Analysis of xx-top500-256-base.sdk
Contents
Original Sudoku
level: medium
position: ....5.2.861............9.....74...1.3...2.......6...4.2.....5.....1.7............ initial
Autosolve
position: 79435126861..74.......69174.6749..1234172....9..61.74.27.9465.14591.7.2.1.65.2497 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 2,8 => CTR => B3: 3 * PRF # B3: 3 => SOL * DIS # C3: 2,8 => CTR => C3: 3,5 * PRF # C6: 2,8 => SOL * DIS # C6: 5 => CTR => C6: 2,8 * PRF # C3: 5,8 => SOL * DIS # C3: 2,3 => CTR => C3: 5,8 * DIS # B3: 2,8 => CTR => B3: 3 * PRF # B3: 3 => SOL * DIS # C3: 2,8 => CTR => C3: 3,5 * DIS # I2: 3,9 => CTR => I2: 5 * PRF # I2: 5 => SOL * DIS # I2: 9 => CTR => I2: 3,5 * DIS # C6: 2 => CTR => C6: 5,8 * DIS # F4: 5,8 => CTR => F4: 3 * PRF # F4: 3 => SOL * PRF # C6: 2,8 => SOL * DIS # C6: 5 => CTR => C6: 2,8 * DIS # B3: 2,8 => CTR => B3: 3 * PRF # B3: 3 => SOL * DIS # F4: 5,8 => CTR => F4: 3 * PRF # F4: 3 => SOL * PRF # F6: 5,8 => SOL * DIS # F6: 3 => CTR => F6: 5,8 * PRF # F4: 3,8 => SOL * DIS # F4: 5 => CTR => F4: 3,8 * DIS # G8: 6 => CTR => G8: 3,8 * PRF # F6: 3,5 => SOL * DIS # F6: 8 => CTR => F6: 3,5 * DIS # I2: 9 => CTR => I2: 3,5 * DIS # C3: 3,8 => CTR => C3: 2,5 * PRF # C3: 2,5 => SOL * DIS # B3: 2 => CTR => B3: 3,8 * DIS # G8: 6 => CTR => G8: 3,8 * DIS # G8: 6 => CTR => G8: 3,8 * PRF # G8: 3,6 => SOL * DIS # G8: 8 => CTR => G8: 3,6 * CNT 37 HDP CHAINS / 46 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B3: 2,8 => CTR => B3: 3 * PRF B3: 3 => SOL * STA B3: 3 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....5.2.861............9.....74...1.3...2.......6...4.2.....5.....1.7............ | initial |
| 79435126861..74.......69174.6749..1234172....9..61.74.27.9465.14591.7.2.1.65.2497 | autosolve |
| 794351268612874935835269174567493812341728659928615743273946581459187326186532497 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) C2: 2,8 A3: 5,8 D2: 2,8 D3: 2,8 G2: 3,9 H2: 3,5 A4: 5,8 B6: 2,8 F5: 5,8 G4: 3,8 G5: 6,9 H5: 5,8 I5: 6,9 I6: 3,5 C7: 3,8 B9: 3,8 E8: 3,8 E9: 3,8 H7: 3,8 I8: 3,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D2,D3: 2.. / D2 = 2 => 0 pairs (X) / D3 = 2 => 18 pairs (_) B6,C6: 2.. / B6 = 2 => 21 pairs (_) / C6 = 2 => 0 pairs (X) C2,D2: 2.. / C2 = 2 => 18 pairs (_) / D2 = 2 => 0 pairs (X) B3,B6: 2.. / B3 = 2 => 0 pairs (X) / B6 = 2 => 21 pairs (_) B3,C3: 3.. / B3 = 3 => 0 pairs (*) / C3 = 3 => 0 pairs (X) F4,F6: 3.. / F4 = 3 => 0 pairs (*) / F6 = 3 => 0 pairs (X) G4,I6: 3.. / G4 = 3 => 0 pairs (X) / I6 = 3 => 0 pairs (_) C7,B9: 3.. / C7 = 3 => 0 pairs (*) / B9 = 3 => 0 pairs (X) E8,E9: 3.. / E8 = 3 => 0 pairs (X) / E9 = 3 => 0 pairs (_) F4,G4: 3.. / F4 = 3 => 0 pairs (*) / G4 = 3 => 0 pairs (X) F6,I6: 3.. / F6 = 3 => 0 pairs (X) / I6 = 3 => 0 pairs (_) C7,H7: 3.. / C7 = 3 => 0 pairs (*) / H7 = 3 => 0 pairs (X) B9,E9: 3.. / B9 = 3 => 0 pairs (X) / E9 = 3 => 0 pairs (_) B3,B9: 3.. / B3 = 3 => 0 pairs (*) / B9 = 3 => 0 pairs (X) C3,C7: 3.. / C3 = 3 => 0 pairs (X) / C7 = 3 => 0 pairs (_) H2,H7: 3.. / H2 = 3 => 0 pairs (*) / H7 = 3 => 0 pairs (X) A3,C3: 5.. / A3 = 5 => 0 pairs (X) / C3 = 5 => 0 pairs (_) H2,I2: 5.. / H2 = 5 => 0 pairs (X) / I2 = 5 => 0 pairs (_) A4,C6: 5.. / A4 = 5 => 0 pairs (*) / C6 = 5 => 0 pairs (X) H5,I6: 5.. / H5 = 5 => 0 pairs (*) / I6 = 5 => 0 pairs (X) A4,F4: 5.. / A4 = 5 => 0 pairs (*) / F4 = 5 => 0 pairs (X) F5,H5: 5.. / F5 = 5 => 0 pairs (X) / H5 = 5 => 0 pairs (_) A3,A4: 5.. / A3 = 5 => 0 pairs (X) / A4 = 5 => 0 pairs (_) C3,C6: 5.. / C3 = 5 => 0 pairs (*) / C6 = 5 => 0 pairs (X) H2,H5: 5.. / H2 = 5 => 0 pairs (X) / H5 = 5 => 0 pairs (_) I2,I6: 5.. / I2 = 5 => 0 pairs (*) / I6 = 5 => 0 pairs (X) G5,I5: 6.. / G5 = 6 => 18 pairs (_) / I5 = 6 => 0 pairs (X) G8,I8: 6.. / G8 = 6 => 0 pairs (X) / I8 = 6 => 18 pairs (_) G5,G8: 6.. / G5 = 6 => 18 pairs (_) / G8 = 6 => 0 pairs (X) I5,I8: 6.. / I5 = 6 => 0 pairs (X) / I8 = 6 => 18 pairs (_) D2,D3: 8.. / D2 = 8 => 18 pairs (_) / D3 = 8 => 0 pairs (X) G4,H5: 8.. / G4 = 8 => 0 pairs (*) / H5 = 8 => 0 pairs (X) C7,B9: 8.. / C7 = 8 => 0 pairs (X) / B9 = 8 => 0 pairs (_) E8,E9: 8.. / E8 = 8 => 0 pairs (*) / E9 = 8 => 0 pairs (X) H7,G8: 8.. / H7 = 8 => 0 pairs (*) / G8 = 8 => 0 pairs (X) C2,D2: 8.. / C2 = 8 => 0 pairs (X) / D2 = 8 => 18 pairs (_) F5,H5: 8.. / F5 = 8 => 0 pairs (*) / H5 = 8 => 0 pairs (X) C7,H7: 8.. / C7 = 8 => 0 pairs (X) / H7 = 8 => 0 pairs (_) E8,G8: 8.. / E8 = 8 => 0 pairs (*) / G8 = 8 => 0 pairs (X) B9,E9: 8.. / B9 = 8 => 0 pairs (*) / E9 = 8 => 0 pairs (X) A3,A4: 8.. / A3 = 8 => 0 pairs (*) / A4 = 8 => 0 pairs (X) G4,G8: 8.. / G4 = 8 => 0 pairs (*) / G8 = 8 => 0 pairs (X) H5,H7: 8.. / H5 = 8 => 0 pairs (X) / H7 = 8 => 0 pairs (_) G2,I2: 9.. / G2 = 9 => 18 pairs (_) / I2 = 9 => 0 pairs (X) G5,I5: 9.. / G5 = 9 => 0 pairs (X) / I5 = 9 => 18 pairs (_) G2,G5: 9.. / G2 = 9 => 18 pairs (_) / G5 = 9 => 0 pairs (X) I2,I5: 9.. / I2 = 9 => 0 pairs (X) / I5 = 9 => 18 pairs (_) * DURATION: 0:01:15.255425 START: 11:32:10.416691 END: 11:33:25.672116 2017-05-04 * CP COUNT: (47) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B6,B9,C2,C7,D2,D3,E8,E9,F5,G2,G4,G5,H2,H5,H7,I5,I6,I8) * 79435126861..74.......69174.6749..1234172....9..61.74.27.9465.14591.7.2.1.65.2497 * PAIR C2: 2,8 BLK 1 B3: 2,8,3 # reduction candidate for 2,8 B3: 2,8 => CTR * 79435126861..74.....3.69174.6749..1234172....9.561.7432789465314591.7.2.1.65.2497 B3: 3 => SOLVED * 794351268612874935835269174567493812341728659928615743273946581459187326186532497 C3: 2,8,3,5 # reduction candidate for 2,8 C3: 2,8 => CTR * 79435126861..74...53..6917486749531234172....9..61.74.27.9465.14591.7.2.1.65.2497 C3: 3,5 # 21 pairs * PAIR C2: 2,8 COL C C6: 2,8,5 # reduction candidate for 2,8 C6: 2,8 => SOLVED * 794351268612874935835269174567493812341728659928615743273946581459187326186532497 C6: 5 => CTR * 79435126861..74.......69174.6749..1234172....92561874327.9465.14591.7.2.1.65.2497 * PAIR A3: 5,8 BLK 1 C3: 5,8,2,3 # reduction candidate for 5,8 C3: 5,8 => SOLVED * 794351268612874935835269174567493812341728659928615743273946581459187326186532497 C3: 2,3 => CTR * 79435126861..74...5...6917486749531234172....9..61.74.27.9465.14591.7.2.1.65.2497 * PAIR D3: 2,8 ROW 3 B3: 2,8,3 # reduction candidate for 2,8 B3: 2,8 => CTR * 79435126861..74.....3.69174.6749..1234172....9.561.7432789465314591.7.2.1.65.2497 B3: 3 => SOLVED * 794351268612874935835269174567493812341728659928615743273946581459187326186532497 C3: 2,8,3,5 # reduction candidate for 2,8 C3: 2,8 => CTR * 79435126861..74...53..6917486749531234172....9..61.74.27.9465.14591.7.2.1.65.2497 C3: 3,5 # 21 pairs * PAIR G2: 3,9 BLK 3 I2: 3,9,5 # reduction candidate for 3,9 I2: 3,9 => CTR * 79435126861..74.5.....69174.6749..12341725.8.9..61.745278946531459137826136582497 I2: 5 => SOLVED * 794351268612874935835269174567493812341728659928615743273946581459187326186532497 * PAIR H2: 3,5 BLK 3 I2: 3,5,9 # reduction candidate for 3,5 I2: 9 => CTR * 79435126861..74.59....69174.6749..123417259869..61.7452789465314591.7.2.1.65.2497 I2: 3,5 # 18 pairs * PAIR A4: 5,8 BLK 4 C6: 5,8,2 # reduction candidate for 5,8 C6: 2 => CTR * 79435126861..74.....5.6917456749..1234172....98261.74.27.9465.14591.7.2.1.65.2497 C6: 5,8 # 21 pairs * PAIR A4: 5,8 ROW 4 F4: 5,8,3 # reduction candidate for 5,8 F4: 5,8 => CTR * 79435126861..74.......69174.6749.31234172..8.9..613745278946531459137826136582497 F4: 3 => SOLVED * 794351268612874935835269174567493812341728659928615743273946581459187326186532497 * PAIR B6: 2,8 BLK 4 C6: 2,8,5 # reduction candidate for 2,8 C6: 2,8 => SOLVED * 794351268612874935835269174567493812341728659928615743273946581459187326186532497 C6: 5 => CTR * 79435126861..74.......69174.6749..1234172....92561874327.9465.14591.7.2.1.65.2497 * PAIR B6: 2,8 COL B B3: 2,8,3 # reduction candidate for 2,8 B3: 2,8 => CTR * 79435126861..74.....3.69174.6749..1234172....9.561.7432789465314591.7.2.1.65.2497 B3: 3 => SOLVED * 794351268612874935835269174567493812341728659928615743273946581459187326186532497 * PAIR F5: 5,8 BLK 5 F4: 5,8,3 # reduction candidate for 5,8 F4: 5,8 => CTR * 79435126861..74.......69174.6749.31234172..8.9..613745278946531459137826136582497 F4: 3 => SOLVED * 794351268612874935835269174567493812341728659928615743273946581459187326186532497 F6: 5,8,3 # reduction candidate for 5,8 F6: 5,8 => SOLVED * 794351268612874935835269174567493812341728659928615743273946581459187326186532497 F6: 3 => CTR * 79435126861..74.5...5.69174567498312341725.8.9..61374527.9465.14591.7.2.1.65.2497 * PAIR G4: 3,8 ROW 4 F4: 3,8,5 # reduction candidate for 3,8 F4: 3,8 => SOLVED * 794351268612874935835269174567493812341728659928615743273946581459187326186532497 F4: 5 => CTR * 79435126861..74.......69174.67495312341728...9..61.74.27.9465.14591.7.2.1.65.2497 * PAIR G4: 3,8 COL G G8: 3,8,6 # reduction candidate for 3,8 G8: 6 => CTR * 79435126861..74.......69174.6749.812341728.5.9..61.74327.9465.14591.7.2.1.65.2497 G8: 3,8 # 18 pairs * PAIR I6: 3,5 ROW 6 F6: 3,5,8 # reduction candidate for 3,5 F6: 3,5 => SOLVED * 794351268612874935835269174567493812341728659928615743273946581459187326186532497 F6: 8 => CTR * 79435126861..74.......69174.6749381234172....9..61.74.27.9465.14591.7.2.1.65.2497 * PAIR I6: 3,5 COL I I2: 3,5,9 # reduction candidate for 3,5 I2: 9 => CTR * 79435126861..74.59....69174.6749..123417259869..61.7452789465314591.7.2.1.65.2497 I2: 3,5 # 18 pairs * PAIR C7: 3,8 COL C C3: 3,8,2,5 # reduction candidate for 3,8 C3: 3,8 => CTR * 79435126861..74...5...6917486749531234172....9..61.74.27.9465.14591.7.2.1.65.2497 C3: 2,5 => SOLVED * 794351268612874935835269174567493812341728659928615743273946581459187326186532497 * PAIR B9: 3,8 COL B B3: 3,8,2 # reduction candidate for 3,8 B3: 2 => CTR * 79435126861..74....2386917486749..1234172....9..61.74.27.9465.14591.7.2.1.65.2497 B3: 3,8 # 21 pairs * PAIR E8: 3,8 ROW 8 G8: 3,8,6 # reduction candidate for 3,8 G8: 6 => CTR * 79435126861..74.......69174.6749.812341728.5.9..61.74327.9465.14591.7.2.1.65.2497 G8: 3,8 # 18 pairs * PAIR H7: 3,8 BLK 9 G8: 3,8,6 # reduction candidate for 3,8 G8: 6 => CTR * 79435126861..74.......69174.6749.812341728.5.9..61.74327.9465.14591.7.2.1.65.2497 G8: 3,8 # 18 pairs * PAIR I8: 3,6 BLK 9 G8: 3,6,8 # reduction candidate for 3,6 G8: 3,6 => SOLVED * 794351268612874935835269174567493812341728659928615743273946581459187326186532497 G8: 8 => CTR * 79435126861..749......69174.6749.31234172.6899..613745278946531459137826136582497 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-256-base-pr-000.dot * REASONING * DIS # B3: 2,8 => CTR => B3: 3 * PRF # B3: 3 => SOL * DIS # C3: 2,8 => CTR => C3: 3,5 * PRF # C6: 2,8 => SOL * DIS # C6: 5 => CTR => C6: 2,8 * PRF # C3: 5,8 => SOL * DIS # C3: 2,3 => CTR => C3: 5,8 * DIS # B3: 2,8 => CTR => B3: 3 * PRF # B3: 3 => SOL * DIS # C3: 2,8 => CTR => C3: 3,5 * DIS # I2: 3,9 => CTR => I2: 5 * PRF # I2: 5 => SOL * DIS # I2: 9 => CTR => I2: 3,5 * DIS # C6: 2 => CTR => C6: 5,8 * DIS # F4: 5,8 => CTR => F4: 3 * PRF # F4: 3 => SOL * PRF # C6: 2,8 => SOL * DIS # C6: 5 => CTR => C6: 2,8 * DIS # B3: 2,8 => CTR => B3: 3 * PRF # B3: 3 => SOL * DIS # F4: 5,8 => CTR => F4: 3 * PRF # F4: 3 => SOL * PRF # F6: 5,8 => SOL * DIS # F6: 3 => CTR => F6: 5,8 * PRF # F4: 3,8 => SOL * DIS # F4: 5 => CTR => F4: 3,8 * DIS # G8: 6 => CTR => G8: 3,8 * PRF # F6: 3,5 => SOL * DIS # F6: 8 => CTR => F6: 3,5 * DIS # I2: 9 => CTR => I2: 3,5 * DIS # C3: 3,8 => CTR => C3: 2,5 * PRF # C3: 2,5 => SOL * DIS # B3: 2 => CTR => B3: 3,8 * DIS # G8: 6 => CTR => G8: 3,8 * DIS # G8: 6 => CTR => G8: 3,8 * PRF # G8: 3,6 => SOL * DIS # G8: 8 => CTR => G8: 3,6 * CNT 37 HDP CHAINS / 46 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B6,B9,C2,C7,D2,D3,E8,E9,F5,G2,G4,G5,H2,H5,H7,I5,I6,I8) * 79435126861..74.......69174.6749..1234172....9..61.74.27.9465.14591.7.2.1.65.2497 * PAIR C2: 2,8 BLK 1 B3: 2,8,3 # reduction candidate for 2,8 B3: 2,8 => CTR * 79435126861..74.....3.69174.6749..1234172....9.561.7432789465314591.7.2.1.65.2497 B3: 3 => SOLVED * 794351268612874935835269174567493812341728659928615743273946581459187326186532497 * DURATION: 0:00:01.530263 START: 11:34:12.148005 END: 11:34:13.678268 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-256-base-pr-001.dot * REASONING * DIS # B3: 2,8 => CTR => B3: 3 * PRF B3: 3 => SOL * STA B3: 3 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 256 solution: 794351268612874935835269174567493812341728659928615743273946581459187326186532497 info: 2078 FNBTWXY S8.f 4830 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 794351268612874935835269174567493812341728659928615743273946581459187326186532497 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 # B3: 2,8 => CTR => B3: 3 * PRF # B3: 3 => SOL * DIS # C3: 2,8 => CTR => C3: 3,5 * INC # C3: 3,5 => UNS * PRF # C6: 2,8 => SOL * DIS # C6: 5 => CTR => C6: 2,8 * PRF # C3: 5,8 => SOL * DIS # C3: 2,3 => CTR => C3: 5,8 * DIS # B3: 2,8 => CTR => B3: 3 * PRF # B3: 3 => SOL * DIS # C3: 2,8 => CTR => C3: 3,5 * INC # C3: 3,5 => UNS * DIS # I2: 3,9 => CTR => I2: 5 * PRF # I2: 5 => SOL * INC # I2: 3,5 => UNS * DIS # I2: 9 => CTR => I2: 3,5 * INC # C6: 5,8 => UNS * DIS # C6: 2 => CTR => C6: 5,8 * DIS # F4: 5,8 => CTR => F4: 3 * PRF # F4: 3 => SOL * PRF # C6: 2,8 => SOL * DIS # C6: 5 => CTR => C6: 2,8 * DIS # B3: 2,8 => CTR => B3: 3 * PRF # B3: 3 => SOL * DIS # F4: 5,8 => CTR => F4: 3 * PRF # F4: 3 => SOL * PRF # F6: 5,8 => SOL * DIS # F6: 3 => CTR => F6: 5,8 * PRF # F4: 3,8 => SOL * DIS # F4: 5 => CTR => F4: 3,8 * INC # G8: 3,8 => UNS * DIS # G8: 6 => CTR => G8: 3,8 * PRF # F6: 3,5 => SOL * DIS # F6: 8 => CTR => F6: 3,5 * INC # I2: 3,5 => UNS * DIS # I2: 9 => CTR => I2: 3,5 * DIS # C3: 3,8 => CTR => C3: 2,5 * PRF # C3: 2,5 => SOL * INC # B3: 3,8 => UNS * DIS # B3: 2 => CTR => B3: 3,8 * INC # G8: 3,8 => UNS * DIS # G8: 6 => CTR => G8: 3,8 * INC # G8: 3,8 => UNS * DIS # G8: 6 => CTR => G8: 3,8 * PRF # G8: 3,6 => SOL * DIS # G8: 8 => CTR => G8: 3,6 * CNT 46 HDP CHAINS / 46 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B3: 2,8 => CTR => B3: 3 * PRF B3: 3 => SOL * STA B3: 3 * CNT 2 HDP CHAINS / 1 HYP OPENED