Analysis of xx-top500-115-base.sdk
Contents
Original Sudoku
level: medium
position: 4.1.........8...2.........36..5.4....7.....8.....1.7...2.3...........4.1......9.. initial
Autosolve
position: 4.16..897...84.12.2.81.7.436825743191759..284.4.2187...243.1..8...7..4.1.1.4..9.2 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F1: 3,5 => CTR => F1: 2 * DIS # F2: 3 => CTR => F2: 5,9 * DIS # B3: 5,9 => CTR => B3: 6 * PRF # B3: 6 => SOL * DIS # E8: 5,9 => CTR => E8: 2,6,8 * DIS # B3: 9 => CTR => B3: 5,6 * DIS # A2: 3,9 => CTR => A2: 5,7 * DIS # A8: 3,9 => CTR => A8: 5,8 * DIS # H7: 5,6 => CTR => H7: 7 * DIS # E8: 5,6 => CTR => E8: 2,8,9 * DIS # F8: 5,6 => CTR => F8: 2,9 * DIS # E9: 5,6 => CTR => E9: 8 * DIS # H7: 5,6 => CTR => H7: 7 * DIS # E7: 9 => CTR => E7: 5,6 * CNT 14 HDP CHAINS / 43 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F1: 3,5 => CTR => F1: 2 * DIS F1: 2 # F2: 3 => CTR => F2: 5,9 * DIS F1: 2 + F2: 5,9 # A2: 3,9 => CTR => A2: 7 * PRF F1: 2 + F2: 5,9 + A2: 7 => SOL * STA F1: 2 + F2: 5,9 + A2: 7 * CNT 4 HDP CHAINS / 13 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 4.1.........8...2.........36..5.4....7.....8.....1.7...2.3...........4.1......9.. | initial |
| 4.16..897...84.12.2.81.7.436825743191759..284.4.2187...243.1..8...7..4.1.1.4..9.2 | autosolve |
| 451632897793845126268197543682574319175963284349218765924351678836729451517486932 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) B1: 3,5 E3: 5,9 I2: 5,6 G3: 5,6 A6: 3,9 C6: 3,9 E5: 3,6 F5: 3,6 H6: 5,6 I6: 5,6 F9: 5,6 G7: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,F1: 2.. / E1 = 2 => 0 pairs (X) / F1 = 2 => 13 pairs (_) E8,F8: 2.. / E8 = 2 => 13 pairs (_) / F8 = 2 => 0 pairs (X) E1,E8: 2.. / E1 = 2 => 0 pairs (X) / E8 = 2 => 13 pairs (_) F1,F8: 2.. / F1 = 2 => 13 pairs (_) / F8 = 2 => 0 pairs (X) A6,C6: 3.. / A6 = 3 => 11 pairs (_) / C6 = 3 => 0 pairs (X) E5,F5: 3.. / E5 = 3 => 15 pairs (_) / F5 = 3 => 13 pairs (_) H8,H9: 3.. / H8 = 3 => 13 pairs (_) / H9 = 3 => 15 pairs (_) E1,E5: 3.. / E1 = 3 => 13 pairs (_) / E5 = 3 => 15 pairs (_) I2,G3: 5.. / I2 = 5 => 0 pairs (X) / G3 = 5 => 0 pairs (_) H6,I6: 5.. / H6 = 5 => 0 pairs (X) / I6 = 5 => 0 pairs (_) G3,G7: 5.. / G3 = 5 => 0 pairs (*) / G7 = 5 => 0 pairs (X) I2,I6: 5.. / I2 = 5 => 0 pairs (X) / I6 = 5 => 0 pairs (_) I2,G3: 6.. / I2 = 6 => 0 pairs (*) / G3 = 6 => 0 pairs (X) E5,F5: 6.. / E5 = 6 => 13 pairs (_) / F5 = 6 => 15 pairs (_) H6,I6: 6.. / H6 = 6 => 0 pairs (*) / I6 = 6 => 0 pairs (X) B3,G3: 6.. / B3 = 6 => 0 pairs (*) / G3 = 6 => 0 pairs (X) G3,G7: 6.. / G3 = 6 => 0 pairs (X) / G7 = 6 => 0 pairs (_) I2,I6: 6.. / I2 = 6 => 0 pairs (*) / I6 = 6 => 0 pairs (X) A2,C2: 7.. / A2 = 7 => 14 pairs (_) / C2 = 7 => 13 pairs (_) H7,H9: 7.. / H7 = 7 => 13 pairs (_) / H9 = 7 => 0 pairs (X) A7,H7: 7.. / A7 = 7 => 0 pairs (X) / H7 = 7 => 13 pairs (_) C2,C9: 7.. / C2 = 7 => 13 pairs (_) / C9 = 7 => 14 pairs (_) A8,A9: 8.. / A8 = 8 => 12 pairs (_) / A9 = 8 => 0 pairs (X) E8,E9: 8.. / E8 = 8 => 0 pairs (X) / E9 = 8 => 12 pairs (_) A8,E8: 8.. / A8 = 8 => 12 pairs (_) / E8 = 8 => 0 pairs (X) A9,E9: 8.. / A9 = 8 => 0 pairs (X) / E9 = 8 => 12 pairs (_) F2,E3: 9.. / F2 = 9 => 0 pairs (X) / E3 = 9 => 16 pairs (_) A6,C6: 9.. / A6 = 9 => 0 pairs (X) / C6 = 9 => 11 pairs (_) B3,E3: 9.. / B3 = 9 => 0 pairs (X) / E3 = 9 => 16 pairs (_) A7,E7: 9.. / A7 = 9 => 16 pairs (_) / E7 = 9 => 0 pairs (X) F2,F8: 9.. / F2 = 9 => 0 pairs (X) / F8 = 9 => 16 pairs (_) * DURATION: 0:00:57.532854 START: 06:41:41.601615 END: 06:42:39.134469 2017-05-04 * CP COUNT: (31) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B1,C6,E3,E5,F5,F9,G3,G7,H6,I2,I6) * 4.16..897...84.12.2.81.7.436825743191759..284.4.2187...243.1..8...7..4.1.1.4..9.2 * PAIR B1: 3,5 BLK 1 A2: 3,5,7,9 # reduction candidate for 3,5 A2: 3,5 # 17 pairs B2: 3,5,6,9 # reduction candidate for 3,5 B2: 3,5 # 16 pairs * PAIR B1: 3,5 ROW 1 E1: 3,5,2 # reduction candidate for 3,5 E1: 3,5 # 13 pairs F1: 3,5,2 # reduction candidate for 3,5 F1: 3,5 => CTR * 451623897...849125298157643682574319175936284.4.218756.243915685.97824318134659.2 F1: 2 # 13 pairs * PAIR B1: 3,5 COL B B8: 3,5,6,9 # reduction candidate for 3,5 B8: 3,5 # 16 pairs B8: 6,9 # 14 pairs * PAIR E3: 5,9 BLK 2 F2: 5,9,3 # reduction candidate for 5,9 F2: 3 => CTR * 431652897.9.843125258197643682574319175936284349218756924361578...7294.1.1.4859.2 F2: 5,9 # 15 pairs * PAIR E3: 5,9 ROW 3 B3: 5,9,6 # reduction candidate for 5,9 B3: 5,9 => CTR * 4.16..897...8491252981576436825743191759..284.4.218756.24391568..97..431.134..9.2 B3: 6 => SOLVED * 451632897793845126268197543682574319175963284349218765924351678836729451517486932 * PAIR E3: 5,9 COL E E7: 5,9,6 # reduction candidate for 5,9 E7: 5,9 # 16 pairs E8: 5,9,2,6,8 # reduction candidate for 5,9 E8: 5,9 => CTR * 451623897...849125298157643682574319175936284.4.2187565243.1..88..7.24.1.1.4859.2 E8: 2,6,8 # 12 pairs * PAIR I2: 5,6 ROW 2 B2: 5,6,3,9 # reduction candidate for 5,6 B2: 5,6 # 15 pairs B2: 3,9 # 13 pairs * PAIR G3: 5,6 ROW 3 B3: 5,6,9 # reduction candidate for 5,6 B3: 9 => CTR * 4516..897..68491252981576436825743191759..284.4.218756.24391568.697..4.1.1.4..9.2 B3: 5,6 # 16 pairs * PAIR A6: 3,9 COL A A2: 3,9,5,7 # reduction candidate for 3,9 A2: 3,9 => CTR * 4.16..897..784912.2981576436825743191759..2849432187.6.24391568.3.7..4.1.1.4..9.2 A2: 5,7 # 13 pairs A8: 3,9,5,8 # reduction candidate for 3,9 A8: 3,9 => CTR * 4.162.897...84912.298157643682574319175936284.4.2187.6.24391568.56782431813465972 A8: 5,8 # 13 pairs * PAIR C6: 3,9 COL C C2: 3,9,6,7 # reduction candidate for 3,9 C2: 3,9 # 16 pairs C8: 3,9,6 # reduction candidate for 3,9 C8: 3,9 # 15 pairs * PAIR H6: 5,6 COL H H7: 5,6,7 # reduction candidate for 5,6 H7: 5,6 => CTR * 4516..8973.784912.2981576436825743191759..284.4.2187.6724391568...7..431.1.4..972 H7: 7 # 13 pairs H8: 5,6,3 # reduction candidate for 5,6 H8: 5,6 # 15 pairs H9: 5,6,3,7 # reduction candidate for 5,6 H9: 5,6 # 17 pairs * PAIR F9: 5,6 BLK 8 E7: 5,6,9 # reduction candidate for 5,6 E7: 5,6 # 16 pairs E8: 5,6,2,8,9 # reduction candidate for 5,6 E8: 5,6 => CTR * 451623897...849125298157643682574319175936284.4.2187565243.1..88..7.24.1.1.4859.2 E8: 2,8,9 # 12 pairs F8: 5,6,2,9 # reduction candidate for 5,6 F8: 5,6 => CTR * 451632897...849125298157643682574319175963284.4.218756.243915688.972543151348.9.2 F8: 2,9 # 13 pairs E9: 5,6,8 # reduction candidate for 5,6 E9: 5,6 => CTR * 451623897.3.84912.298157643682574319175936284.4.2187.6.24391568...782431813465972 E9: 8 # 12 pairs * PAIR F9: 5,6 ROW 9 H9: 5,6,3,7 # reduction candidate for 5,6 H9: 5,6 # 17 pairs H9: 3,7 # 13 pairs * PAIR G7: 5,6 BLK 9 H7: 5,6,7 # reduction candidate for 5,6 H7: 5,6 => CTR * 4516..8973.784912.2981576436825743191759..284.4.2187.6724391568...7..431.1.4..972 H7: 7 # 13 pairs H8: 5,6,3 # reduction candidate for 5,6 H8: 5,6 # 15 pairs H9: 5,6,3,7 # reduction candidate for 5,6 H9: 5,6 # 17 pairs * PAIR G7: 5,6 ROW 7 E7: 5,6,9 # reduction candidate for 5,6 E7: 9 => CTR * 4516..897.3.84912.2981576436825743191759..284.4.2187.6.24391568...7..431.1.4..972 E7: 5,6 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-115-base-pr-000.dot * REASONING * DIS # F1: 3,5 => CTR => F1: 2 * DIS # F2: 3 => CTR => F2: 5,9 * DIS # B3: 5,9 => CTR => B3: 6 * PRF # B3: 6 => SOL * DIS # E8: 5,9 => CTR => E8: 2,6,8 * DIS # B3: 9 => CTR => B3: 5,6 * DIS # A2: 3,9 => CTR => A2: 5,7 * DIS # A8: 3,9 => CTR => A8: 5,8 * DIS # H7: 5,6 => CTR => H7: 7 * DIS # E8: 5,6 => CTR => E8: 2,8,9 * DIS # F8: 5,6 => CTR => F8: 2,9 * DIS # E9: 5,6 => CTR => E9: 8 * DIS # H7: 5,6 => CTR => H7: 7 * DIS # E7: 9 => CTR => E7: 5,6 * CNT 14 HDP CHAINS / 43 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B1,C6,E3,E5,F5,F9,G3,G7,H6,I2,I6) * 4.16..897...84.12.2.81.7.436825743191759..284.4.2187...243.1..8...7..4.1.1.4..9.2 * PAIR B1: 3,5 BLK 1 A2: 3,5,7,9 # reduction candidate for 3,5 A2: 3,5 # 17 pairs B2: 3,5,6,9 # reduction candidate for 3,5 B2: 3,5 # 16 pairs * PAIR B1: 3,5 ROW 1 E1: 3,5,2 # reduction candidate for 3,5 E1: 3,5 # 13 pairs F1: 3,5,2 # reduction candidate for 3,5 F1: 3,5 => CTR * 451623897...849125298157643682574319175936284.4.218756.243915685.97824318134659.2 * RESTART * PAIR B1: 3,5 COL B B8: 3,5,6,9 # reduction candidate for 3,5 B8: 3,5 # 17 pairs B8: 6,9 # 15 pairs * PAIR RESTART * PAIR B1: 3,5 BLK 1 A2: 3,5,7,9 # reduction candidate for 3,5 A2: 3,5 # 18 pairs B2: 3,5,6,9 # reduction candidate for 3,5 B2: 3,5 # 17 pairs * PAIR B1: 3,5 COL B B8: 3,5,6,9 # reduction candidate for 3,5 B8: 3,5 # 17 pairs B8: 6,9 # 15 pairs * PAIR E3: 5,9 BLK 2 F2: 5,9,3 # reduction candidate for 5,9 F2: 3 => CTR * 4316528975978431262.8197.43682574319175936284.4.2187..9243615788..7294.1.1.4859.2 * PAIR A6: 3,9 COL A A2: 3,9,7 # reduction candidate for 3,9 A2: 3,9 => CTR * 451632897..7849125298157643682574319175963284943218756.2439156883.72.4.1.1.48.9.2 A2: 7 => SOLVED * 451632897793845126268197543682574319175963284349218765924351678836729451517486932 * DURATION: 0:00:15.834250 START: 06:43:21.895717 END: 06:43:37.729967 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-115-base-pr-001.dot * REASONING * DIS # F1: 3,5 => CTR => F1: 2 * DIS F1: 2 # F2: 3 => CTR => F2: 5,9 * DIS F1: 2 + F2: 5,9 # A2: 3,9 => CTR => A2: 7 * PRF F1: 2 + F2: 5,9 + A2: 7 => SOL * STA F1: 2 + F2: 5,9 + A2: 7 * CNT 4 HDP CHAINS / 13 HYP OPENED
Header Info
Top 500 Minimum 17 115 solution: 451632897793845126268197543682574319175963284349218765924351678836729451517486932 info: 1702 FNBTHWXY S8.f 31248 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 451632897793845126268197543682574319175963284349218765924351678836729451517486932 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 # A2: 3,5 => UNS * INC # B2: 3,5 => UNS * INC # E1: 3,5 => UNS * DIS # F1: 3,5 => CTR => F1: 2 * INC # F1: 2 => UNS * INC # B8: 3,5 => UNS * INC # B8: 6,9 => UNS * INC # F2: 5,9 => UNS * DIS # F2: 3 => CTR => F2: 5,9 * DIS # B3: 5,9 => CTR => B3: 6 * PRF # B3: 6 => SOL * INC # E7: 5,9 => UNS * DIS # E8: 5,9 => CTR => E8: 2,6,8 * INC # E8: 2,6,8 => UNS * INC # B2: 5,6 => UNS * INC # B2: 3,9 => UNS * INC # B3: 5,6 => UNS * DIS # B3: 9 => CTR => B3: 5,6 * DIS # A2: 3,9 => CTR => A2: 5,7 * INC # A2: 5,7 => UNS * DIS # A8: 3,9 => CTR => A8: 5,8 * INC # A8: 5,8 => UNS * INC # C2: 3,9 => UNS * INC # C8: 3,9 => UNS * DIS # H7: 5,6 => CTR => H7: 7 * INC # H7: 7 => UNS * INC # H8: 5,6 => UNS * INC # H9: 5,6 => UNS * INC # E7: 5,6 => UNS * DIS # E8: 5,6 => CTR => E8: 2,8,9 * INC # E8: 2,8,9 => UNS * DIS # F8: 5,6 => CTR => F8: 2,9 * INC # F8: 2,9 => UNS * DIS # E9: 5,6 => CTR => E9: 8 * INC # E9: 8 => UNS * INC # H9: 5,6 => UNS * INC # H9: 3,7 => UNS * DIS # H7: 5,6 => CTR => H7: 7 * INC # H7: 7 => UNS * INC # H8: 5,6 => UNS * INC # H9: 5,6 => UNS * INC # E7: 5,6 => UNS * DIS # E7: 9 => CTR => E7: 5,6 * CNT 43 HDP CHAINS / 43 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A2: 3,5 => UNS * INC # B2: 3,5 => UNS * INC # E1: 3,5 => UNS * DIS # F1: 3,5 => CTR => F1: 2 * INC F1: 2 # B8: 3,5 => UNS * INC F1: 2 # B8: 6,9 => UNS * INC F1: 2 # A2: 3,5 => UNS * INC F1: 2 # B2: 3,5 => UNS * INC F1: 2 # B8: 3,5 => UNS * INC F1: 2 # B8: 6,9 => UNS * INC F1: 2 # F2: 5,9 => UNS * DIS F1: 2 # F2: 3 => CTR => F2: 5,9 * DIS F1: 2 + F2: 5,9 # A2: 3,9 => CTR => A2: 7 * PRF F1: 2 + F2: 5,9 + A2: 7 => SOL * STA F1: 2 + F2: 5,9 + A2: 7 * CNT 14 HDP CHAINS / 13 HYP OPENED