Analysis of xx-top500-316-base.sdk
Contents
Original Sudoku
level: medium
position: .......128...4...........6..9.2.....7.....4.....5.1....15..........3.9..6.2...... initial
Autosolve
position: .......128...4...........64.9.2.4...7.....4.....5.1...915......4...3.9..632...... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 3,5 => CTR => A3: 1,2 * DIS # F1: 3,5 => CTR => F1: 6,7,8,9 * DIS # G1: 3,5 => CTR => G1: 7,8 * PRF # A4: 3,5 => SOL * DIS # A4: 1 => CTR => A4: 3,5 * DIS # H6: 2,3 => CTR => H6: 7,8,9 * DIS # A3: 2,3 => CTR => A3: 1,5 * PRF # A3: 1,5 => SOL * DIS # I8: 5 => CTR => I8: 1,6 * DIS # D2: 3,7 => CTR => D2: 1,6 * DIS # F8: 6 => CTR => F8: 2,5 * DIS # H5: 8,9 => CTR => H5: 2,5 * CNT 12 HDP CHAINS / 21 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 3,5 => CTR => A3: 1,2 * DIS A3: 1,2 # F1: 3,5 => CTR => F1: 6,7,8,9 * DIS A3: 1,2 + F1: 6,7,8,9 # G1: 3,5 => CTR => G1: 7,8 * PRF A3: 1,2 + F1: 6,7,8,9 + G1: 7,8 # A4: 3,5 => SOL * STA A3: 1,2 + F1: 6,7,8,9 + G1: 7,8 + A4: 3,5 * CNT 4 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .......128...4...........6..9.2.....7.....4.....5.1....15..........3.9..6.2...... | initial |
| .......128...4...........64.9.2.4...7.....4.....5.1...915......4...3.9..632...... | autosolve |
| 349756812826143579157829364593264187761398425284571693915487236478632951632915748 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) A1: 3,5 A6: 2,3 B8: 7,8 C8: 7,8 D8: 1,6 H8: 2,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,D2: 1.. / C2 = 1 => 0 pairs (X) / D2 = 1 => 0 pairs (_) C5,I5: 1.. / C5 = 1 => 0 pairs (*) / I5 = 1 => 0 pairs (X) D8,I8: 1.. / D8 = 1 => 0 pairs (X) / I8 = 1 => 0 pairs (_) A3,A4: 1.. / A3 = 1 => 0 pairs (*) / A4 = 1 => 0 pairs (X) E3,E9: 1.. / E3 = 1 => 0 pairs (X) / E9 = 1 => 0 pairs (_) G4,G9: 1.. / G4 = 1 => 0 pairs (*) / G9 = 1 => 0 pairs (X) B2,F2: 2.. / B2 = 2 => 0 pairs (*) / F2 = 2 => 0 pairs (X) B5,H5: 2.. / B5 = 2 => 0 pairs (X) / H5 = 2 => 0 pairs (_) F8,H8: 2.. / F8 = 2 => 0 pairs (*) / H8 = 2 => 0 pairs (X) A3,A6: 2.. / A3 = 2 => 0 pairs (X) / A6 = 2 => 0 pairs (_) E3,E7: 2.. / E3 = 2 => 0 pairs (*) / E7 = 2 => 0 pairs (X) G6,G7: 2.. / G6 = 2 => 0 pairs (X) / G7 = 2 => 0 pairs (_) D5,F5: 3.. / D5 = 3 => 6 pairs (_) / F5 = 3 => 6 pairs (_) B1,C1: 4.. / B1 = 4 => 6 pairs (_) / C1 = 4 => 6 pairs (_) B6,C6: 4.. / B6 = 4 => 6 pairs (_) / C6 = 4 => 6 pairs (_) D7,D9: 4.. / D7 = 4 => 6 pairs (_) / D9 = 4 => 6 pairs (_) H7,H9: 4.. / H7 = 4 => 6 pairs (_) / H9 = 4 => 6 pairs (_) D7,H7: 4.. / D7 = 4 => 6 pairs (_) / H7 = 4 => 6 pairs (_) D9,H9: 4.. / D9 = 4 => 6 pairs (_) / H9 = 4 => 6 pairs (_) B1,B6: 4.. / B1 = 4 => 6 pairs (_) / B6 = 4 => 6 pairs (_) C1,C6: 4.. / C1 = 4 => 6 pairs (_) / C6 = 4 => 6 pairs (_) A4,B5: 5.. / A4 = 5 => 0 pairs (*) / B5 = 5 => 0 pairs (X) E4,E6: 7.. / E4 = 7 => 6 pairs (_) / E6 = 7 => 7 pairs (_) B8,C8: 7.. / B8 = 7 => 6 pairs (_) / C8 = 7 => 4 pairs (_) G1,G3: 8.. / G1 = 8 => 6 pairs (_) / G3 = 8 => 6 pairs (_) B8,C8: 8.. / B8 = 8 => 4 pairs (_) / C8 = 8 => 6 pairs (_) C1,C3: 9.. / C1 = 9 => 6 pairs (_) / C3 = 9 => 6 pairs (_) H2,I2: 9.. / H2 = 9 => 6 pairs (_) / I2 = 9 => 6 pairs (_) * DURATION: 0:00:40.333143 START: 13:47:58.503360 END: 13:48:38.836503 2017-05-04 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B8,C8,D8,H8) * .......128...4...........64.9.2.4...7.....4.....5.1...915......4...3.9..632...... * PAIR A1: 3,5 BLK 1 A3: 3,5,1,2 # reduction candidate for 3,5 A3: 3,5 => CTR * .......128...4...........6419.2.4...75....4212..5.1...915...2..4..132956632...1.. A3: 1,2 # 7 pairs * PAIR A1: 3,5 ROW 1 F1: 3,5,6,7,8,9 # reduction candidate for 3,5 F1: 3,5 => CTR * 5....3.128...42...27.....6419.2.4...72.3..4.13..5.12..915.2....48713.92.632.5.1.. F1: 6,7,8,9 # 6 pairs G1: 3,5,7,8 # reduction candidate for 3,5 G1: 3,5 => CTR * 5.....31286..42...27....86419.2.4...72....4.13..5.12..915.2....48713.92.632.5.1.. G1: 7,8 # 7 pairs * PAIR A1: 3,5 COL A A4: 3,5,1 # reduction candidate for 3,5 A4: 3,5 => SOLVED * 349756812826143579157829364593264187761398425284571693915487236478632951632915748 A4: 1 => CTR * .......128...4...........6419.2.4...75....421...5.1...915...2..4..132956632...1.. * PAIR A6: 2,3 ROW 6 G6: 2,3,6,7 # reduction candidate for 2,3 G6: 2,3 # 7 pairs H6: 2,3,7,8,9 # reduction candidate for 2,3 H6: 2,3 => CTR * .......1282..4........2..64.9.2.4...7.....42.2..5.1.3.915...2.34...32956632.1.... H6: 7,8,9 # 6 pairs * PAIR A6: 2,3 COL A A3: 2,3,1,5 # reduction candidate for 2,3 A3: 2,3 => CTR * .......128...4...........6419.2.4...75....421...5.1...915...2..4..132956632...1.. A3: 1,5 => SOLVED * 349756812826143579157829364593264187761398425284571693915487236478632951632915748 * PAIR D8: 1,6 ROW 8 I8: 1,6,5 # reduction candidate for 1,6 I8: 5 => CTR * .......128.1.4........1..6419.2.4...7.....4.....5.1...915......4..136925632...... I8: 1,6 # 8 pairs * PAIR D8: 1,6 COL D D2: 1,6,3,7 # reduction candidate for 1,6 D2: 3,7 => CTR * .......128.1.4...........6419.2.4...75....421...5.1...915...2..4..132956632...1.. D2: 1,6 # 7 pairs * PAIR H8: 2,5 ROW 8 F8: 2,5,6 # reduction candidate for 2,5 F8: 6 => CTR * 5......128.1.425..27..15.6419.2.4...72....4513..5.12..915.2....487136925632.5.1.. F8: 2,5 # 8 pairs * PAIR H8: 2,5 COL H H5: 2,5,8,9 # reduction candidate for 2,5 H5: 8,9 => CTR * 5......128...42...27.....6419.2.4...72....4.53..5.1...915.2....487.3.92.632...15. H5: 2,5 # 7 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-316-base-pr-000.dot * REASONING * DIS # A3: 3,5 => CTR => A3: 1,2 * DIS # F1: 3,5 => CTR => F1: 6,7,8,9 * DIS # G1: 3,5 => CTR => G1: 7,8 * PRF # A4: 3,5 => SOL * DIS # A4: 1 => CTR => A4: 3,5 * DIS # H6: 2,3 => CTR => H6: 7,8,9 * DIS # A3: 2,3 => CTR => A3: 1,5 * PRF # A3: 1,5 => SOL * DIS # I8: 5 => CTR => I8: 1,6 * DIS # D2: 3,7 => CTR => D2: 1,6 * DIS # F8: 6 => CTR => F8: 2,5 * DIS # H5: 8,9 => CTR => H5: 2,5 * CNT 12 HDP CHAINS / 21 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B8,C8,D8,H8) * .......128...4...........64.9.2.4...7.....4.....5.1...915......4...3.9..632...... * PAIR A1: 3,5 BLK 1 A3: 3,5,1,2 # reduction candidate for 3,5 A3: 3,5 => CTR * .......128...4...........6419.2.4...75....4212..5.1...915...2..4..132956632...1.. * PAIR A1: 3,5 ROW 1 F1: 3,5,6,7,8,9 # reduction candidate for 3,5 F1: 3,5 => CTR * 5....3.128...42...27.....6419.2.4...72.3..4.13..5.12..915.2....48713.92.632.5.1.. G1: 3,5,7,8 # reduction candidate for 3,5 G1: 3,5 => CTR * 5.....31286..42...27....86419.2.4...72....4.13..5.12..915.2....48713.92.632.5.1.. * RESTART * PAIR A1: 3,5 COL A A4: 3,5,1 # reduction candidate for 3,5 A4: 3,5 => SOLVED * 349756812826143579157829364593264187761398425284571693915487236478632951632915748 * DURATION: 0:00:05.944936 START: 13:48:55.155335 END: 13:49:01.100271 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-316-base-pr-001.dot * REASONING * DIS # A3: 3,5 => CTR => A3: 1,2 * DIS A3: 1,2 # F1: 3,5 => CTR => F1: 6,7,8,9 * DIS A3: 1,2 + F1: 6,7,8,9 # G1: 3,5 => CTR => G1: 7,8 * PRF A3: 1,2 + F1: 6,7,8,9 + G1: 7,8 # A4: 3,5 => SOL * STA A3: 1,2 + F1: 6,7,8,9 + G1: 7,8 + A4: 3,5 * CNT 4 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 316 solution: 349756812826143579157829364593264187761398425284571693915487236478632951632915748 info: 2899 FNBHWY S8.f 12 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 349756812826143579157829364593264187761398425284571693915487236478632951632915748 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 # A3: 3,5 => CTR => A3: 1,2 * INC # A3: 1,2 => UNS * DIS # F1: 3,5 => CTR => F1: 6,7,8,9 * INC # F1: 6,7,8,9 => UNS * DIS # G1: 3,5 => CTR => G1: 7,8 * INC # G1: 7,8 => UNS * PRF # A4: 3,5 => SOL * DIS # A4: 1 => CTR => A4: 3,5 * INC # G6: 2,3 => UNS * DIS # H6: 2,3 => CTR => H6: 7,8,9 * INC # H6: 7,8,9 => UNS * DIS # A3: 2,3 => CTR => A3: 1,5 * PRF # A3: 1,5 => SOL * INC # I8: 1,6 => UNS * DIS # I8: 5 => CTR => I8: 1,6 * INC # D2: 1,6 => UNS * DIS # D2: 3,7 => CTR => D2: 1,6 * INC # F8: 2,5 => UNS * DIS # F8: 6 => CTR => F8: 2,5 * INC # H5: 2,5 => UNS * DIS # H5: 8,9 => CTR => H5: 2,5 * CNT 21 HDP CHAINS / 21 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A3: 3,5 => CTR => A3: 1,2 * DIS A3: 1,2 # F1: 3,5 => CTR => F1: 6,7,8,9 * DIS A3: 1,2 + F1: 6,7,8,9 # G1: 3,5 => CTR => G1: 7,8 * PRF A3: 1,2 + F1: 6,7,8,9 + G1: 7,8 # A4: 3,5 => SOL * STA A3: 1,2 + F1: 6,7,8,9 + G1: 7,8 + A4: 3,5 * CNT 4 HDP CHAINS / 4 HYP OPENED