Analysis of xx-top500-076-base.sdk
Contents
Original Sudoku
level: medium
position: .1.8...2........3........9....12.7..9...5....3.....4...2.5..6..4....3............ initial
Autosolve
position: .1983.5242..9.513.53.2.189....129753971354268352...419.2359.6414.5.139.219.4.23.5 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 6,7 => CTR => C2: 4,8 * PRF # F6: 6,7 => SOL * DIS # F6: 8 => CTR => F6: 6,7 * DIS # C2: 6,7 => CTR => C2: 4,8 * DIS # E6: 6,7 => CTR => E6: 8 * PRF # E6: 8 => SOL * PRF # F6: 6,7 => SOL * DIS # F6: 8 => CTR => F6: 6,7 * DIS # C9: 7,8 => CTR => C9: 6 * PRF # C9: 6 => SOL * PRF # C9: 6,8 => SOL * DIS # C9: 7 => CTR => C9: 6,8 * PRF # E9: 7,8 => SOL * DIS # E9: 6 => CTR => E9: 7,8 * DIS # F6: 7,8 => CTR => F6: 6 * PRF # F6: 6 => SOL * PRF # E9: 6,7 => SOL * DIS # E9: 8 => CTR => E9: 6,7 * DIS # C9: 7,8 => CTR => C9: 6 * PRF # C9: 6 => SOL * PRF # E9: 7,8 => SOL * DIS # E9: 6 => CTR => E9: 7,8 * CNT 22 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C2: 6,7 => CTR => C2: 4,8 * DIS C2: 4,8 # C3: 4 => CTR => C3: 6,7 * PRF C2: 4,8 + C3: 6,7 # F6: 6,7 => SOL * STA C2: 4,8 + C3: 6,7 + F6: 6,7 * CNT 3 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .1.8...2........3........9....12.7..9...5....3.....4...2.5..6..4....3............ | initial |
| .1983.5242..9.513.53.2.189....129753971354268352...419.2359.6414.5.139.219.4.23.5 | autosolve |
| 619837524248965137537241896864129753971354268352786419723598641485613972196472385 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) A1: 6,7 F1: 6,7 I2: 6,7 I3: 6,7 A4: 6,8 D6: 6,7 A7: 7,8 B8: 6,8 F7: 7,8 D8: 6,7 H8: 7,8 H9: 7,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,E3: 4.. / E2 = 4 => 15 pairs (_) / E3 = 4 => 16 pairs (_) B4,C4: 4.. / B4 = 4 => 14 pairs (_) / C4 = 4 => 16 pairs (_) C3,E3: 4.. / C3 = 4 => 15 pairs (_) / E3 = 4 => 16 pairs (_) B2,B4: 4.. / B2 = 4 => 16 pairs (_) / B4 = 4 => 14 pairs (_) I2,I3: 6.. / I2 = 6 => 14 pairs (_) / I3 = 6 => 13 pairs (_) B8,C9: 6.. / B8 = 6 => 0 pairs (X) / C9 = 6 => 0 pairs (_) D8,E9: 6.. / D8 = 6 => 0 pairs (*) / E9 = 6 => 0 pairs (X) A1,F1: 6.. / A1 = 6 => 0 pairs (*) / F1 = 6 => 0 pairs (X) B8,D8: 6.. / B8 = 6 => 0 pairs (X) / D8 = 6 => 0 pairs (_) C9,E9: 6.. / C9 = 6 => 0 pairs (*) / E9 = 6 => 0 pairs (X) A1,A4: 6.. / A1 = 6 => 0 pairs (*) / A4 = 6 => 0 pairs (X) D6,D8: 6.. / D6 = 6 => 0 pairs (X) / D8 = 6 => 0 pairs (_) F1,F6: 6.. / F1 = 6 => 0 pairs (X) / F6 = 6 => 0 pairs (_) I2,I3: 7.. / I2 = 7 => 13 pairs (_) / I3 = 7 => 14 pairs (_) A7,C9: 7.. / A7 = 7 => 0 pairs (*) / C9 = 7 => 0 pairs (X) H8,H9: 7.. / H8 = 7 => 0 pairs (*) / H9 = 7 => 0 pairs (X) A1,F1: 7.. / A1 = 7 => 0 pairs (X) / F1 = 7 => 0 pairs (_) A7,F7: 7.. / A7 = 7 => 0 pairs (*) / F7 = 7 => 0 pairs (X) D8,H8: 7.. / D8 = 7 => 0 pairs (X) / H8 = 7 => 0 pairs (_) A1,A7: 7.. / A1 = 7 => 0 pairs (X) / A7 = 7 => 0 pairs (_) D6,D8: 7.. / D6 = 7 => 0 pairs (*) / D8 = 7 => 0 pairs (X) B2,C2: 8.. / B2 = 8 => 0 pairs (X) / C2 = 8 => 15 pairs (_) E6,F6: 8.. / E6 = 8 => 0 pairs (*) / F6 = 8 => 0 pairs (X) F7,E9: 8.. / F7 = 8 => 0 pairs (*) / E9 = 8 => 0 pairs (X) H8,H9: 8.. / H8 = 8 => 0 pairs (X) / H9 = 8 => 0 pairs (_) A7,F7: 8.. / A7 = 8 => 0 pairs (X) / F7 = 8 => 0 pairs (_) B8,H8: 8.. / B8 = 8 => 0 pairs (*) / H8 = 8 => 0 pairs (X) A4,A7: 8.. / A4 = 8 => 0 pairs (*) / A7 = 8 => 0 pairs (X) E6,E9: 8.. / E6 = 8 => 0 pairs (*) / E9 = 8 => 0 pairs (X) F6,F7: 8.. / F6 = 8 => 0 pairs (X) / F7 = 8 => 0 pairs (_) * DURATION: 0:01:00.219722 START: 05:19:11.994610 END: 05:20:12.214332 2017-05-04 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,A7,B8,D6,D8,F1,F7,H8,H9,I2,I3) * .1983.5242..9.513.53.2.189....129753971354268352...419.2359.6414.5.139.219.4.23.5 * PAIR A1: 6,7 BLK 1 C2: 6,7,4,8 # reduction candidate for 6,7 C2: 6,7 => CTR * .1983652428.94513.5342.189..4.129753971354268352...419.2359.64146571398219.462375 C2: 4,8 # 13 pairs C3: 6,7,4 # reduction candidate for 6,7 C3: 6,7 # 16 pairs * PAIR F1: 6,7 BLK 2 E2: 6,7,4 # reduction candidate for 6,7 E2: 6,7 # 16 pairs E3: 6,7,4 # reduction candidate for 6,7 E3: 6,7 # 15 pairs * PAIR F1: 6,7 COL F F6: 6,7,8 # reduction candidate for 6,7 F6: 6,7 => SOLVED * 619837524248965137537241896864129753971354268352786419723598641485613972196472385 F6: 8 => CTR * .198365242..9.513.53.2.189.6..129753971354268352..8419823597641465.139.219.4.23.5 * PAIR I2: 6,7 ROW 2 C2: 6,7,4,8 # reduction candidate for 6,7 C2: 6,7 => CTR * .1983652428.94513.5342.189..4.129753971354268352...419.2359.64146571398219.462375 C2: 4,8 # 13 pairs E2: 6,7,4 # reduction candidate for 6,7 E2: 6,7 # 16 pairs * PAIR I3: 6,7 ROW 3 C3: 6,7,4 # reduction candidate for 6,7 C3: 6,7 # 16 pairs E3: 6,7,4 # reduction candidate for 6,7 E3: 6,7 # 15 pairs * PAIR A4: 6,8 BLK 4 B4: 6,8,4 # reduction candidate for 6,8 B4: 6,8 # 16 pairs C4: 6,8,4 # reduction candidate for 6,8 C4: 6,8 # 14 pairs * PAIR D6: 6,7 BLK 5 E6: 6,7,8 # reduction candidate for 6,7 E6: 6,7 => CTR * .1983.5242..9.513.53.2.189....129753971354268352..8419823597641465.139.219.4.23.5 E6: 8 => SOLVED * 619837524248965137537241896864129753971354268352786419723598641485613972196472385 F6: 6,7,8 # reduction candidate for 6,7 F6: 6,7 => SOLVED * 619837524248965137537241896864129753971354268352786419723598641485613972196472385 F6: 8 => CTR * .198365242..9.513.53.2.189.6..129753971354268352..8419823597641465.139.219.4.23.5 * PAIR A7: 7,8 BLK 7 C9: 7,8,6 # reduction candidate for 7,8 C9: 7,8 => CTR * .198365242..9.513.53.2.189.6..129753971354268352687419.2359.64146571398219.462375 C9: 6 => SOLVED * 619837524248965137537241896864129753971354268352786419723598641485613972196472385 * PAIR B8: 6,8 BLK 7 C9: 6,8,7 # reduction candidate for 6,8 C9: 6,8 => SOLVED * 619837524248965137537241896864129753971354268352786419723598641485613972196472385 C9: 7 => CTR * .1983.5242..9.513.53.2.189....129753971354268352...419.2359.6414657139821974.23.5 * PAIR B8: 6,8 COL B B2: 6,8,4 # reduction candidate for 6,8 B2: 6,8 # 14 pairs B4: 6,8,4 # reduction candidate for 6,8 B4: 6,8 # 16 pairs * PAIR F7: 7,8 BLK 8 E9: 7,8,6 # reduction candidate for 7,8 E9: 7,8 => SOLVED * 619837524248965137537241896864129753971354268352786419723598641485613972196472385 E9: 6 => CTR * .1983652428.9.513.53.2.189....129753971354268352.8.419.235986414.5713982198462375 * PAIR F7: 7,8 COL F F6: 7,8,6 # reduction candidate for 7,8 F6: 7,8 => CTR * .198365242..9.513.53.2.189.6..129753971354268352...419823597641465.139.219.4.23.5 F6: 6 => SOLVED * 619837524248965137537241896864129753971354268352786419723598641485613972196472385 * PAIR D8: 6,7 BLK 8 E9: 6,7,8 # reduction candidate for 6,7 E9: 6,7 => SOLVED * 619837524248965137537241896864129753971354268352786419723598641485613972196472385 E9: 8 => CTR * .1983.5242..9.513.53.2.189....129753971354268352...419.2359.6414.561397219.4.23.5 * PAIR H9: 7,8 ROW 9 C9: 7,8,6 # reduction candidate for 7,8 C9: 7,8 => CTR * .198365242..9.513.53.2.189.6..129753971354268352687419.2359.64146571398219.462375 C9: 6 => SOLVED * 619837524248965137537241896864129753971354268352786419723598641485613972196472385 E9: 7,8,6 # reduction candidate for 7,8 E9: 7,8 => SOLVED * 619837524248965137537241896864129753971354268352786419723598641485613972196472385 E9: 6 => CTR * .1983652428.9.513.53.2.189....129753971354268352.8.419.235986414.5713982198462375 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-076-base-pr-000.dot * REASONING * DIS # C2: 6,7 => CTR => C2: 4,8 * PRF # F6: 6,7 => SOL * DIS # F6: 8 => CTR => F6: 6,7 * DIS # C2: 6,7 => CTR => C2: 4,8 * DIS # E6: 6,7 => CTR => E6: 8 * PRF # E6: 8 => SOL * PRF # F6: 6,7 => SOL * DIS # F6: 8 => CTR => F6: 6,7 * DIS # C9: 7,8 => CTR => C9: 6 * PRF # C9: 6 => SOL * PRF # C9: 6,8 => SOL * DIS # C9: 7 => CTR => C9: 6,8 * PRF # E9: 7,8 => SOL * DIS # E9: 6 => CTR => E9: 7,8 * DIS # F6: 7,8 => CTR => F6: 6 * PRF # F6: 6 => SOL * PRF # E9: 6,7 => SOL * DIS # E9: 8 => CTR => E9: 6,7 * DIS # C9: 7,8 => CTR => C9: 6 * PRF # C9: 6 => SOL * PRF # E9: 7,8 => SOL * DIS # E9: 6 => CTR => E9: 7,8 * CNT 22 HDP CHAINS / 34 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,A7,B8,D6,D8,F1,F7,H8,H9,I2,I3) * .1983.5242..9.513.53.2.189....129753971354268352...419.2359.6414.5.139.219.4.23.5 * PAIR A1: 6,7 BLK 1 C2: 6,7,4,8 # reduction candidate for 6,7 C2: 6,7 => CTR * .1983652428.94513.5342.189..4.129753971354268352...419.2359.64146571398219.462375 C3: 6,7,4 # reduction candidate for 6,7 C3: 6,7 # 16 pairs * RESTART * PAIR A1: 6,7 BLK 1 C3: 6,7,4 # reduction candidate for 6,7 C3: 4 => CTR * 7198365242689.513.53.2.189....129753971354268352...419.2359.6414.5.139.219.4.23.5 * PAIR F1: 6,7 COL F F6: 6,7,8 # reduction candidate for 6,7 F6: 6,7 => SOLVED * 619837524248965137537241896864129753971354268352786419723598641485613972196472385 * DURATION: 0:00:07.126240 START: 05:20:56.143238 END: 05:21:03.269478 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-076-base-pr-001.dot * REASONING * DIS # C2: 6,7 => CTR => C2: 4,8 * DIS C2: 4,8 # C3: 4 => CTR => C3: 6,7 * PRF C2: 4,8 + C3: 6,7 # F6: 6,7 => SOL * STA C2: 4,8 + C3: 6,7 + F6: 6,7 * CNT 3 HDP CHAINS / 5 HYP OPENED
Header Info
Top 500 Minimum 17 076 solution: 619837524248965137537241896864129753971354268352786419723598641485613972196472385 info: 1498 FNBHWXY S8.f 15759 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 619837524248965137537241896864129753971354268352786419723598641485613972196472385 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 # C2: 6,7 => CTR => C2: 4,8 * INC # C2: 4,8 => UNS * INC # C3: 6,7 => UNS * INC # E2: 6,7 => UNS * INC # E3: 6,7 => UNS * PRF # F6: 6,7 => SOL * DIS # F6: 8 => CTR => F6: 6,7 * DIS # C2: 6,7 => CTR => C2: 4,8 * INC # C2: 4,8 => UNS * INC # E2: 6,7 => UNS * INC # C3: 6,7 => UNS * INC # E3: 6,7 => UNS * INC # B4: 6,8 => UNS * INC # C4: 6,8 => UNS * DIS # E6: 6,7 => CTR => E6: 8 * PRF # E6: 8 => SOL * PRF # F6: 6,7 => SOL * DIS # F6: 8 => CTR => F6: 6,7 * DIS # C9: 7,8 => CTR => C9: 6 * PRF # C9: 6 => SOL * PRF # C9: 6,8 => SOL * DIS # C9: 7 => CTR => C9: 6,8 * INC # B2: 6,8 => UNS * INC # B4: 6,8 => UNS * PRF # E9: 7,8 => SOL * DIS # E9: 6 => CTR => E9: 7,8 * DIS # F6: 7,8 => CTR => F6: 6 * PRF # F6: 6 => SOL * PRF # E9: 6,7 => SOL * DIS # E9: 8 => CTR => E9: 6,7 * DIS # C9: 7,8 => CTR => C9: 6 * PRF # C9: 6 => SOL * PRF # E9: 7,8 => SOL * DIS # E9: 6 => CTR => E9: 7,8 * CNT 34 HDP CHAINS / 34 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C2: 6,7 => CTR => C2: 4,8 * INC C2: 4,8 # C3: 6,7 => UNS * INC C2: 4,8 # C3: 6,7 => UNS * DIS C2: 4,8 # C3: 4 => CTR => C3: 6,7 * PRF C2: 4,8 + C3: 6,7 # F6: 6,7 => SOL * STA C2: 4,8 + C3: 6,7 + F6: 6,7 * CNT 5 HDP CHAINS / 5 HYP OPENED