Analysis of xx-top500-404-base.sdk
Contents
Original Sudoku
level: medium
position: .6....5.......7..6..72.....2......8...3...4......61...4...5.......3...7..5....... initial
Autosolve
position: .6....5.7...5.7..65.72.6...2......8...3...4......61...4...5.......3...75.5....... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C4: 1,9 => SOL * DIS # A5: 1,9 => CTR => A5: 6,7,8 * DIS # G6: 2,3 => CTR => G6: 7 * PRF # G6: 7 => SOL * PRF # H6: 2,3 => SOL * DIS # H6: 5 => CTR => H6: 2,3 * CNT 6 HDP CHAINS / 12 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C4: 1,9 => SOL * STA C4: 1,9 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .6....5.......7..6..72.....2......8...3...4......61...4...5.......3...7..5....... | initial |
| .6....5.7...5.7..65.72.6...2......8...3...4......61...4...5.......3...75.5....... | autosolve |
| 968143527324597816517286394271435689693872451845961732432759168186324975759618243 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) G4: 6,7 I4: 1,9 H5: 5,6 I5: 1,9 I6: 2,3 B7: 3,7 A9: 3,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I4,I5: 1.. / I4 = 1 => 6 pairs (_) / I5 = 1 => 6 pairs (_) E5,F5: 2.. / E5 = 2 => 7 pairs (_) / F5 = 2 => 0 pairs (*) C1,H1: 2.. / C1 = 2 => 7 pairs (_) / H1 = 2 => 8 pairs (_) B2,B8: 2.. / B2 = 2 => 8 pairs (_) / B8 = 2 => 7 pairs (_) E4,F4: 3.. / E4 = 3 => 7 pairs (_) / F4 = 3 => 0 pairs (X) B7,A9: 3.. / B7 = 3 => 13 pairs (_) / A9 = 3 => 5 pairs (_) F1,F4: 3.. / F1 = 3 => 7 pairs (_) / F4 = 3 => 0 pairs (X) E8,F8: 4.. / E8 = 4 => 0 pairs (X) / F8 = 4 => 7 pairs (_) H9,I9: 4.. / H9 = 4 => 7 pairs (_) / I9 = 4 => 8 pairs (_) I3,I9: 4.. / I3 = 4 => 7 pairs (_) / I9 = 4 => 8 pairs (_) C4,C6: 5.. / C4 = 5 => 0 pairs (X) / C6 = 5 => 0 pairs (_) F4,F5: 5.. / F4 = 5 => 0 pairs (*) / F5 = 5 => 0 pairs (X) H5,H6: 5.. / H5 = 5 => 0 pairs (*) / H6 = 5 => 0 pairs (X) C4,F4: 5.. / C4 = 5 => 0 pairs (X) / F4 = 5 => 0 pairs (_) F5,H5: 5.. / F5 = 5 => 0 pairs (X) / H5 = 5 => 0 pairs (_) C6,H6: 5.. / C6 = 5 => 0 pairs (*) / H6 = 5 => 0 pairs (X) C4,A5: 6.. / C4 = 6 => 0 pairs (X) / A5 = 6 => 0 pairs (_) G4,H5: 6.. / G4 = 6 => 0 pairs (*) / H5 = 6 => 0 pairs (X) D7,D9: 6.. / D7 = 6 => 5 pairs (_) / D9 = 6 => 7 pairs (_) C4,G4: 6.. / C4 = 6 => 0 pairs (X) / G4 = 6 => 0 pairs (_) A5,H5: 6.. / A5 = 6 => 0 pairs (*) / H5 = 6 => 0 pairs (X) A5,A8: 6.. / A5 = 6 => 0 pairs (*) / A8 = 6 => 0 pairs (X) G4,G6: 7.. / G4 = 7 => 0 pairs (X) / G6 = 7 => 0 pairs (_) B7,A9: 7.. / B7 = 7 => 5 pairs (_) / A9 = 7 => 13 pairs (_) B7,D7: 7.. / B7 = 7 => 5 pairs (_) / D7 = 7 => 13 pairs (_) I4,I5: 9.. / I4 = 9 => 6 pairs (_) / I5 = 9 => 6 pairs (_) * DURATION: 0:00:40.123039 START: 16:39:45.772944 END: 16:40:25.895983 2017-05-04 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B7,G4,H5,I4,I5,I6) * .6....5.7...5.7..65.72.6...2......8...3...4......61...4...5.......3...75.5....... * PAIR I4: 1,9 ROW 4 B4: 1,9,4,7 # reduction candidate for 1,9 B4: 1,9 # 9 pairs C4: 1,9,4,5,6 # reduction candidate for 1,9 C4: 1,9 => SOLVED * 968143527324597816517286394271435689693872451845961732432759168186324975759618243 C4: 4,5,6 # 7 pairs * PAIR I5: 1,9 ROW 5 A5: 1,9,6,7,8 # reduction candidate for 1,9 A5: 1,9 => CTR * .6....5.7...5.7..65.72.6...2.6..578...3...4......61...4...5.......3...75.5....... A5: 6,7,8 # 7 pairs B5: 1,9,7,8 # reduction candidate for 1,9 B5: 1,9 # 9 pairs * PAIR I6: 2,3 BLK 6 G6: 2,3,7 # reduction candidate for 2,3 G6: 2,3 => CTR * .6....5.7...5.7..65.72.6...2.....78...3...46.....61.5.4...5....6..3...75.5....... G6: 7 => SOLVED * 968143527324597816517286394271435689693872451845961732432759168186324975759618243 H6: 2,3,5 # reduction candidate for 2,3 H6: 2,3 => SOLVED * 968143527324597816517286394271435689693872451845961732432759168186324975759618243 H6: 5 => CTR * .6....5.7...5.7..65.72.6...2.5...68...3...4......61.5.4...5.......3...75.5....... * PAIR I6: 2,3 COL I I7: 2,3,8 # reduction candidate for 2,3 I7: 2,3 # 10 pairs I9: 2,3,4,8 # reduction candidate for 2,3 I9: 2,3 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-404-base-pr-000.dot * REASONING * PRF # C4: 1,9 => SOL * DIS # A5: 1,9 => CTR => A5: 6,7,8 * DIS # G6: 2,3 => CTR => G6: 7 * PRF # G6: 7 => SOL * PRF # H6: 2,3 => SOL * DIS # H6: 5 => CTR => H6: 2,3 * CNT 6 HDP CHAINS / 12 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B7,G4,H5,I4,I5,I6) * .6....5.7...5.7..65.72.6...2......8...3...4......61...4...5.......3...75.5....... * PAIR I4: 1,9 ROW 4 B4: 1,9,4,7 # reduction candidate for 1,9 B4: 1,9 # 9 pairs C4: 1,9,4,5,6 # reduction candidate for 1,9 C4: 1,9 => SOLVED * 968143527324597816517286394271435689693872451845961732432759168186324975759618243 * DURATION: 0:00:03.421507 START: 16:40:37.282181 END: 16:40:40.703688 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-404-base-pr-001.dot * REASONING * PRF # C4: 1,9 => SOL * STA C4: 1,9 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 404 solution: 968143527324597816517286394271435689693872451845961732432759168186324975759618243 info: 91134 FNBTHXYK S8.f 49075 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 968143527324597816517286394271435689693872451845961732432759168186324975759618243 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 # B4: 1,9 => UNS * PRF # C4: 1,9 => SOL * INC # C4: 4,5,6 => UNS * DIS # A5: 1,9 => CTR => A5: 6,7,8 * INC # A5: 6,7,8 => UNS * INC # B5: 1,9 => UNS * DIS # G6: 2,3 => CTR => G6: 7 * PRF # G6: 7 => SOL * PRF # H6: 2,3 => SOL * DIS # H6: 5 => CTR => H6: 2,3 * INC # I7: 2,3 => UNS * INC # I9: 2,3 => UNS * CNT 12 HDP CHAINS / 12 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B4: 1,9 => UNS * PRF # C4: 1,9 => SOL * STA C4: 1,9 * CNT 2 HDP CHAINS / 2 HYP OPENED