => F6: 3 * DIS # B4: 8,9 => CTR => B4: 1,2 * DIS # I4: 8,9 => CTR => I4: 2,4 * DIS # E4: 1 => CTR => E4: 6,9 * DIS # C6: 6,9 => CTR => C6: 2,3,7,8 * DIS # A6: 7,9 => CTR => A6: 6,8 * CNT 8 HDP CHAINS / 26 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,A8,E2,E3,E6,E7,F2,F3,F4,F7) * .5..41...2.....5...........5..7..3.....2...6....4...513619..845.45186......534... * PAIR A3: 1,4 ROW 3 G3: 1,4,6,7,9 # reduction candidate for 1,4 G3: 6,7,9 => CTR * .5..41...2.....5..4........5.476.3..1..2..46....49..513619..845.45186......5341.6 * PAIR RESTART * PAIR F4: 8,9 BLK 5 F5: 8,9,3,5 # reduction candidate for 8,9 F5: 8,9 => CTR * 65..41...2...975......25...5.671.3.4...25..6....463.51361972845.45186......53461. F6: 8,9,3 # reduction candidate for 8,9 F6: 8,9 => CTR * 65..41...2...975......25...5.671.3.4...253.6....46..51361972845.45186......53461. * PAIR E6: 6,9 BLK 5 E4: 6,9,1 # reduction candidate for 6,9 E4: 1 => CTR * 65..41...2.4.795..1...524..5.67183.4...295768...463.51361927845.45186......534... * PAIR A8: 7,9 BLK 7 B9: 7,9,2 # reduction candidate for 7,9 B9: 7,9 # 11 pairs C9: 7,9,2 # reduction candidate for 7,9 C9: 7,9 => CTR * 957.416..2846795131.6.524..5127683944..215768678493251361927845.45186932829534176 * RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A1,A8,B5,B9,C1,C5,D1,D3,H9,I3,I8) * .5..416.22846795131.6.524..5197683244..215968628493751361927845.4518623.8.25341.6 * PAIR A1: 7,9 BLK 1 B3: 7,9,3 # reduction candidate for 7,9 B3: 3 => SOLVED * 957341682284679513136852497519768324473215968628493751361927845745186239892534176 * DURATION: 0:00:15.393901 START: 18:48:00.262519 END: 18:48:15.656420 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-471-base-pr-001.dot * REASONING * DIS # G3: 6,7,9 => CTR => G3: 1,4 * DIS G3: 1,4 # F5: 8,9 => CTR => F5: 3,5 * DIS G3: 1,4 + F5: 3,5 # F6: 8,9 => CTR => F6: 3 * DIS G3: 1,4 + F5: 3,5 + F6: 3 # E4: 1 => CTR => E4: 6,9 * DIS G3: 1,4 + F5: 3,5 + F6: 3 + E4: 6,9 # C9: 7,9 => CTR => C9: 2 * PRF G3: 1,4 + F5: 3,5 + F6: 3 + E4: 6,9 + C9: 2 # B3: 3 => SOL * STA G3: 1,4 + F5: 3,5 + F6: 3 + E4: 6,9 + C9: 2 + B3: 3 * CNT 6 HDP CHAINS / 10 HYP OPENED
Header Info
Top 500 Minimum 17 471 solution: 957341682284679513136852497519768324473215968628493751361927845745186239892534176 info: 95641 FNBTHWXYK S8.f 40794 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 957341682284679513136852497519768324473215968628493751361927845745186239892534176 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 # G3: 1,4 => UNS * DIS # G3: 6,7,9 => CTR => G3: 1,4 * DIS # F5: 8,9 => CTR => F5: 3,5 * INC # F5: 3,5 => UNS * DIS # F6: 8,9 => CTR => F6: 3 * INC # F6: 3 => UNS * DIS # B4: 8,9 => CTR => B4: 1,2 * INC # B4: 1,2 => UNS * INC # C4: 8,9 => UNS * INC # H4: 8,9 => UNS * DIS # I4: 8,9 => CTR => I4: 2,4 * INC # I4: 2,4 => UNS * INC # E4: 6,9 => UNS * DIS # E4: 1 => CTR => E4: 6,9 * INC # A6: 6,9 => UNS * DIS # C6: 6,9 => CTR => C6: 2,3,7,8 * INC # C6: 2,3,7,8 => UNS * INC # A9: 7,9 => UNS * INC # B9: 7,9 => UNS * INC # C9: 7,9 => UNS * INC # G8: 7,9 => UNS * INC # H8: 7,9 => UNS * INC # I8: 7,9 => UNS * INC # A1: 7,9 => UNS * DIS # A6: 7,9 => CTR => A6: 6,8 * INC # A6: 6,8 => UNS * CNT 26 HDP CHAINS / 26 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G3: 1,4 => UNS * DIS # G3: 6,7,9 => CTR => G3: 1,4 * DIS G3: 1,4 # F5: 8,9 => CTR => F5: 3,5 * DIS G3: 1,4 + F5: 3,5 # F6: 8,9 => CTR => F6: 3 * INC G3: 1,4 + F5: 3,5 + F6: 3 # E4: 6,9 => UNS * DIS G3: 1,4 + F5: 3,5 + F6: 3 # E4: 1 => CTR => E4: 6,9 * INC G3: 1,4 + F5: 3,5 + F6: 3 + E4: 6,9 # B9: 7,9 => UNS * DIS G3: 1,4 + F5: 3,5 + F6: 3 + E4: 6,9 # C9: 7,9 => CTR => C9: 2 * INC G3: 1,4 + F5: 3,5 + F6: 3 + E4: 6,9 + C9: 2 # B3: 7,9 => UNS * PRF G3: 1,4 + F5: 3,5 + F6: 3 + E4: 6,9 + C9: 2 # B3: 3 => SOL * STA G3: 1,4 + F5: 3,5 + F6: 3 + E4: 6,9 + C9: 2 + B3: 3 * CNT 10 HDP CHAINS / 10 HYP OPENED