Analysis of xx-top500-044-base.sdk
Contents
Original Sudoku
level: medium
position: 1.....73....5.6........9.......1...3.......564.........6.2.........8.4..59....... initial
Autosolve
position: 156...739...5.6......1.9...6...1..43.......564.........6.2.........8.4..59....... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F1: 2 => CTR => F1: 4,8 * DIS # E5: 2,4 => CTR => E5: 9 * PRF # E5: 9 => SOL * DIS # A2: 3,7 => CTR => A2: 2,8,9 * DIS # B3: 3,7 => CTR => B3: 2,4,8 * DIS # D6: 3,8 => CTR => D6: 6,9 * DIS # D9: 4,6 => CTR => D9: 3,7 * PRF # F7: 3,5 => SOL * DIS # D9: 3,6 => CTR => D9: 4,7 * CNT 9 HDP CHAINS / 24 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F1: 2 => CTR => F1: 4,8 * DIS F1: 4,8 # A2: 3,7 => CTR => A2: 2,8,9 * DIS F1: 4,8 + A2: 2,8,9 # B3: 3,7 => CTR => B3: 2,4,8 * DIS F1: 4,8 + A2: 2,8,9 + B3: 2,4,8 # D6: 3,8 => CTR => D6: 6,9 * PRF F1: 4,8 + A2: 2,8,9 + B3: 2,4,8 + D6: 6,9 # F7: 3,5 => SOL * STA F1: 4,8 + A2: 2,8,9 + B3: 2,4,8 + D6: 6,9 + F7: 3,5 * CNT 5 HDP CHAINS / 17 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1.....73....5.6........9.......1...3.......564.........6.2.........8.4..59....... | initial |
| 156...739...5.6......1.9...6...1..43.......564.........6.2.........8.4..59....... | autosolve |
| 156428739972536814348179625625817943781394256439652178867243591213985467594761382 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) D1: 4,8 E1: 2,4 E2: 3,7 E3: 3,7 G3: 5,6 D8: 6,9 E9: 4,6 G7: 3,5 H8: 6,9 G9: 3,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,F1: 2.. / E1 = 2 => 11 pairs (_) / F1 = 2 => 0 pairs (X) E2,E3: 3.. / E2 = 3 => 8 pairs (_) / E3 = 3 => 8 pairs (_) G7,G9: 3.. / G7 = 3 => 0 pairs (X) / G9 = 3 => 0 pairs (_) B2,B3: 4.. / B2 = 4 => 0 pairs (X) / B3 = 4 => 10 pairs (_) I2,I3: 4.. / I2 = 4 => 10 pairs (_) / I3 = 4 => 0 pairs (X) C7,C9: 4.. / C7 = 4 => 11 pairs (_) / C9 = 4 => 0 pairs (*) B2,I2: 4.. / B2 = 4 => 0 pairs (X) / I2 = 4 => 10 pairs (_) B3,I3: 4.. / B3 = 4 => 10 pairs (_) / I3 = 4 => 0 pairs (X) G3,I3: 5.. / G3 = 5 => 0 pairs (X) / I3 = 5 => 0 pairs (_) C4,C6: 5.. / C4 = 5 => 10 pairs (_) / C6 = 5 => 0 pairs (X) C4,F4: 5.. / C4 = 5 => 10 pairs (_) / F4 = 5 => 0 pairs (X) F8,I8: 5.. / F8 = 5 => 0 pairs (*) / I8 = 5 => 0 pairs (X) E6,E7: 5.. / E6 = 5 => 0 pairs (*) / E7 = 5 => 0 pairs (X) G3,G7: 5.. / G3 = 5 => 0 pairs (X) / G7 = 5 => 0 pairs (_) G3,H3: 6.. / G3 = 6 => 0 pairs (*) / H3 = 6 => 0 pairs (X) D6,E6: 6.. / D6 = 6 => 0 pairs (*) / E6 = 6 => 0 pairs (X) D8,H8: 6.. / D8 = 6 => 0 pairs (X) / H8 = 6 => 0 pairs (_) E6,E9: 6.. / E6 = 6 => 0 pairs (X) / E9 = 6 => 0 pairs (_) G3,G9: 6.. / G3 = 6 => 0 pairs (*) / G9 = 6 => 0 pairs (X) E2,E3: 7.. / E2 = 7 => 8 pairs (_) / E3 = 7 => 8 pairs (_) H6,I6: 7.. / H6 = 7 => 10 pairs (_) / I6 = 7 => 10 pairs (_) D1,F1: 8.. / D1 = 8 => 11 pairs (_) / F1 = 8 => 9 pairs (_) A2,C2: 9.. / A2 = 9 => 10 pairs (_) / C2 = 9 => 0 pairs (X) E7,D8: 9.. / E7 = 9 => 0 pairs (X) / D8 = 9 => 0 pairs (_) H7,H8: 9.. / H7 = 9 => 0 pairs (*) / H8 = 9 => 0 pairs (X) E7,H7: 9.. / E7 = 9 => 0 pairs (X) / H7 = 9 => 0 pairs (_) D8,H8: 9.. / D8 = 9 => 0 pairs (*) / H8 = 9 => 0 pairs (X) A2,A5: 9.. / A2 = 9 => 10 pairs (_) / A5 = 9 => 0 pairs (X) * DURATION: 0:00:45.864038 START: 04:10:07.856323 END: 04:10:53.720361 2017-05-04 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D1,D8,E1,E2,E3,E9,G3,G7,G9,H8) * 156...739...5.6......1.9...6...1..43.......564.........6.2.........8.4..59....... * PAIR D1: 4,8 BLK 2 F1: 4,8,2 # reduction candidate for 4,8 F1: 2 => CTR * 156842739...5.6......1.96.56...1..43.......564..6......6.2..5.....98.4..59..6.3.. F1: 4,8 # 11 pairs * PAIR D1: 4,8 COL D D5: 4,8,3,7,9 # reduction candidate for 4,8 D5: 4,8 # 12 pairs D5: 3,7,9 # 10 pairs * PAIR E1: 2,4 BLK 2 F1: 2,4,8 # reduction candidate for 2,4 F1: 2,4 # 11 pairs F1: 8 # 9 pairs * PAIR E1: 2,4 COL E E5: 2,4,9 # reduction candidate for 2,4 E5: 2,4 => CTR * 156...739...5.6......1.9...6...1..43.......564..6......6.2........98.46.59..6.3.. E5: 9 => SOLVED * 156428739972536814348179625625817943781394256439652178867243591213985467594761382 * PAIR E2: 3,7 ROW 2 A2: 3,7,2,8,9 # reduction candidate for 3,7 A2: 3,7 => CTR * 156...739..95.6......1.9...6...1..439......564..6......6.2........98.46.59..6.3.. A2: 2,8,9 # 10 pairs B2: 3,7,2,4,8 # reduction candidate for 3,7 B2: 3,7 # 11 pairs C2: 3,7,2,8,9 # reduction candidate for 3,7 C2: 3,7 # 11 pairs * PAIR E3: 3,7 ROW 3 A3: 3,7,2,8 # reduction candidate for 3,7 A3: 3,7 # 12 pairs B3: 3,7,2,4,8 # reduction candidate for 3,7 B3: 3,7 => CTR * 156.2.739.4.5.6......1.95646...1..43....9..564...6.....6425.3.....68.49559..4.6.. B3: 2,4,8 # 10 pairs C3: 3,7,2,8 # reduction candidate for 3,7 C3: 3,7 # 12 pairs * PAIR D8: 6,9 COL D D6: 6,9,3,8 # reduction candidate for 6,9 D6: 3,8 => CTR * 156...739...5.6......1.9...6...1..43.......564...6.....6.25.39....98.46.59....... D6: 6,9 # 12 pairs * PAIR E9: 4,6 BLK 8 D9: 4,6,3,7 # reduction candidate for 4,6 D9: 4,6 => CTR * 156...739...5.6......1.96.56...1..43.......564.........6425.3......8.4..59....... D9: 3,7 # 11 pairs * PAIR G7: 3,5 ROW 7 F7: 3,5,1,4,7 # reduction candidate for 3,5 F7: 3,5 => SOLVED * 156428739972536814348179625625817943781394256439652178867243591213985467594761382 F7: 1,4,7 # 10 pairs * PAIR G9: 3,6 ROW 9 D9: 3,6,4,7 # reduction candidate for 3,6 D9: 3,6 => CTR * 156...739...5.6......1.9...6...1..43.......564...6.....6.25.39....98.46.59....... D9: 4,7 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-044-base-pr-000.dot * REASONING * DIS # F1: 2 => CTR => F1: 4,8 * DIS # E5: 2,4 => CTR => E5: 9 * PRF # E5: 9 => SOL * DIS # A2: 3,7 => CTR => A2: 2,8,9 * DIS # B3: 3,7 => CTR => B3: 2,4,8 * DIS # D6: 3,8 => CTR => D6: 6,9 * DIS # D9: 4,6 => CTR => D9: 3,7 * PRF # F7: 3,5 => SOL * DIS # D9: 3,6 => CTR => D9: 4,7 * CNT 9 HDP CHAINS / 24 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D1,D8,E1,E2,E3,E9,G3,G7,G9,H8) * 156...739...5.6......1.9...6...1..43.......564.........6.2.........8.4..59....... * PAIR D1: 4,8 BLK 2 F1: 4,8,2 # reduction candidate for 4,8 F1: 2 => CTR * 156842739...5.6......1.96.56...1..43.......564..6......6.2..5.....98.4..59..6.3.. * PAIR D1: 4,8 COL D D5: 4,8,3,7,9 # reduction candidate for 4,8 D5: 4,8 # 13 pairs D5: 3,7,9 # 11 pairs * PAIR E2: 3,7 ROW 2 A2: 3,7,2,8,9 # reduction candidate for 3,7 A2: 3,7 => CTR * 156.2.739..95.6......1.96.56...1..439...4..564..6......6.2..5.....98.4..59..6.3.. B2: 3,7,2,4,8 # reduction candidate for 3,7 B2: 3,7 # 12 pairs C2: 3,7,2,8,9 # reduction candidate for 3,7 C2: 3,7 # 12 pairs * PAIR RESTART * PAIR E2: 3,7 ROW 2 B2: 3,7,2,4,8 # reduction candidate for 3,7 B2: 3,7 # 12 pairs C2: 3,7,2,8,9 # reduction candidate for 3,7 C2: 3,7 # 12 pairs * PAIR E3: 3,7 ROW 3 A3: 3,7,2,8 # reduction candidate for 3,7 A3: 3,7 # 13 pairs B3: 3,7,2,4,8 # reduction candidate for 3,7 B3: 3,7 => CTR * 156.2.739.4.5.6......1.95646...1..43....9..564...6.....6425.3.....68.49559..4.6.. C3: 3,7,2,8 # reduction candidate for 3,7 C3: 3,7 # 13 pairs * PAIR RESTART * PAIR E3: 3,7 ROW 3 A3: 3,7,2,8 # reduction candidate for 3,7 A3: 3,7 # 13 pairs C3: 3,7,2,8 # reduction candidate for 3,7 C3: 3,7 # 13 pairs * PAIR D8: 6,9 COL D D6: 6,9,3,8 # reduction candidate for 6,9 D6: 3,8 => CTR * 156.2.739...5.6......1.9...6...1..43.......564...6.....6.25.39....98.46.59....... * PAIR RESTART * PAIR G7: 3,5 ROW 7 F7: 3,5,1,4,7 # reduction candidate for 3,5 F7: 3,5 => SOLVED * 156428739972536814348179625625817943781394256439652178867243591213985467594761382 * DURATION: 0:00:15.855536 START: 04:11:13.695201 END: 04:11:29.550737 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-044-base-pr-001.dot * REASONING * DIS # F1: 2 => CTR => F1: 4,8 * DIS F1: 4,8 # A2: 3,7 => CTR => A2: 2,8,9 * DIS F1: 4,8 + A2: 2,8,9 # B3: 3,7 => CTR => B3: 2,4,8 * DIS F1: 4,8 + A2: 2,8,9 + B3: 2,4,8 # D6: 3,8 => CTR => D6: 6,9 * PRF F1: 4,8 + A2: 2,8,9 + B3: 2,4,8 + D6: 6,9 # F7: 3,5 => SOL * STA F1: 4,8 + A2: 2,8,9 + B3: 2,4,8 + D6: 6,9 + F7: 3,5 * CNT 5 HDP CHAINS / 17 HYP OPENED
Header Info
Top 500 Minimum 17 044 solution: 156428739972536814348179625625817943781394256439652178867243591213985467594761382 info: 1375 FNBHY S8.f 25103 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 156428739972536814348179625625817943781394256439652178867243591213985467594761382 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 # F1: 4,8 => UNS * DIS # F1: 2 => CTR => F1: 4,8 * INC # D5: 4,8 => UNS * INC # D5: 3,7,9 => UNS * INC # F1: 2,4 => UNS * INC # F1: 8 => UNS * DIS # E5: 2,4 => CTR => E5: 9 * PRF # E5: 9 => SOL * DIS # A2: 3,7 => CTR => A2: 2,8,9 * INC # A2: 2,8,9 => UNS * INC # B2: 3,7 => UNS * INC # C2: 3,7 => UNS * INC # A3: 3,7 => UNS * DIS # B3: 3,7 => CTR => B3: 2,4,8 * INC # B3: 2,4,8 => UNS * INC # C3: 3,7 => UNS * INC # D6: 6,9 => UNS * DIS # D6: 3,8 => CTR => D6: 6,9 * DIS # D9: 4,6 => CTR => D9: 3,7 * INC # D9: 3,7 => UNS * PRF # F7: 3,5 => SOL * INC # F7: 1,4,7 => UNS * DIS # D9: 3,6 => CTR => D9: 4,7 * INC # D9: 4,7 => UNS * CNT 24 HDP CHAINS / 24 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F1: 4,8 => UNS * DIS # F1: 2 => CTR => F1: 4,8 * INC F1: 4,8 # D5: 4,8 => UNS * INC F1: 4,8 # D5: 3,7,9 => UNS * DIS F1: 4,8 # A2: 3,7 => CTR => A2: 2,8,9 * INC F1: 4,8 + A2: 2,8,9 # B2: 3,7 => UNS * INC F1: 4,8 + A2: 2,8,9 # C2: 3,7 => UNS * INC F1: 4,8 + A2: 2,8,9 # B2: 3,7 => UNS * INC F1: 4,8 + A2: 2,8,9 # C2: 3,7 => UNS * INC F1: 4,8 + A2: 2,8,9 # A3: 3,7 => UNS * DIS F1: 4,8 + A2: 2,8,9 # B3: 3,7 => CTR => B3: 2,4,8 * INC F1: 4,8 + A2: 2,8,9 + B3: 2,4,8 # C3: 3,7 => UNS * INC F1: 4,8 + A2: 2,8,9 + B3: 2,4,8 # A3: 3,7 => UNS * INC F1: 4,8 + A2: 2,8,9 + B3: 2,4,8 # C3: 3,7 => UNS * INC F1: 4,8 + A2: 2,8,9 + B3: 2,4,8 # D6: 6,9 => UNS * DIS F1: 4,8 + A2: 2,8,9 + B3: 2,4,8 # D6: 3,8 => CTR => D6: 6,9 * PRF F1: 4,8 + A2: 2,8,9 + B3: 2,4,8 + D6: 6,9 # F7: 3,5 => SOL * STA F1: 4,8 + A2: 2,8,9 + B3: 2,4,8 + D6: 6,9 + F7: 3,5 * CNT 17 HDP CHAINS / 17 HYP OPENED