Analysis of xx-top500-271-base.sdk
Contents
Original Sudoku
level: medium
position: 46.8........2..1....3....9.27...........9.3......1....5..7....2.......4...1...... initial
Autosolve
position: 4698.127.8572.91.4123.7..9827.38.9.161..9.3..93..1.4..5967438123821..749741928... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # I9: 3,5 => SOL * DIS # I9: 6 => CTR => I9: 3,5 * PRF # H9: 3,6 => SOL * DIS # H9: 5 => CTR => H9: 3,6 * DIS # F3: 5,6 => CTR => F3: 4 * DIS # C5: 8 => CTR => C5: 4,5 * DIS # F4: 4,5 => CTR => F4: 6 * PRF # F4: 6 => SOL * DIS # C5: 4 => CTR => C5: 5,8 * DIS # F4: 4,5 => CTR => F4: 6 * PRF # F4: 6 => SOL * DIS # C5: 8 => CTR => C5: 4,5 * DIS # D3: 4,5 => CTR => D3: 6 * PRF # D3: 6 => SOL * DIS # F4: 4 => CTR => F4: 5,6 * DIS # I6: 7 => CTR => I6: 5,6 * DIS # D3: 4 => CTR => D3: 5,6 * DIS # I6: 7 => CTR => I6: 5,6 * DIS # F4: 4 => CTR => F4: 5,6 * DIS # H9: 5,6 => CTR => H9: 3 * PRF # H9: 3 => SOL * DIS # I6: 5,7 => CTR => I6: 6 * PRF # I6: 6 => SOL * DIS # F3: 5,6 => CTR => F3: 4 * DIS # H9: 5,6 => CTR => H9: 3 * PRF # H9: 3 => SOL * PRF # I9: 5,6 => SOL * DIS # I9: 3 => CTR => I9: 5,6 * CNT 28 HDP CHAINS / 40 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # I9: 3,5 => SOL * STA I9: 3,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 46.8........2..1....3....9.27...........9.3......1....5..7....2.......4...1...... | initial |
| 4698.127.8572.91.4123.7..9827.38.9.161..9.3..93..1.4..5967438123821..749741928... | autosolve |
| 469851273857239164123674598274386951615492387938517426596743812382165749741928635 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) E1: 3,5 E2: 3,6 I1: 3,5 H2: 3,6 G3: 5,6 C4: 4,5 C6: 5,8 D5: 4,5 F5: 2,7 D6: 5,6 F6: 2,7 H4: 5,6 H5: 2,8 I5: 5,7 H6: 2,8 E8: 5,6 F8: 5,6 G9: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F5,F6: 2.. / F5 = 2 => 14 pairs (_) / F6 = 2 => 0 pairs (X) H5,H6: 2.. / H5 = 2 => 0 pairs (X) / H6 = 2 => 14 pairs (_) F5,H5: 2.. / F5 = 2 => 14 pairs (_) / H5 = 2 => 0 pairs (X) F6,H6: 2.. / F6 = 2 => 0 pairs (X) / H6 = 2 => 14 pairs (_) E1,E2: 3.. / E1 = 3 => 0 pairs (X) / E2 = 3 => 0 pairs (_) I1,H2: 3.. / I1 = 3 => 0 pairs (*) / H2 = 3 => 0 pairs (X) H9,I9: 3.. / H9 = 3 => 0 pairs (*) / I9 = 3 => 0 pairs (X) E1,I1: 3.. / E1 = 3 => 0 pairs (X) / I1 = 3 => 0 pairs (_) E2,H2: 3.. / E2 = 3 => 0 pairs (*) / H2 = 3 => 0 pairs (X) H2,H9: 3.. / H2 = 3 => 0 pairs (X) / H9 = 3 => 0 pairs (_) I1,I9: 3.. / I1 = 3 => 0 pairs (*) / I9 = 3 => 0 pairs (X) D3,F3: 4.. / D3 = 4 => 0 pairs (X) / F3 = 4 => 19 pairs (_) C4,C5: 4.. / C4 = 4 => 19 pairs (_) / C5 = 4 => 0 pairs (X) F4,D5: 4.. / F4 = 4 => 0 pairs (X) / D5 = 4 => 19 pairs (_) C4,F4: 4.. / C4 = 4 => 19 pairs (_) / F4 = 4 => 0 pairs (X) C5,D5: 4.. / C5 = 4 => 0 pairs (X) / D5 = 4 => 19 pairs (_) D3,D5: 4.. / D3 = 4 => 0 pairs (X) / D5 = 4 => 19 pairs (_) F3,F4: 4.. / F3 = 4 => 19 pairs (_) / F4 = 4 => 0 pairs (X) I1,G3: 5.. / I1 = 5 => 0 pairs (X) / G3 = 5 => 0 pairs (_) E8,F8: 5.. / E8 = 5 => 0 pairs (X) / F8 = 5 => 0 pairs (_) E1,I1: 5.. / E1 = 5 => 0 pairs (*) / I1 = 5 => 0 pairs (X) E1,E8: 5.. / E1 = 5 => 0 pairs (*) / E8 = 5 => 0 pairs (X) G3,G9: 5.. / G3 = 5 => 0 pairs (*) / G9 = 5 => 0 pairs (X) H4,H9: 5.. / H4 = 5 => 0 pairs (*) / H9 = 5 => 0 pairs (X) H2,G3: 6.. / H2 = 6 => 0 pairs (*) / G3 = 6 => 0 pairs (X) F4,D6: 6.. / F4 = 6 => 0 pairs (*) / D6 = 6 => 0 pairs (X) H4,I6: 6.. / H4 = 6 => 0 pairs (X) / I6 = 6 => 0 pairs (_) E8,F8: 6.. / E8 = 6 => 0 pairs (*) / F8 = 6 => 0 pairs (X) E2,H2: 6.. / E2 = 6 => 0 pairs (X) / H2 = 6 => 0 pairs (_) F4,H4: 6.. / F4 = 6 => 0 pairs (*) / H4 = 6 => 0 pairs (X) D6,I6: 6.. / D6 = 6 => 0 pairs (X) / I6 = 6 => 0 pairs (_) D3,D6: 6.. / D3 = 6 => 0 pairs (*) / D6 = 6 => 0 pairs (X) E2,E8: 6.. / E2 = 6 => 0 pairs (X) / E8 = 6 => 0 pairs (_) G3,G9: 6.. / G3 = 6 => 0 pairs (X) / G9 = 6 => 0 pairs (_) I6,I9: 6.. / I6 = 6 => 0 pairs (*) / I9 = 6 => 0 pairs (X) F5,F6: 7.. / F5 = 7 => 0 pairs (X) / F6 = 7 => 14 pairs (_) I5,I6: 7.. / I5 = 7 => 14 pairs (_) / I6 = 7 => 0 pairs (X) F5,I5: 7.. / F5 = 7 => 0 pairs (X) / I5 = 7 => 14 pairs (_) F6,I6: 7.. / F6 = 7 => 14 pairs (_) / I6 = 7 => 0 pairs (X) C5,C6: 8.. / C5 = 8 => 0 pairs (X) / C6 = 8 => 14 pairs (_) H5,H6: 8.. / H5 = 8 => 14 pairs (_) / H6 = 8 => 0 pairs (X) C5,H5: 8.. / C5 = 8 => 0 pairs (X) / H5 = 8 => 14 pairs (_) C6,H6: 8.. / C6 = 8 => 14 pairs (_) / H6 = 8 => 0 pairs (X) * DURATION: 0:01:21.683869 START: 12:10:21.197647 END: 12:11:42.881516 2017-05-04 * CP COUNT: (43) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C4,C6,D5,D6,E1,E2,E8,F5,F6,F8,G3,G9,H2,H4,H5,H6,I1,I5) * 4698.127.8572.91.4123.7..9827.38.9.161..9.3..93..1.4..5967438123821..749741928... * PAIR I1: 3,5 COL I I9: 3,5,6 # reduction candidate for 3,5 I9: 3,5 => SOLVED * 469851273857239164123674598274386951615492387938517426596743812382165749741928635 I9: 6 => CTR * 4698.1273857239164123.7.59827.38695161..9.3..93..1.4..5967438123821..749741928... * PAIR H2: 3,6 COL H H9: 3,6,5 # reduction candidate for 3,6 H9: 3,6 => SOLVED * 469851273857239164123674598274386951615492387938517426596743812382165749741928635 H9: 5 => CTR * 4698.127.8572.9134123.7.69827.38.96161..9.3..93.61.4..5967438123821.67497419285.. * PAIR G3: 5,6 ROW 3 D3: 5,6,4 # reduction candidate for 5,6 D3: 5,6 # 19 pairs F3: 5,6,4 # reduction candidate for 5,6 F3: 5,6 => CTR * 4698.127.8572.91.412347..9827.38496161459.3879386174255967438123821..749741928.5. F3: 4 # 19 pairs * PAIR C4: 4,5 BLK 4 C5: 4,5,8 # reduction candidate for 4,5 C5: 8 => CTR * 4698.127.8572.91.4123.7..9827438.9.161849.3259356124875967438123821..749741928.5. C5: 4,5 # 14 pairs * PAIR C4: 4,5 ROW 4 F4: 4,5,6 # reduction candidate for 4,5 F4: 4,5 => CTR * 4698.127.8572.91.4123.7..9827.38.96161..9.3..93.61.4..5967438123821..749741928.5. F4: 6 => SOLVED * 469851273857239164123674598274386951615492387938517426596743812382165749741928635 * PAIR C6: 5,8 BLK 4 C5: 5,8,4 # reduction candidate for 5,8 C5: 4 => CTR * 4698.127.8572.91.4123.7..9827.38.9.161459.3879386174255967438123821..749741928.5. C5: 5,8 # 19 pairs * PAIR D5: 4,5 BLK 5 F4: 4,5,6 # reduction candidate for 4,5 F4: 4,5 => CTR * 4698.127.8572.91.4123.7..9827.38.96161..9.3..93.61.4..5967438123821..749741928.5. F4: 6 => SOLVED * 469851273857239164123674598274386951615492387938517426596743812382165749741928635 * PAIR D5: 4,5 ROW 5 C5: 4,5,8 # reduction candidate for 4,5 C5: 8 => CTR * 4698.127.8572.91.4123.7..9827438.9.161849.3259356124875967438123821..749741928.5. C5: 4,5 # 14 pairs * PAIR D5: 4,5 COL D D3: 4,5,6 # reduction candidate for 4,5 D3: 4,5 => CTR * 4698.1273857239164123.7..9827.38.9.161..9.3..93.61.4..5967438123821..749741928..6 D3: 6 => SOLVED * 469851273857239164123674598274386951615492387938517426596743812382165749741928635 * PAIR D6: 5,6 BLK 5 F4: 5,6,4 # reduction candidate for 5,6 F4: 4 => CTR * 4698.127.8572.91.4123.7..9827.38496161459.3879386174255967438123821..749741928.5. F4: 5,6 # 19 pairs * PAIR D6: 5,6 ROW 6 I6: 5,6,7 # reduction candidate for 5,6 I6: 7 => CTR * 4698.127.8572.91.4123.7..9827.38.96161..9.3.593.61.4.75967438123821..749741928.5. I6: 5,6 # 14 pairs * PAIR D6: 5,6 COL D D3: 5,6,4 # reduction candidate for 5,6 D3: 4 => CTR * 4698.127.8572.91.412347..9827.38496161459.3879386174255967438123821..749741928.5. D3: 5,6 # 19 pairs * PAIR H4: 5,6 BLK 6 I6: 5,6,7 # reduction candidate for 5,6 I6: 7 => CTR * 4698.127.8572.91.4123.7..9827.38.96161..9.3.593.61.4.75967438123821..749741928.5. I6: 5,6 # 14 pairs * PAIR H4: 5,6 ROW 4 F4: 5,6,4 # reduction candidate for 5,6 F4: 4 => CTR * 4698.127.8572.91.4123.7..9827.38496161459.3879386174255967438123821..749741928.5. F4: 5,6 # 19 pairs * PAIR H4: 5,6 COL H H9: 5,6,3 # reduction candidate for 5,6 H9: 5,6 => CTR * 4698.127.8572.9134123.7.69827.38.9.161..9.3..93.61.4..5967438123821.67497419285.. H9: 3 => SOLVED * 469851273857239164123674598274386951615492387938517426596743812382165749741928635 * PAIR I5: 5,7 BLK 6 I6: 5,7,6 # reduction candidate for 5,7 I6: 5,7 => CTR * 4698.127.8572.91.4123.7..9827.38.96161..9.3..93.61.4..5967438123821..749741928.5. I6: 6 => SOLVED * 469851273857239164123674598274386951615492387938517426596743812382165749741928635 * PAIR F8: 5,6 COL F F3: 5,6,4 # reduction candidate for 5,6 F3: 5,6 => CTR * 4698.127.8572.91.412347..9827.38496161459.3879386174255967438123821..749741928.5. F3: 4 # 19 pairs F4: 5,6,4 # reduction candidate for 5,6 F4: 5,6 # 19 pairs * PAIR G9: 5,6 BLK 9 H9: 5,6,3 # reduction candidate for 5,6 H9: 5,6 => CTR * 4698.127.8572.9134123.7.69827.38.9.161..9.3..93.61.4..5967438123821.67497419285.. H9: 3 => SOLVED * 469851273857239164123674598274386951615492387938517426596743812382165749741928635 I9: 5,6,3 # reduction candidate for 5,6 I9: 5,6 => SOLVED * 469851273857239164123674598274386951615492387938517426596743812382165749741928635 I9: 3 => CTR * 469831275857269134123.7.69827.38695161.49.3.793.51.4.65967438123821..749741928..3 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-271-base-pr-000.dot * REASONING * PRF # I9: 3,5 => SOL * DIS # I9: 6 => CTR => I9: 3,5 * PRF # H9: 3,6 => SOL * DIS # H9: 5 => CTR => H9: 3,6 * DIS # F3: 5,6 => CTR => F3: 4 * DIS # C5: 8 => CTR => C5: 4,5 * DIS # F4: 4,5 => CTR => F4: 6 * PRF # F4: 6 => SOL * DIS # C5: 4 => CTR => C5: 5,8 * DIS # F4: 4,5 => CTR => F4: 6 * PRF # F4: 6 => SOL * DIS # C5: 8 => CTR => C5: 4,5 * DIS # D3: 4,5 => CTR => D3: 6 * PRF # D3: 6 => SOL * DIS # F4: 4 => CTR => F4: 5,6 * DIS # I6: 7 => CTR => I6: 5,6 * DIS # D3: 4 => CTR => D3: 5,6 * DIS # I6: 7 => CTR => I6: 5,6 * DIS # F4: 4 => CTR => F4: 5,6 * DIS # H9: 5,6 => CTR => H9: 3 * PRF # H9: 3 => SOL * DIS # I6: 5,7 => CTR => I6: 6 * PRF # I6: 6 => SOL * DIS # F3: 5,6 => CTR => F3: 4 * DIS # H9: 5,6 => CTR => H9: 3 * PRF # H9: 3 => SOL * PRF # I9: 5,6 => SOL * DIS # I9: 3 => CTR => I9: 5,6 * CNT 28 HDP CHAINS / 40 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C4,C6,D5,D6,E1,E2,E8,F5,F6,F8,G3,G9,H2,H4,H5,H6,I1,I5) * 4698.127.8572.91.4123.7..9827.38.9.161..9.3..93..1.4..5967438123821..749741928... * PAIR I1: 3,5 COL I I9: 3,5,6 # reduction candidate for 3,5 I9: 3,5 => SOLVED * 469851273857239164123674598274386951615492387938517426596743812382165749741928635 * DURATION: 0:00:02.163387 START: 12:12:28.952397 END: 12:12:31.115784 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-271-base-pr-001.dot * REASONING * PRF # I9: 3,5 => SOL * STA I9: 3,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 271 solution: 469851273857239164123674598274386951615492387938517426596743812382165749741928635 info: 2200 FNBHWXY S8.f 43202 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 469851273857239164123674598274386951615492387938517426596743812382165749741928635 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 # I9: 3,5 => SOL * DIS # I9: 6 => CTR => I9: 3,5 * PRF # H9: 3,6 => SOL * DIS # H9: 5 => CTR => H9: 3,6 * INC # D3: 5,6 => UNS * DIS # F3: 5,6 => CTR => F3: 4 * INC # F3: 4 => UNS * INC # C5: 4,5 => UNS * DIS # C5: 8 => CTR => C5: 4,5 * DIS # F4: 4,5 => CTR => F4: 6 * PRF # F4: 6 => SOL * INC # C5: 5,8 => UNS * DIS # C5: 4 => CTR => C5: 5,8 * DIS # F4: 4,5 => CTR => F4: 6 * PRF # F4: 6 => SOL * INC # C5: 4,5 => UNS * DIS # C5: 8 => CTR => C5: 4,5 * DIS # D3: 4,5 => CTR => D3: 6 * PRF # D3: 6 => SOL * INC # F4: 5,6 => UNS * DIS # F4: 4 => CTR => F4: 5,6 * INC # I6: 5,6 => UNS * DIS # I6: 7 => CTR => I6: 5,6 * INC # D3: 5,6 => UNS * DIS # D3: 4 => CTR => D3: 5,6 * INC # I6: 5,6 => UNS * DIS # I6: 7 => CTR => I6: 5,6 * INC # F4: 5,6 => UNS * DIS # F4: 4 => CTR => F4: 5,6 * DIS # H9: 5,6 => CTR => H9: 3 * PRF # H9: 3 => SOL * DIS # I6: 5,7 => CTR => I6: 6 * PRF # I6: 6 => SOL * DIS # F3: 5,6 => CTR => F3: 4 * INC # F3: 4 => UNS * INC # F4: 5,6 => UNS * DIS # H9: 5,6 => CTR => H9: 3 * PRF # H9: 3 => SOL * PRF # I9: 5,6 => SOL * DIS # I9: 3 => CTR => I9: 5,6 * CNT 40 HDP CHAINS / 40 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # I9: 3,5 => SOL * STA I9: 3,5 * CNT 1 HDP CHAINS / 1 HYP OPENED