Analysis of xx-top500-154-base.sdk
Contents
Original Sudoku
level: medium
position: .74..........1.6......8....89....1.....4.2...5...........7...43...3...2.1........ initial
Autosolve
position: 6749..2183..2146.721.68743.8925..1.47314.2.8.5461.83.296.721.434.73...2112384.7.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C2: 5,8 => SOL * DIS # C2: 9 => CTR => C2: 5,8 * DIS # C2: 5,9 => CTR => C2: 8 * PRF # C2: 8 => SOL * DIS # C2: 5,9 => CTR => C2: 8 * PRF # C2: 8 => SOL * PRF # H9: 5,9 => SOL * DIS # H9: 6 => CTR => H9: 5,9 * PRF # I5: 5,9 => SOL * DIS # I5: 6 => CTR => I5: 5,9 * DIS # I9: 5,9 => CTR => I9: 6 * PRF # I9: 6 => SOL * DIS # E4: 3,6 => CTR => E4: 7 * PRF # E4: 7 => SOL * PRF # I5: 6,9 => SOL * DIS # I5: 5 => CTR => I5: 6,9 * PRF # E4: 6,7 => SOL * DIS # E4: 3 => CTR => E4: 6,7 * PRF # I5: 5,9 => SOL * DIS # I5: 6 => CTR => I5: 5,9 * PRF # G8: 5,9 => SOL * DIS # G8: 8 => CTR => G8: 5,9 * PRF # C2: 5,8 => SOL * DIS # C2: 9 => CTR => C2: 5,8 * DIS # G8: 5,8 => CTR => G8: 9 * PRF # G8: 9 => SOL * PRF # F8: 5,6 => SOL * DIS # F8: 9 => CTR => F8: 5,6 * DIS # F8: 5,9 => CTR => F8: 6 * PRF # F8: 6 => SOL * PRF # H9: 5,9 => SOL * DIS # H9: 6 => CTR => H9: 5,9 * DIS # I9: 5,9 => CTR => I9: 6 * PRF # I9: 6 => SOL * DIS # G8: 5,8 => CTR => G8: 9 * PRF # G8: 9 => SOL * CNT 36 HDP CHAINS / 36 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C2: 5,8 => SOL * STA C2: 5,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .74..........1.6......8....89....1.....4.2...5...........7...43...3...2.1........ | initial |
| 6749..2183..2146.721.68743.8925..1.47314.2.8.5461.83.296.721.434.73...2112384.7.. | autosolve |
| 674935218358214697219687435892573164731462589546198372965721843487356921123849756 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) B2: 5,8 C3: 5,9 E1: 3,5 F1: 3,5 H2: 5,9 I3: 5,9 F4: 3,6 E5: 6,9 E6: 7,9 H4: 6,7 G5: 5,9 H6: 7,9 C7: 5,8 B8: 5,8 E8: 5,6 F9: 5,9 G7: 5,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,F1: 3.. / E1 = 3 => 0 pairs (*) / F1 = 3 => 0 pairs (X) E4,F4: 3.. / E4 = 3 => 0 pairs (X) / F4 = 3 => 0 pairs (_) E1,E4: 3.. / E1 = 3 => 0 pairs (*) / E4 = 3 => 0 pairs (X) F1,F4: 3.. / F1 = 3 => 0 pairs (X) / F4 = 3 => 0 pairs (_) E1,F1: 5.. / E1 = 5 => 0 pairs (X) / F1 = 5 => 0 pairs (_) H2,I3: 5.. / H2 = 5 => 0 pairs (X) / I3 = 5 => 0 pairs (_) G5,I5: 5.. / G5 = 5 => 0 pairs (*) / I5 = 5 => 0 pairs (X) C7,B8: 5.. / C7 = 5 => 0 pairs (*) / B8 = 5 => 0 pairs (X) C3,I3: 5.. / C3 = 5 => 0 pairs (X) / I3 = 5 => 0 pairs (_) C7,G7: 5.. / C7 = 5 => 0 pairs (*) / G7 = 5 => 0 pairs (X) B2,B8: 5.. / B2 = 5 => 0 pairs (*) / B8 = 5 => 0 pairs (X) E1,E8: 5.. / E1 = 5 => 0 pairs (X) / E8 = 5 => 0 pairs (_) H2,H9: 5.. / H2 = 5 => 0 pairs (X) / H9 = 5 => 0 pairs (_) H4,I5: 6.. / H4 = 6 => 0 pairs (*) / I5 = 6 => 0 pairs (X) E8,F8: 6.. / E8 = 6 => 0 pairs (X) / F8 = 6 => 0 pairs (_) H9,I9: 6.. / H9 = 6 => 0 pairs (X) / I9 = 6 => 0 pairs (_) E5,I5: 6.. / E5 = 6 => 0 pairs (*) / I5 = 6 => 0 pairs (X) F4,F8: 6.. / F4 = 6 => 0 pairs (X) / F8 = 6 => 0 pairs (_) H4,H9: 6.. / H4 = 6 => 0 pairs (*) / H9 = 6 => 0 pairs (X) I5,I9: 6.. / I5 = 6 => 0 pairs (X) / I9 = 6 => 0 pairs (_) E4,E6: 7.. / E4 = 7 => 0 pairs (*) / E6 = 7 => 0 pairs (X) H4,H6: 7.. / H4 = 7 => 0 pairs (X) / H6 = 7 => 0 pairs (_) E4,H4: 7.. / E4 = 7 => 0 pairs (*) / H4 = 7 => 0 pairs (X) E6,H6: 7.. / E6 = 7 => 0 pairs (X) / H6 = 7 => 0 pairs (_) B2,C2: 8.. / B2 = 8 => 0 pairs (X) / C2 = 8 => 0 pairs (_) C7,B8: 8.. / C7 = 8 => 0 pairs (X) / B8 = 8 => 0 pairs (_) G7,G8: 8.. / G7 = 8 => 0 pairs (*) / G8 = 8 => 0 pairs (X) C7,G7: 8.. / C7 = 8 => 0 pairs (X) / G7 = 8 => 0 pairs (_) B8,G8: 8.. / B8 = 8 => 0 pairs (*) / G8 = 8 => 0 pairs (X) B2,B8: 8.. / B2 = 8 => 0 pairs (X) / B8 = 8 => 0 pairs (_) C2,C7: 8.. / C2 = 8 => 0 pairs (*) / C7 = 8 => 0 pairs (X) C2,C3: 9.. / C2 = 9 => 0 pairs (X) / C3 = 9 => 0 pairs (_) H2,I3: 9.. / H2 = 9 => 0 pairs (*) / I3 = 9 => 0 pairs (X) E5,E6: 9.. / E5 = 9 => 0 pairs (X) / E6 = 9 => 0 pairs (_) F8,F9: 9.. / F8 = 9 => 0 pairs (X) / F9 = 9 => 0 pairs (_) C2,H2: 9.. / C2 = 9 => 0 pairs (X) / H2 = 9 => 0 pairs (_) C3,I3: 9.. / C3 = 9 => 0 pairs (*) / I3 = 9 => 0 pairs (X) E6,H6: 9.. / E6 = 9 => 0 pairs (*) / H6 = 9 => 0 pairs (X) F8,G8: 9.. / F8 = 9 => 0 pairs (X) / G8 = 9 => 0 pairs (_) G5,G8: 9.. / G5 = 9 => 0 pairs (X) / G8 = 9 => 0 pairs (_) * DURATION: 0:01:17.367262 START: 08:00:34.500854 END: 08:01:51.868116 2017-05-04 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B8,C3,C7,E1,E5,E6,E8,F1,F4,F9,G5,G7,H2,H4,H6,I3) * 6749..2183..2146.721.68743.8925..1.47314.2.8.5461.83.296.721.434.73...2112384.7.. * PAIR B2: 5,8 BLK 1 C2: 5,8,9 # reduction candidate for 5,8 C2: 5,8 => SOLVED * 674935218358214697219687435892573164731462589546198372965721843487356921123849756 C2: 9 => CTR * 6749..2183892146572156874398925..1.47314.2.8.5461.83.2968721543457369821123845796 * PAIR C3: 5,9 BLK 1 C2: 5,9,8 # reduction candidate for 5,9 C2: 5,9 => CTR * 6749..21838.2146.721.68743.8925..1.47314.2.8.5461.83.29687215434573698211238457.. C2: 8 => SOLVED * 674935218358214697219687435892573164731462589546198372965721843487356921123849756 * PAIR H2: 5,9 ROW 2 C2: 5,9,8 # reduction candidate for 5,9 C2: 5,9 => CTR * 6749..21838.2146.721.68743.8925..1.47314.2.8.5461.83.29687215434573698211238457.. C2: 8 => SOLVED * 674935218358214697219687435892573164731462589546198372965721843487356921123849756 * PAIR H2: 5,9 COL H H9: 5,9,6 # reduction candidate for 5,9 H9: 5,9 => SOLVED * 674935218358214697219687435892573164731462589546198372965721843487356921123849756 H9: 6 => CTR * 6749..2183..2146572156874398925..1.47314.2.8.5461.83929687215434.73...2112384.7.. * PAIR I3: 5,9 COL I I5: 5,9,6 # reduction candidate for 5,9 I5: 5,9 => SOLVED * 674935218358214697219687435892573164731462589546198372965721843487356921123849756 I5: 6 => CTR * 6749..2183..2146.721.68743.8925..1.47314.25865461.83929657218434873..921123849765 I9: 5,9,6 # reduction candidate for 5,9 I9: 5,9 => CTR * 6749..2183..2146572156874398925..174731492586546178392968721.434.73...2112384.76. I9: 6 => SOLVED * 674935218358214697219687435892573164731462589546198372965721843487356921123849756 * PAIR F4: 3,6 BLK 5 E4: 3,6,7 # reduction candidate for 3,6 E4: 3,6 => CTR * 6749..2183.921465721568743.8925..1747314.2.8654617839296.721.434.73..921123849765 E4: 7 => SOLVED * 674935218358214697219687435892573164731462589546198372965721843487356921123849756 * PAIR E5: 6,9 ROW 5 I5: 6,9,5 # reduction candidate for 6,9 I5: 6,9 => SOLVED * 674935218358214697219687435892573164731462589546198372965721843487356921123849756 I5: 5 => CTR * 6749..2183..2146.721.68743.8925..16473146298554619837296.721.434.735..2112384.7.. * PAIR H4: 6,7 ROW 4 E4: 6,7,3 # reduction candidate for 6,7 E4: 6,7 => SOLVED * 674935218358214697219687435892573164731462589546198372965721843487356921123849756 E4: 3 => CTR * 6749..2183..2146.721.68743.892536174731492586546178392965721843487365921123849765 * PAIR G5: 5,9 BLK 6 I5: 5,9,6 # reduction candidate for 5,9 I5: 5,9 => SOLVED * 674935218358214697219687435892573164731462589546198372965721843487356921123849756 I5: 6 => CTR * 6749..2183..2146.721.68743.8925..1.47314.25865461.83929657218434873..921123849765 * PAIR G5: 5,9 COL G G8: 5,9,8 # reduction candidate for 5,9 G8: 5,9 => SOLVED * 674935218358214697219687435892573164731462589546198372965721843487356921123849756 G8: 8 => CTR * 6749..2183..2146.721.68743.8925..1.47314.298554619837296.72154345736..2112384.7.. * PAIR C7: 5,8 COL C C2: 5,8,9 # reduction candidate for 5,8 C2: 5,8 => SOLVED * 674935218358214697219687435892573164731462589546198372965721843487356921123849756 C2: 9 => CTR * 6749..2183892146572156874398925..1.47314.2.8.5461.83.2968721543457369821123845796 * PAIR B8: 5,8 ROW 8 G8: 5,8,9 # reduction candidate for 5,8 G8: 5,8 => CTR * 6749..2183..2146.721.68743.8925..1.47314.298554619837296.721.434.73.9.211238457.6 G8: 9 => SOLVED * 674935218358214697219687435892573164731462589546198372965721843487356921123849756 * PAIR E8: 5,6 BLK 8 F8: 5,6,9 # reduction candidate for 5,6 F8: 5,6 => SOLVED * 674935218358214697219687435892573164731462589546198372965721843487356921123849756 F8: 9 => CTR * 6749..2183..2146.721.68743.8925.61747314925865461783929657218434873...2112384.7.. * PAIR F9: 5,9 BLK 8 F8: 5,9,6 # reduction candidate for 5,9 F8: 5,9 => CTR * 6749..2183..2146.721.68743.8925.6174731492586546178392965721843487365921123849765 F8: 6 => SOLVED * 674935218358214697219687435892573164731462589546198372965721843487356921123849756 * PAIR F9: 5,9 ROW 9 H9: 5,9,6 # reduction candidate for 5,9 H9: 5,9 => SOLVED * 674935218358214697219687435892573164731462589546198372965721843487356921123849756 H9: 6 => CTR * 6749..2183..2146572156874398925..1.47314.2.8.5461.83929687215434.73...2112384.7.. I9: 5,9,6 # reduction candidate for 5,9 I9: 5,9 => CTR * 6749..2183..2146572156874398925..174731492586546178392968721.434.73...2112384.76. I9: 6 => SOLVED * 674935218358214697219687435892573164731462589546198372965721843487356921123849756 * PAIR G7: 5,8 BLK 9 G8: 5,8,9 # reduction candidate for 5,8 G8: 5,8 => CTR * 6749..2183..2146.721.68743.8925..1.47314.298554619837296.721.434.73.9.211238457.6 G8: 9 => SOLVED * 674935218358214697219687435892573164731462589546198372965721843487356921123849756 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-154-base-pr-000.dot * REASONING * PRF # C2: 5,8 => SOL * DIS # C2: 9 => CTR => C2: 5,8 * DIS # C2: 5,9 => CTR => C2: 8 * PRF # C2: 8 => SOL * DIS # C2: 5,9 => CTR => C2: 8 * PRF # C2: 8 => SOL * PRF # H9: 5,9 => SOL * DIS # H9: 6 => CTR => H9: 5,9 * PRF # I5: 5,9 => SOL * DIS # I5: 6 => CTR => I5: 5,9 * DIS # I9: 5,9 => CTR => I9: 6 * PRF # I9: 6 => SOL * DIS # E4: 3,6 => CTR => E4: 7 * PRF # E4: 7 => SOL * PRF # I5: 6,9 => SOL * DIS # I5: 5 => CTR => I5: 6,9 * PRF # E4: 6,7 => SOL * DIS # E4: 3 => CTR => E4: 6,7 * PRF # I5: 5,9 => SOL * DIS # I5: 6 => CTR => I5: 5,9 * PRF # G8: 5,9 => SOL * DIS # G8: 8 => CTR => G8: 5,9 * PRF # C2: 5,8 => SOL * DIS # C2: 9 => CTR => C2: 5,8 * DIS # G8: 5,8 => CTR => G8: 9 * PRF # G8: 9 => SOL * PRF # F8: 5,6 => SOL * DIS # F8: 9 => CTR => F8: 5,6 * DIS # F8: 5,9 => CTR => F8: 6 * PRF # F8: 6 => SOL * PRF # H9: 5,9 => SOL * DIS # H9: 6 => CTR => H9: 5,9 * DIS # I9: 5,9 => CTR => I9: 6 * PRF # I9: 6 => SOL * DIS # G8: 5,8 => CTR => G8: 9 * PRF # G8: 9 => SOL * CNT 36 HDP CHAINS / 36 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B8,C3,C7,E1,E5,E6,E8,F1,F4,F9,G5,G7,H2,H4,H6,I3) * 6749..2183..2146.721.68743.8925..1.47314.2.8.5461.83.296.721.434.73...2112384.7.. * PAIR B2: 5,8 BLK 1 C2: 5,8,9 # reduction candidate for 5,8 C2: 5,8 => SOLVED * 674935218358214697219687435892573164731462589546198372965721843487356921123849756 * DURATION: 0:00:02.002292 START: 08:02:36.714409 END: 08:02:38.716701 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-154-base-pr-001.dot * REASONING * PRF # C2: 5,8 => SOL * STA C2: 5,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 154 solution: 674935218358214697219687435892573164731462589546198372965721843487356921123849756 info: 1817 FNBWY S8.f 23079 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 674935218358214697219687435892573164731462589546198372965721843487356921123849756 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 # C2: 5,8 => SOL * DIS # C2: 9 => CTR => C2: 5,8 * DIS # C2: 5,9 => CTR => C2: 8 * PRF # C2: 8 => SOL * DIS # C2: 5,9 => CTR => C2: 8 * PRF # C2: 8 => SOL * PRF # H9: 5,9 => SOL * DIS # H9: 6 => CTR => H9: 5,9 * PRF # I5: 5,9 => SOL * DIS # I5: 6 => CTR => I5: 5,9 * DIS # I9: 5,9 => CTR => I9: 6 * PRF # I9: 6 => SOL * DIS # E4: 3,6 => CTR => E4: 7 * PRF # E4: 7 => SOL * PRF # I5: 6,9 => SOL * DIS # I5: 5 => CTR => I5: 6,9 * PRF # E4: 6,7 => SOL * DIS # E4: 3 => CTR => E4: 6,7 * PRF # I5: 5,9 => SOL * DIS # I5: 6 => CTR => I5: 5,9 * PRF # G8: 5,9 => SOL * DIS # G8: 8 => CTR => G8: 5,9 * PRF # C2: 5,8 => SOL * DIS # C2: 9 => CTR => C2: 5,8 * DIS # G8: 5,8 => CTR => G8: 9 * PRF # G8: 9 => SOL * PRF # F8: 5,6 => SOL * DIS # F8: 9 => CTR => F8: 5,6 * DIS # F8: 5,9 => CTR => F8: 6 * PRF # F8: 6 => SOL * PRF # H9: 5,9 => SOL * DIS # H9: 6 => CTR => H9: 5,9 * DIS # I9: 5,9 => CTR => I9: 6 * PRF # I9: 6 => SOL * DIS # G8: 5,8 => CTR => G8: 9 * PRF # G8: 9 => SOL * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C2: 5,8 => SOL * STA C2: 5,8 * CNT 1 HDP CHAINS / 1 HYP OPENED