Analysis of xx-top500-281-base.sdk
Contents
Original Sudoku
level: medium
position: 1...2.7...635.................4...352...1...........6.7.....1...5.6......8....... initial
Autosolve
position: 1...2.7...635...............1.4...352...1...........617.....1...5.6..3...8....... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C1: 4,9 => SOL * DIS # A3: 4,9 => CTR => A3: 5,8 * DIS # F1: 4,9 => CTR => F1: 3,6,8 * DIS # H1: 4,9 => CTR => H1: 5,8 * DIS # I1: 4,9 => CTR => I1: 3,6,8 * DIS # B6: 4,9 => CTR => B6: 3,7 * DIS # B7: 4,9 => CTR => B7: 2,3 * DIS # B7: 4,9 => CTR => B7: 2,3 * PRF # C7: 4,9 => SOL * DIS # A9: 4,9 => CTR => A9: 3,6 * DIS # A3: 4,9 => CTR => A3: 5,8 * DIS # A6: 4,9 => CTR => A6: 3,5,8 * CNT 12 HDP CHAINS / 33 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C1: 4,9 => SOL * STA C1: 4,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1...2.7...635.................4...352...1...........6.7.....1...5.6......8....... | initial |
| 1...2.7...635...............1.4...352...1...........617.....1...5.6..3...8....... | autosolve |
| 194826753863574912527139684918467235246315897375982461739258146452691378681743529 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) B1: 4,9 B3: 2,7 C3: 2,7 G3: 5,6 C5: 5,6 F5: 5,6 A8: 4,9 G9: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H2,H3: 1.. / H2 = 1 => 8 pairs (_) / H3 = 1 => 0 pairs (X) C8,C9: 1.. / C8 = 1 => 8 pairs (_) / C9 = 1 => 8 pairs (_) F2,H2: 1.. / F2 = 1 => 0 pairs (X) / H2 = 1 => 8 pairs (_) C8,F8: 1.. / C8 = 1 => 8 pairs (_) / F8 = 1 => 8 pairs (_) D3,D9: 1.. / D3 = 1 => 8 pairs (_) / D9 = 1 => 0 pairs (X) B3,C3: 2.. / B3 = 2 => 6 pairs (_) / C3 = 2 => 0 pairs (X) H2,I2: 2.. / H2 = 2 => 0 pairs (X) / I2 = 2 => 8 pairs (_) G4,G6: 2.. / G4 = 2 => 8 pairs (_) / G6 = 2 => 10 pairs (_) F4,G4: 2.. / F4 = 2 => 10 pairs (_) / G4 = 2 => 8 pairs (_) B3,B7: 2.. / B3 = 2 => 6 pairs (_) / B7 = 2 => 0 pairs (X) I1,I3: 3.. / I1 = 3 => 0 pairs (*) / I3 = 3 => 0 pairs (X) B7,A9: 3.. / B7 = 3 => 0 pairs (*) / A9 = 3 => 0 pairs (X) B5,D5: 3.. / B5 = 3 => 0 pairs (X) / D5 = 3 => 15 pairs (_) A6,A9: 3.. / A6 = 3 => 0 pairs (*) / A9 = 3 => 0 pairs (X) C1,A3: 5.. / C1 = 5 => 0 pairs (X) / A3 = 5 => 0 pairs (_) C1,H1: 5.. / C1 = 5 => 0 pairs (X) / H1 = 5 => 0 pairs (_) C5,F5: 5.. / C5 = 5 => 0 pairs (X) / F5 = 5 => 0 pairs (_) A3,A6: 5.. / A3 = 5 => 0 pairs (*) / A6 = 5 => 0 pairs (X) G3,G9: 5.. / G3 = 5 => 0 pairs (X) / G9 = 5 => 0 pairs (_) F1,I1: 6.. / F1 = 6 => 0 pairs (*) / I1 = 6 => 0 pairs (X) C5,F5: 6.. / C5 = 6 => 0 pairs (*) / F5 = 6 => 0 pairs (X) C7,I7: 6.. / C7 = 6 => 0 pairs (X) / I7 = 6 => 0 pairs (_) A4,A9: 6.. / A4 = 6 => 0 pairs (X) / A9 = 6 => 0 pairs (_) E3,E4: 6.. / E3 = 6 => 0 pairs (X) / E4 = 6 => 0 pairs (_) G3,G9: 6.. / G3 = 6 => 0 pairs (*) / G9 = 6 => 0 pairs (X) B3,C3: 7.. / B3 = 7 => 0 pairs (X) / C3 = 7 => 6 pairs (_) E2,F2: 7.. / E2 = 7 => 8 pairs (_) / F2 = 7 => 8 pairs (_) H5,I5: 7.. / H5 = 7 => 8 pairs (_) / I5 = 7 => 8 pairs (_) B3,B6: 7.. / B3 = 7 => 0 pairs (X) / B6 = 7 => 6 pairs (_) D6,D9: 7.. / D6 = 7 => 0 pairs (X) / D9 = 7 => 8 pairs (_) * DURATION: 0:00:48.777995 START: 12:32:35.483396 END: 12:33:24.261391 2017-05-04 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B1,B3,C3,C5,F5,G3,G9) * 1...2.7...635...............1.4...352...1...........617.....1...5.6..3...8....... * PAIR B1: 4,9 BLK 1 C1: 4,9,5,8 # reduction candidate for 4,9 C1: 4,9 => SOLVED * 194826753863574912527139684918467235246315897375982461739258146452691378681743529 C1: 5,8 # 9 pairs A2: 4,9,8 # reduction candidate for 4,9 A2: 4,9 # 13 pairs A3: 4,9,5,8 # reduction candidate for 4,9 A3: 4,9 => CTR * 1.5.2.7..8635...............1.4...352.6.15...5......617.....1.6.5.6..3...8....... A3: 5,8 # 9 pairs * PAIR B1: 4,9 ROW 1 F1: 4,9,3,6,8 # reduction candidate for 4,9 F1: 4,9 => CTR * 1...2.7.6.635...........5.3.1.4...352...1....5......617.6...1...5.6..3...8....... F1: 3,6,8 # 8 pairs H1: 4,9,5,8 # reduction candidate for 4,9 H1: 4,9 => CTR * 1.5.2.7...635...............1.4...352.6.15...5......617.....1.6.5.6..3...8....... H1: 5,8 # 9 pairs I1: 4,9,3,6,8 # reduction candidate for 4,9 I1: 4,9 => CTR * 1..3267...635...........6.3.1.46..35236.15..........617...531.6.5.6..3..68....5.. I1: 3,6,8 # 8 pairs * PAIR B1: 4,9 COL B B5: 4,9,3 # reduction candidate for 4,9 B5: 4,9 # 15 pairs B6: 4,9,3,7 # reduction candidate for 4,9 B6: 4,9 => CTR * 1...2.756.635......72......61.4...35235.16..........6172....1...5.6..3..38....... B6: 3,7 # 9 pairs B7: 4,9,2,3 # reduction candidate for 4,9 B7: 4,9 => CTR * 1...2.756.635......271.....61.4...35235.16....7.....617.....1...5.6..3..38.7..... B7: 2,3 # 9 pairs * PAIR A8: 4,9 BLK 7 B7: 4,9,2,3 # reduction candidate for 4,9 B7: 4,9 => CTR * 1...2.756.635......271.....61.4...35235.16....7.....617.....1...5.6..3..38.7..... B7: 2,3 # 9 pairs C7: 4,9,2,6 # reduction candidate for 4,9 C7: 4,9 => SOLVED * 194826753863574912527139684918467235246315897375982461739258146452691378681743529 C7: 2,6 # 9 pairs C8: 4,9,1,2 # reduction candidate for 4,9 C8: 4,9 # 16 pairs A9: 4,9,3,6 # reduction candidate for 4,9 A9: 4,9 => CTR * 1...2.756.635..............61.4...352.5.16...3......6173....1...5.6..3...8....... A9: 3,6 # 9 pairs C9: 4,9,1,2,6 # reduction candidate for 4,9 C9: 4,9 # 14 pairs * PAIR A8: 4,9 ROW 8 E8: 4,9,7,8 # reduction candidate for 4,9 E8: 4,9 # 10 pairs F8: 4,9,1,2,7,8 # reduction candidate for 4,9 F8: 4,9 # 10 pairs H8: 4,9,2,7,8 # reduction candidate for 4,9 H8: 4,9 # 11 pairs I8: 4,9,2,7,8 # reduction candidate for 4,9 I8: 4,9 # 11 pairs * PAIR A8: 4,9 COL A A2: 4,9,8 # reduction candidate for 4,9 A2: 4,9 # 13 pairs A3: 4,9,5,8 # reduction candidate for 4,9 A3: 4,9 => CTR * 1.5.2.7..8635...............1.4...352.6.15...5......617.....1.6.5.6..3...8....... A3: 5,8 # 9 pairs A6: 4,9,3,5,8 # reduction candidate for 4,9 A6: 4,9 => CTR * 1...2.7...635.....5.....6...1.46..352.6.15.....5....617.....1.6.5.6..3...8....... A6: 3,5,8 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-281-base-pr-000.dot * REASONING * PRF # C1: 4,9 => SOL * DIS # A3: 4,9 => CTR => A3: 5,8 * DIS # F1: 4,9 => CTR => F1: 3,6,8 * DIS # H1: 4,9 => CTR => H1: 5,8 * DIS # I1: 4,9 => CTR => I1: 3,6,8 * DIS # B6: 4,9 => CTR => B6: 3,7 * DIS # B7: 4,9 => CTR => B7: 2,3 * DIS # B7: 4,9 => CTR => B7: 2,3 * PRF # C7: 4,9 => SOL * DIS # A9: 4,9 => CTR => A9: 3,6 * DIS # A3: 4,9 => CTR => A3: 5,8 * DIS # A6: 4,9 => CTR => A6: 3,5,8 * CNT 12 HDP CHAINS / 33 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B1,B3,C3,C5,F5,G3,G9) * 1...2.7...635...............1.4...352...1...........617.....1...5.6..3...8....... * PAIR B1: 4,9 BLK 1 C1: 4,9,5,8 # reduction candidate for 4,9 C1: 4,9 => SOLVED * 194826753863574912527139684918467235246315897375982461739258146452691378681743529 * DURATION: 0:00:02.756341 START: 12:33:50.690353 END: 12:33:53.446694 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-281-base-pr-001.dot * REASONING * PRF # C1: 4,9 => SOL * STA C1: 4,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 281 solution: 194826753863574912527139684918467235246315897375982461739258146452691378681743529 info: 2266 FNBHWXY S8.f 25224 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 194826753863574912527139684918467235246315897375982461739258146452691378681743529 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:
* PRF # C1: 4,9 => SOL * INC # C1: 5,8 => UNS * INC # A2: 4,9 => UNS * DIS # A3: 4,9 => CTR => A3: 5,8 * INC # A3: 5,8 => UNS * DIS # F1: 4,9 => CTR => F1: 3,6,8 * INC # F1: 3,6,8 => UNS * DIS # H1: 4,9 => CTR => H1: 5,8 * INC # H1: 5,8 => UNS * DIS # I1: 4,9 => CTR => I1: 3,6,8 * INC # I1: 3,6,8 => UNS * INC # B5: 4,9 => UNS * DIS # B6: 4,9 => CTR => B6: 3,7 * INC # B6: 3,7 => UNS * DIS # B7: 4,9 => CTR => B7: 2,3 * INC # B7: 2,3 => UNS * DIS # B7: 4,9 => CTR => B7: 2,3 * INC # B7: 2,3 => UNS * PRF # C7: 4,9 => SOL * INC # C7: 2,6 => UNS * INC # C8: 4,9 => UNS * DIS # A9: 4,9 => CTR => A9: 3,6 * INC # A9: 3,6 => UNS * INC # C9: 4,9 => UNS * INC # E8: 4,9 => UNS * INC # F8: 4,9 => UNS * INC # H8: 4,9 => UNS * INC # I8: 4,9 => UNS * INC # A2: 4,9 => UNS * DIS # A3: 4,9 => CTR => A3: 5,8 * INC # A3: 5,8 => UNS * DIS # A6: 4,9 => CTR => A6: 3,5,8 * INC # A6: 3,5,8 => UNS * CNT 33 HDP CHAINS / 33 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C1: 4,9 => SOL * STA C1: 4,9 * CNT 1 HDP CHAINS / 1 HYP OPENED