Analysis of xx-top500-475-base.sdk
Contents
Original Sudoku
level: medium
position: ..1....452...8................5.1...3.....8.....64.....541......6.....7.......2.. initial
Autosolve
position: ..1....452...8........1.......531...3.....8.....648....541......62....7.......2.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I5: 6 => CTR => I5: 1,4 * DIS # H5: 1 => CTR => H5: 5,6 * DIS # E9: 6,7 => CTR => E9: 5,9 * PRF # G8: 5,9 => SOL * DIS # G8: 1,3,4 => CTR => G8: 5,9 * CNT 5 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I5: 6 => CTR => I5: 1,4 * DIS I5: 1,4 # E9: 6,7 => CTR => E9: 5,9 * PRF I5: 1,4 + E9: 5,9 # G8: 5,9 => SOL * STA I5: 1,4 + E9: 5,9 + G8: 5,9 * CNT 3 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..1....452...8................5.1...3.....8.....64.....541......6.....7.......2.. | initial |
| ..1....452...8........1.......531...3.....8.....648....541......62....7.......2.. | autosolve |
| 681327945295486137473915682827531469346279851519648723754162398162893574938754216 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) H3: 2,8 I3: 2,8 B5: 1,4 C5: 5,6 E8: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H3,I3: 2.. / H3 = 2 => 4 pairs (_) / I3 = 2 => 3 pairs (_) B4,B6: 2.. / B4 = 2 => 6 pairs (_) / B6 = 2 => 5 pairs (_) E7,F7: 2.. / E7 = 2 => 6 pairs (_) / F7 = 2 => 6 pairs (_) D1,D5: 2.. / D1 = 2 => 6 pairs (_) / D5 = 2 => 7 pairs (_) B9,C9: 3.. / B9 = 3 => 5 pairs (_) / C9 = 3 => 5 pairs (_) B5,I5: 4.. / B5 = 4 => 0 pairs (*) / I5 = 4 => 0 pairs (X) A3,A4: 4.. / A3 = 4 => 0 pairs (*) / A4 = 4 => 0 pairs (X) G4,G8: 4.. / G4 = 4 => 0 pairs (*) / G8 = 4 => 0 pairs (X) F2,F3: 5.. / F2 = 5 => 5 pairs (_) / F3 = 5 => 0 pairs (*) E8,E9: 5.. / E8 = 5 => 0 pairs (X) / E9 = 5 => 0 pairs (_) G8,H9: 5.. / G8 = 5 => 0 pairs (*) / H9 = 5 => 0 pairs (X) C2,F2: 5.. / C2 = 5 => 0 pairs (*) / F2 = 5 => 0 pairs (X) C5,H5: 5.. / C5 = 5 => 0 pairs (X) / H5 = 5 => 0 pairs (_) E8,G8: 5.. / E8 = 5 => 0 pairs (X) / G8 = 5 => 0 pairs (_) E9,H9: 5.. / E9 = 5 => 0 pairs (*) / H9 = 5 => 0 pairs (X) A3,A6: 5.. / A3 = 5 => 0 pairs (X) / A6 = 5 => 0 pairs (_) G6,G8: 5.. / G6 = 5 => 0 pairs (X) / G8 = 5 => 0 pairs (_) A1,B1: 8.. / A1 = 8 => 0 pairs (X) / B1 = 8 => 5 pairs (_) H3,I3: 8.. / H3 = 8 => 3 pairs (_) / I3 = 8 => 4 pairs (_) D8,D9: 8.. / D8 = 8 => 6 pairs (_) / D9 = 8 => 5 pairs (_) C4,C9: 8.. / C4 = 8 => 5 pairs (_) / C9 = 8 => 0 pairs (*) * DURATION: 0:00:37.510910 START: 18:53:33.297924 END: 18:54:10.808834 2017-05-04 * CP COUNT: (21) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,C5,E8,H3,I3) * ..1....452...8........1.......531...3.....8.....648....541......62....7.......2.. * PAIR B5: 1,4 ROW 5 I5: 1,4,6 # reduction candidate for 1,4 I5: 6 => CTR * ..1....452...8....4...1.......531...345...816...648....541......62....7.......2.. I5: 1,4 # 7 pairs * PAIR C5: 5,6 ROW 5 H5: 5,6,1 # reduction candidate for 5,6 H5: 1 => CTR * ..1....452...85...5...1....4..531...3.5...816...648....541......62....7.......2.. H5: 5,6 # 7 pairs * PAIR C5: 5,6 COL C C2: 5,6,3,7,9 # reduction candidate for 5,6 C2: 5,6 # 7 pairs C3: 5,6,3,7,9 # reduction candidate for 5,6 C3: 5,6 # 7 pairs * PAIR E8: 5,9 BLK 8 E9: 5,9,6,7 # reduction candidate for 5,9 E9: 6,7 => CTR * ..1....452...85...5...1....4.6531...315...864...6485...541......62.5.47...8...25. E9: 5,9 # 8 pairs * PAIR E8: 5,9 ROW 8 G8: 5,9,1,3,4 # reduction candidate for 5,9 G8: 5,9 => SOLVED * 681327945295486137473915682827531469346279851519648723754162398162893574938754216 G8: 1,3,4 => CTR * 681....452...851.65...16...4..531...315...864...6485...541......62.5.47.......25. * INCONCLUSIVE * SAVE PR GRAPH xx-top500-475-base-pr-000.dot * REASONING * DIS # I5: 6 => CTR => I5: 1,4 * DIS # H5: 1 => CTR => H5: 5,6 * DIS # E9: 6,7 => CTR => E9: 5,9 * PRF # G8: 5,9 => SOL * DIS # G8: 1,3,4 => CTR => G8: 5,9 * CNT 5 HDP CHAINS / 10 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,C5,E8,H3,I3) * ..1....452...8........1.......531...3.....8.....648....541......62....7.......2.. * PAIR B5: 1,4 ROW 5 I5: 1,4,6 # reduction candidate for 1,4 I5: 6 => CTR * ..1....452...8....4...1.......531...345...816...648....541......62....7.......2.. * PAIR RESTART * PAIR C5: 5,6 COL C C2: 5,6,3,7,9 # reduction candidate for 5,6 C2: 5,6 # 9 pairs C3: 5,6,3,7,9 # reduction candidate for 5,6 C3: 5,6 # 9 pairs * PAIR E8: 5,9 BLK 8 E9: 5,9,6,7 # reduction candidate for 5,9 E9: 6,7 => CTR * ..1....452...85...5...1....4.6531...315...864...6485...541......62.5.47...8...25. * PAIR E8: 5,9 ROW 8 G8: 5,9,1,3,4 # reduction candidate for 5,9 G8: 5,9 => SOLVED * 681327945295486137473915682827531469346279851519648723754162398162893574938754216 * DURATION: 0:00:07.984733 START: 18:54:19.908133 END: 18:54:27.892866 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-475-base-pr-001.dot * REASONING * DIS # I5: 6 => CTR => I5: 1,4 * DIS I5: 1,4 # E9: 6,7 => CTR => E9: 5,9 * PRF I5: 1,4 + E9: 5,9 # G8: 5,9 => SOL * STA I5: 1,4 + E9: 5,9 + G8: 5,9 * CNT 3 HDP CHAINS / 7 HYP OPENED
Header Info
Top 500 Minimum 17 475 solution: 681327945295486137473915682827531469346279851519648723754162398162893574938754216 info: 95730 FNBTHYK S8.f 44753 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 681327945295486137473915682827531469346279851519648723754162398162893574938754216 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 # I5: 1,4 => UNS * DIS # I5: 6 => CTR => I5: 1,4 * INC # H5: 5,6 => UNS * DIS # H5: 1 => CTR => H5: 5,6 * INC # C2: 5,6 => UNS * INC # C3: 5,6 => UNS * INC # E9: 5,9 => UNS * DIS # E9: 6,7 => CTR => E9: 5,9 * PRF # G8: 5,9 => SOL * DIS # G8: 1,3,4 => CTR => G8: 5,9 * CNT 10 HDP CHAINS / 10 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # I5: 1,4 => UNS * DIS # I5: 6 => CTR => I5: 1,4 * INC I5: 1,4 # C2: 5,6 => UNS * INC I5: 1,4 # C3: 5,6 => UNS * INC I5: 1,4 # E9: 5,9 => UNS * DIS I5: 1,4 # E9: 6,7 => CTR => E9: 5,9 * PRF I5: 1,4 + E9: 5,9 # G8: 5,9 => SOL * STA I5: 1,4 + E9: 5,9 + G8: 5,9 * CNT 7 HDP CHAINS / 7 HYP OPENED