Analysis of xx-top500-449-base.sdk
Contents
Original Sudoku
level: medium
position: .5.2.8.........7.....5.....7...3.6........28...1......4...7...1.8.....5....9..... initial
Autosolve
position: .572.8..6......7.5...5.7...7...3.61....7..28...1...57.4...7...1.8.....57.7.9..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 3,9 => CTR => B3: 1,2,4,6 * DIS # G1: 3,9 => CTR => G1: 1,4 * DIS # A5: 3,9 => CTR => A5: 5,6 * PRF # A6: 3,9 => SOL * DIS # A8: 3,9 => CTR => A8: 1,2,6 * DIS # D6: 4,8 => CTR => D6: 6 * PRF # C4: 4,8 => SOL * DIS # C4: 2,5,9 => CTR => C4: 4,8 * DIS # B4: 4,9 => CTR => B4: 2 * DIS # C4: 4,9 => CTR => C4: 2,5,8 * DIS # F4: 4,9 => CTR => F4: 2,5 * DIS # E9: 2,8 => CTR => E9: 1,4,5,6 * PRF # E9: 1,4,5,6 => SOL * CNT 13 HDP CHAINS / 28 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B3: 3,9 => CTR => B3: 1,2,4,6 * DIS B3: 1,2,4,6 # G1: 3,9 => CTR => G1: 1,4 * DIS B3: 1,2,4,6 + G1: 1,4 # A5: 3,9 => CTR => A5: 5,6 * PRF B3: 1,2,4,6 + G1: 1,4 + A5: 5,6 # A6: 3,9 => SOL * STA B3: 1,2,4,6 + G1: 1,4 + A5: 5,6 + A6: 3,9 * CNT 4 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .5.2.8.........7.....5.....7...3.6........28...1......4...7...1.8.....5....9..... | initial |
| .572.8..6......7.5...5.7...7...3.61....7..28...1...57.4...7...1.8.....57.7.9..... | autosolve |
| 357298146842163795619547832728435619564719283931682574495876321186324957273951468 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) A1: 3,9 I3: 2,8 D4: 4,8 I4: 4,9 I9: 2,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,B3: 1.. / B2 = 1 => 0 pairs (X) / B3 = 1 => 6 pairs (_) G1,G3: 1.. / G1 = 1 => 6 pairs (_) / G3 = 1 => 0 pairs (X) E5,F5: 1.. / E5 = 1 => 0 pairs (*) / F5 = 1 => 0 pairs (X) A8,A9: 1.. / A8 = 1 => 0 pairs (*) / A9 = 1 => 0 pairs (X) E1,G1: 1.. / E1 = 1 => 0 pairs (X) / G1 = 1 => 6 pairs (_) D2,D8: 1.. / D2 = 1 => 9 pairs (_) / D8 = 1 => 0 pairs (X) I3,I9: 2.. / I3 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) D2,F2: 3.. / D2 = 3 => 0 pairs (X) / F2 = 3 => 5 pairs (_) I5,I6: 3.. / I5 = 3 => 6 pairs (_) / I6 = 3 => 6 pairs (_) C4,F4: 5.. / C4 = 5 => 0 pairs (X) / F4 = 5 => 0 pairs (_) C7,F7: 5.. / C7 = 5 => 0 pairs (*) / F7 = 5 => 0 pairs (X) A5,A9: 5.. / A5 = 5 => 0 pairs (*) / A9 = 5 => 0 pairs (X) E5,E9: 5.. / E5 = 5 => 0 pairs (X) / E9 = 5 => 0 pairs (_) H7,H9: 6.. / H7 = 6 => 6 pairs (_) / H9 = 6 => 5 pairs (_) A2,C2: 8.. / A2 = 8 => 0 pairs (*) / C2 = 8 => 0 pairs (X) G3,I3: 8.. / G3 = 8 => 0 pairs (*) / I3 = 8 => 0 pairs (X) C4,A6: 8.. / C4 = 8 => 0 pairs (*) / A6 = 8 => 0 pairs (X) D7,E9: 8.. / D7 = 8 => 0 pairs (*) / E9 = 8 => 0 pairs (X) C4,D4: 8.. / C4 = 8 => 0 pairs (*) / D4 = 8 => 0 pairs (X) D7,G7: 8.. / D7 = 8 => 0 pairs (*) / G7 = 8 => 0 pairs (X) A2,A6: 8.. / A2 = 8 => 0 pairs (*) / A6 = 8 => 0 pairs (X) C2,C4: 8.. / C2 = 8 => 0 pairs (X) / C4 = 8 => 0 pairs (_) E6,E9: 8.. / E6 = 8 => 0 pairs (*) / E9 = 8 => 0 pairs (X) I3,I9: 8.. / I3 = 8 => 3 pairs (_) / I9 = 8 => 0 pairs (*) * DURATION: 0:00:36.925856 START: 18:05:25.916508 END: 18:06:02.842364 2017-05-04 * CP COUNT: (24) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,D4,I3,I4,I9) * .572.8..6......7.5...5.7...7...3.61....7..28...1...57.4...7...1.8.....57.7.9..... * PAIR A1: 3,9 BLK 1 A3: 3,9,2,6 # reduction candidate for 3,9 A3: 3,9 # 7 pairs B3: 3,9,1,2,4,6 # reduction candidate for 3,9 B3: 3,9 => CTR * .572.8..681.3.97.52..5.7..87.84356195..79128...168257.4.587...168.12..5717295.... B3: 1,2,4,6 # 5 pairs C3: 3,9,2,4,6 # reduction candidate for 3,9 C3: 3,9 # 7 pairs * PAIR A1: 3,9 ROW 1 G1: 3,9,1,4 # reduction candidate for 3,9 G1: 3,9 => CTR * .57218.4681.3.97252..5.71.87...3561.5..7.128...1.8257.4.587...1.8.12.45717.9548.2 G1: 1,4 # 6 pairs H1: 3,9,4 # reduction candidate for 3,9 H1: 3,9 # 8 pairs * PAIR A1: 3,9 COL A A5: 3,9,5,6 # reduction candidate for 3,9 A5: 3,9 => CTR * .572.81.6...1.37.5.1.5.7...7.583.61....75128.8.1...57.4...758.118.....5757.91...2 A5: 5,6 # 6 pairs A6: 3,9,2,6,8 # reduction candidate for 3,9 A6: 3,9 => SOLVED * 357298146842163795619547832728435619564719283931682574495876321186324957273951468 A6: 2,6,8 # 5 pairs A8: 3,9,1,2,6 # reduction candidate for 3,9 A8: 3,9 => CTR * .572.8..68.....7.52..5.7..87.84356195..7..28.6.1.8257.4.587...1.8..2..5717.95.... A8: 1,2,6 # 5 pairs * PAIR D4: 4,8 BLK 5 D6: 4,8,6 # reduction candidate for 4,8 D6: 4,8 => CTR * .572.8..6......7.5...5.7..87...3.61....75128...1...57.4...7.8.1.8.....57.7.98...2 D6: 6 # 6 pairs E6: 4,8,2,6,9 # reduction candidate for 4,8 E6: 4,8 # 8 pairs * PAIR D4: 4,8 ROW 4 C4: 4,8,2,5,9 # reduction candidate for 4,8 C4: 4,8 => SOLVED * 357298146842163795619547832728435619564719283931682574495876321186324957273951468 C4: 2,5,9 => CTR * .572.8..6..8...7.5...5.7..87..83.61....75128.8.1...57.4...7.8.1.8.....57.7.98...2 * PAIR I4: 4,9 BLK 6 I5: 4,9,3 # reduction candidate for 4,9 I5: 4,9 # 6 pairs I6: 4,9,3 # reduction candidate for 4,9 I6: 4,9 # 6 pairs * PAIR I4: 4,9 ROW 4 B4: 4,9,2 # reduction candidate for 4,9 B4: 4,9 => CTR * .572.8..6..8...7.5...5.7..87..83.61....75128.8.1...57.4...7.8.1.8.....57.7.98...2 B4: 2 # 5 pairs C4: 4,9,2,5,8 # reduction candidate for 4,9 C4: 4,9 => CTR * .572.8..6..8...7.5...5.7...7..83561....7..28.8.1...57.4.5.7.8.1.8.....57.7.9..... C4: 2,5,8 # 5 pairs F4: 4,9,2,5 # reduction candidate for 4,9 F4: 4,9 => CTR * .572.8..6......7.5...5.7...7.583.61....7..28.8.1...57.4...758.1.8.....5757.981..2 F4: 2,5 # 6 pairs * PAIR I9: 2,8 ROW 9 E9: 2,8,1,4,5,6 # reduction candidate for 2,8 E9: 2,8 => CTR * .572.8..6......7.5...5.7...7...3.61....75128...1...57.4...7...1.8.....57.7.9..... E9: 1,4,5,6 => SOLVED * 357298146842163795619547832728435619564719283931682574495876321186324957273951468 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-449-base-pr-000.dot * REASONING * DIS # B3: 3,9 => CTR => B3: 1,2,4,6 * DIS # G1: 3,9 => CTR => G1: 1,4 * DIS # A5: 3,9 => CTR => A5: 5,6 * PRF # A6: 3,9 => SOL * DIS # A8: 3,9 => CTR => A8: 1,2,6 * DIS # D6: 4,8 => CTR => D6: 6 * PRF # C4: 4,8 => SOL * DIS # C4: 2,5,9 => CTR => C4: 4,8 * DIS # B4: 4,9 => CTR => B4: 2 * DIS # C4: 4,9 => CTR => C4: 2,5,8 * DIS # F4: 4,9 => CTR => F4: 2,5 * DIS # E9: 2,8 => CTR => E9: 1,4,5,6 * PRF # E9: 1,4,5,6 => SOL * CNT 13 HDP CHAINS / 28 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,D4,I3,I4,I9) * .572.8..6......7.5...5.7...7...3.61....7..28...1...57.4...7...1.8.....57.7.9..... * PAIR A1: 3,9 BLK 1 A3: 3,9,2,6 # reduction candidate for 3,9 A3: 3,9 # 7 pairs B3: 3,9,1,2,4,6 # reduction candidate for 3,9 B3: 3,9 => CTR * .572.8..681.3.97.52..5.7..87.84356195..79128...168257.4.587...168.12..5717295.... C3: 3,9,2,4,6 # reduction candidate for 3,9 C3: 3,9 # 7 pairs * PAIR A1: 3,9 ROW 1 G1: 3,9,1,4 # reduction candidate for 3,9 G1: 3,9 => CTR * .57218.4681.3.97252..5.71.87...3561.5..7.128...1.8257.4.587...1.8.12.45717.9548.2 H1: 3,9,4 # reduction candidate for 3,9 H1: 3,9 # 8 pairs * RESTART * PAIR A1: 3,9 ROW 1 H1: 3,9,4 # reduction candidate for 3,9 H1: 3,9 # 8 pairs H1: 4 # 5 pairs * PAIR A1: 3,9 COL A A5: 3,9,5,6 # reduction candidate for 3,9 A5: 3,9 => CTR * .572.81.6...1.37.5.1.5.7...7.583.61....75128.8.1...57.4...758.118.....5757.91...2 A6: 3,9,2,6,8 # reduction candidate for 3,9 A6: 3,9 => SOLVED * 357298146842163795619547832728435619564719283931682574495876321186324957273951468 * DURATION: 0:00:09.402971 START: 18:06:25.314901 END: 18:06:34.717872 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-449-base-pr-001.dot * REASONING * DIS # B3: 3,9 => CTR => B3: 1,2,4,6 * DIS B3: 1,2,4,6 # G1: 3,9 => CTR => G1: 1,4 * DIS B3: 1,2,4,6 + G1: 1,4 # A5: 3,9 => CTR => A5: 5,6 * PRF B3: 1,2,4,6 + G1: 1,4 + A5: 5,6 # A6: 3,9 => SOL * STA B3: 1,2,4,6 + G1: 1,4 + A5: 5,6 + A6: 3,9 * CNT 4 HDP CHAINS / 9 HYP OPENED
Header Info
Top 500 Minimum 17 449 solution: 357298146842163795619547832728435619564719283931682574495876321186324957273951468 info: 95365 FNBWYK S8.f 20176 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 357298146842163795619547832728435619564719283931682574495876321186324957273951468 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 # A3: 3,9 => UNS * DIS # B3: 3,9 => CTR => B3: 1,2,4,6 * INC # B3: 1,2,4,6 => UNS * INC # C3: 3,9 => UNS * DIS # G1: 3,9 => CTR => G1: 1,4 * INC # G1: 1,4 => UNS * INC # H1: 3,9 => UNS * DIS # A5: 3,9 => CTR => A5: 5,6 * INC # A5: 5,6 => UNS * PRF # A6: 3,9 => SOL * INC # A6: 2,6,8 => UNS * DIS # A8: 3,9 => CTR => A8: 1,2,6 * INC # A8: 1,2,6 => UNS * DIS # D6: 4,8 => CTR => D6: 6 * INC # D6: 6 => UNS * INC # E6: 4,8 => UNS * PRF # C4: 4,8 => SOL * DIS # C4: 2,5,9 => CTR => C4: 4,8 * INC # I5: 4,9 => UNS * INC # I6: 4,9 => UNS * DIS # B4: 4,9 => CTR => B4: 2 * INC # B4: 2 => UNS * DIS # C4: 4,9 => CTR => C4: 2,5,8 * INC # C4: 2,5,8 => UNS * DIS # F4: 4,9 => CTR => F4: 2,5 * INC # F4: 2,5 => UNS * DIS # E9: 2,8 => CTR => E9: 1,4,5,6 * PRF # E9: 1,4,5,6 => SOL * CNT 28 HDP CHAINS / 28 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A3: 3,9 => UNS * DIS # B3: 3,9 => CTR => B3: 1,2,4,6 * INC B3: 1,2,4,6 # C3: 3,9 => UNS * DIS B3: 1,2,4,6 # G1: 3,9 => CTR => G1: 1,4 * INC B3: 1,2,4,6 + G1: 1,4 # H1: 3,9 => UNS * INC B3: 1,2,4,6 + G1: 1,4 # H1: 3,9 => UNS * INC B3: 1,2,4,6 + G1: 1,4 # H1: 4 => UNS * DIS B3: 1,2,4,6 + G1: 1,4 # A5: 3,9 => CTR => A5: 5,6 * PRF B3: 1,2,4,6 + G1: 1,4 + A5: 5,6 # A6: 3,9 => SOL * STA B3: 1,2,4,6 + G1: 1,4 + A5: 5,6 + A6: 3,9 * CNT 9 HDP CHAINS / 9 HYP OPENED