Analysis of xx-top500-368-base.sdk
Contents
Original Sudoku
level: medium
position: 1.4...5.......27.....3......736...........1...2.......8...4..2.....1...6.......3. initial
Autosolve
position: 134.6.5.2...1.27432.73.461..736.12.....23.1...2147.3..8...4392.3.2.1...67...26.3. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # H6: 8,9 => SOL * DIS # I4: 8,9 => CTR => I4: 4,5 * PRF # F6: 5 => SOL * DIS # I4: 8,9 => CTR => I4: 4,5 * PRF # F6: 5,9 => SOL * DIS # F6: 8 => CTR => F6: 5,9 * DIS # B7: 5,6 => CTR => B7: 1 * DIS # I7: 1 => CTR => I7: 5,7 * DIS # I7: 1 => CTR => I7: 5,7 * CNT 9 HDP CHAINS / 48 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # H6: 8,9 => SOL * STA H6: 8,9 * CNT 1 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1.4...5.......27.....3......736...........1...2.......8...4..2.....1...6.......3. | initial |
| 134.6.5.2...1.27432.73.461..736.12.....23.1...2147.3..8...4392.3.2.1...67...26.3. | autosolve |
| 134867592568192743297354618973681254485239167621475389816743925352918476749526831 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) H1: 8,9 I3: 8,9 E4: 8,9 F5: 5,9 C7: 5,6 C9: 5,9 D7: 5,7 G8: 4,8 H8: 5,7 G9: 4,8 I9: 1,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B7,B9: 1.. / B7 = 1 => 10 pairs (_) / B9 = 1 => 0 pairs (X) I7,I9: 1.. / I7 = 1 => 0 pairs (X) / I9 = 1 => 10 pairs (_) B7,I7: 1.. / B7 = 1 => 10 pairs (_) / I7 = 1 => 0 pairs (X) B9,I9: 1.. / B9 = 1 => 0 pairs (X) / I9 = 1 => 10 pairs (_) A4,A5: 4.. / A4 = 4 => 12 pairs (_) / A5 = 4 => 12 pairs (_) I4,I5: 4.. / I4 = 4 => 12 pairs (_) / I5 = 4 => 12 pairs (_) B8,B9: 4.. / B8 = 4 => 11 pairs (_) / B9 = 4 => 10 pairs (_) G8,G9: 4.. / G8 = 4 => 10 pairs (_) / G9 = 4 => 11 pairs (_) A4,I4: 4.. / A4 = 4 => 12 pairs (_) / I4 = 4 => 12 pairs (_) A5,I5: 4.. / A5 = 4 => 12 pairs (_) / I5 = 4 => 12 pairs (_) B8,G8: 4.. / B8 = 4 => 11 pairs (_) / G8 = 4 => 10 pairs (_) B9,G9: 4.. / B9 = 4 => 10 pairs (_) / G9 = 4 => 11 pairs (_) E2,E3: 5.. / E2 = 5 => 15 pairs (_) / E3 = 5 => 13 pairs (_) F5,F6: 5.. / F5 = 5 => 12 pairs (_) / F6 = 5 => 0 pairs (*) B3,E3: 5.. / B3 = 5 => 15 pairs (_) / E3 = 5 => 13 pairs (_) H5,H6: 6.. / H5 = 6 => 15 pairs (_) / H6 = 6 => 12 pairs (_) B7,C7: 6.. / B7 = 6 => 0 pairs (X) / C7 = 6 => 11 pairs (_) A6,H6: 6.. / A6 = 6 => 15 pairs (_) / H6 = 6 => 12 pairs (_) D1,F1: 7.. / D1 = 7 => 15 pairs (_) / F1 = 7 => 13 pairs (_) H5,I5: 7.. / H5 = 7 => 13 pairs (_) / I5 = 7 => 14 pairs (_) I7,H8: 7.. / I7 = 7 => 13 pairs (_) / H8 = 7 => 14 pairs (_) D7,I7: 7.. / D7 = 7 => 14 pairs (_) / I7 = 7 => 13 pairs (_) F1,F8: 7.. / F1 = 7 => 13 pairs (_) / F8 = 7 => 15 pairs (_) H5,H8: 7.. / H5 = 7 => 13 pairs (_) / H8 = 7 => 14 pairs (_) I5,I7: 7.. / I5 = 7 => 14 pairs (_) / I7 = 7 => 13 pairs (_) H1,I3: 8.. / H1 = 8 => 0 pairs (X) / I3 = 8 => 0 pairs (_) B5,C5: 8.. / B5 = 8 => 13 pairs (_) / C5 = 8 => 11 pairs (_) E4,F6: 8.. / E4 = 8 => 0 pairs (*) / F6 = 8 => 0 pairs (X) G8,G9: 8.. / G8 = 8 => 11 pairs (_) / G9 = 8 => 10 pairs (_) D9,G9: 8.. / D9 = 8 => 11 pairs (_) / G9 = 8 => 10 pairs (_) C2,C5: 8.. / C2 = 8 => 13 pairs (_) / C5 = 8 => 11 pairs (_) H1,I3: 9.. / H1 = 9 => 0 pairs (*) / I3 = 9 => 0 pairs (X) * DURATION: 0:00:51.354533 START: 15:25:13.952546 END: 15:26:05.307079 2017-05-04 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C7,C9,D7,E4,F5,G8,G9,H1,H8,I3,I9) * 134.6.5.2...1.27432.73.461..736.12.....23.1...2147.3..8...4392.3.2.1...67...26.3. * PAIR H1: 8,9 ROW 1 D1: 8,9,7 # reduction candidate for 8,9 D1: 8,9 # 13 pairs F1: 8,9,7 # reduction candidate for 8,9 F1: 8,9 # 15 pairs * PAIR H1: 8,9 COL H H4: 8,9,5 # reduction candidate for 8,9 H4: 8,9 # 15 pairs H6: 8,9,5,6 # reduction candidate for 8,9 H6: 8,9 => SOLVED * 134867592568192743297354618973681254485239167621475389816743925352918476749526831 H6: 5,6 # 12 pairs * PAIR I3: 8,9 ROW 3 B3: 8,9,5 # reduction candidate for 8,9 B3: 8,9 # 13 pairs E3: 8,9,5 # reduction candidate for 8,9 E3: 8,9 # 15 pairs * PAIR I3: 8,9 COL I I4: 8,9,4,5 # reduction candidate for 8,9 I4: 8,9 => CTR * 134.6.5.2...1.27432.73.461.4736.125....23.1.4.2147.3..8...439273.2.1...67...26.3. I4: 4,5 # 12 pairs I6: 8,9,5 # reduction candidate for 8,9 I6: 8,9 # 13 pairs * PAIR E4: 8,9 BLK 5 F6: 8,9,5 # reduction candidate for 8,9 F6: 5 => SOLVED * 134867592568192743297354618973681254485239167621475389816743925352918476749526831 F6: 8,9 # 12 pairs * PAIR E4: 8,9 ROW 4 H4: 8,9,5 # reduction candidate for 8,9 H4: 8,9 # 15 pairs I4: 8,9,4,5 # reduction candidate for 8,9 I4: 8,9 => CTR * 134.6.5.2...1.27432.73.461.4736.125....23.1.4.2147.3..8...439273.2.1...67...26.3. I4: 4,5 # 12 pairs * PAIR E4: 8,9 COL E E2: 8,9,5 # reduction candidate for 8,9 E2: 8,9 # 13 pairs E3: 8,9,5 # reduction candidate for 8,9 E3: 8,9 # 15 pairs * PAIR F5: 5,9 BLK 5 F6: 5,9,8 # reduction candidate for 5,9 F6: 5,9 => SOLVED * 134867592568192743297354618973681254485239167621475389816743925352918476749526831 F6: 8 => CTR * 134.6.582...1.27432.73.4619.7369125....2351...214783..8...4392.3.2.1...67...26.3. * PAIR F5: 5,9 ROW 5 A5: 5,9,4,6 # reduction candidate for 5,9 A5: 5,9 # 14 pairs B5: 5,9,6,8 # reduction candidate for 5,9 B5: 5,9 # 16 pairs C5: 5,9,6,8 # reduction candidate for 5,9 C5: 5,9 # 18 pairs H5: 5,9,6,7 # reduction candidate for 5,9 H5: 5,9 # 18 pairs I5: 5,9,4,7 # reduction candidate for 5,9 I5: 5,9 # 14 pairs * PAIR C7: 5,6 BLK 7 B7: 5,6,1 # reduction candidate for 5,6 B7: 5,6 => CTR * 134967582...1.27432.73.4619.7369125....23.1.7.2147.3..8..743921342519876719826435 B7: 1 # 10 pairs * PAIR C7: 5,6 COL C C2: 5,6,8,9 # reduction candidate for 5,6 C2: 5,6 # 13 pairs C5: 5,6,8,9 # reduction candidate for 5,6 C5: 5,6 # 16 pairs * PAIR C9: 5,9 BLK 7 B8: 5,9,4 # reduction candidate for 5,9 B8: 5,9 # 10 pairs B9: 5,9,1,4 # reduction candidate for 5,9 B9: 5,9 # 11 pairs * PAIR C9: 5,9 ROW 9 D9: 5,9,8 # reduction candidate for 5,9 D9: 8 # 11 pairs D9: 5,9 # 10 pairs * PAIR C9: 5,9 COL C C2: 5,9,6,8 # reduction candidate for 5,9 C2: 5,9 # 12 pairs C5: 5,9,6,8 # reduction candidate for 5,9 C5: 5,9 # 18 pairs * PAIR D7: 5,7 BLK 8 D8: 5,7,8,9 # reduction candidate for 5,7 D8: 5,7 # 16 pairs D8: 8,9 # 12 pairs * PAIR D7: 5,7 ROW 7 I7: 5,7,1 # reduction candidate for 5,7 I7: 1 => CTR * 134967582...1.27432.73.4619.736.12.44..23.1.7.2147.3..8..743921342519876719826435 I7: 5,7 # 10 pairs * PAIR H8: 5,7 BLK 9 I7: 5,7,1 # reduction candidate for 5,7 I7: 1 => CTR * 134967582...1.27432.73.4619.736.12.44..23.1.7.2147.3..8..743921342519876719826435 I7: 5,7 # 10 pairs * PAIR H8: 5,7 ROW 8 D8: 5,7,8,9 # reduction candidate for 5,7 D8: 5,7 # 16 pairs D8: 8,9 # 12 pairs * PAIR H8: 5,7 COL H H5: 5,7,6,9 # reduction candidate for 5,7 H5: 5,7 # 16 pairs H5: 6,9 # 15 pairs * PAIR I9: 1,5 BLK 9 I7: 1,5,7 # reduction candidate for 1,5 I7: 1,5 # 14 pairs I7: 7 # 13 pairs * PAIR I9: 1,5 ROW 9 B9: 1,5,4,9 # reduction candidate for 1,5 B9: 4,9 # 11 pairs B9: 1,5 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-368-base-pr-000.dot * REASONING * PRF # H6: 8,9 => SOL * DIS # I4: 8,9 => CTR => I4: 4,5 * PRF # F6: 5 => SOL * DIS # I4: 8,9 => CTR => I4: 4,5 * PRF # F6: 5,9 => SOL * DIS # F6: 8 => CTR => F6: 5,9 * DIS # B7: 5,6 => CTR => B7: 1 * DIS # I7: 1 => CTR => I7: 5,7 * DIS # I7: 1 => CTR => I7: 5,7 * CNT 9 HDP CHAINS / 48 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C7,C9,D7,E4,F5,G8,G9,H1,H8,I3,I9) * 134.6.5.2...1.27432.73.461..736.12.....23.1...2147.3..8...4392.3.2.1...67...26.3. * PAIR H1: 8,9 ROW 1 D1: 8,9,7 # reduction candidate for 8,9 D1: 8,9 # 13 pairs F1: 8,9,7 # reduction candidate for 8,9 F1: 8,9 # 15 pairs * PAIR H1: 8,9 COL H H4: 8,9,5 # reduction candidate for 8,9 H4: 8,9 # 15 pairs H6: 8,9,5,6 # reduction candidate for 8,9 H6: 8,9 => SOLVED * 134867592568192743297354618973681254485239167621475389816743925352918476749526831 * DURATION: 0:00:04.668630 START: 15:26:47.655668 END: 15:26:52.324298 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-368-base-pr-001.dot * REASONING * PRF # H6: 8,9 => SOL * STA H6: 8,9 * CNT 1 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 368 solution: 134867592568192743297354618973681254485239167621475389816743925352918476749526831 info: 5147 FNBTWX S8.f 26045 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 134867592568192743297354618973681254485239167621475389816743925352918476749526831 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 # D1: 8,9 => UNS * INC # F1: 8,9 => UNS * INC # H4: 8,9 => UNS * PRF # H6: 8,9 => SOL * INC # H6: 5,6 => UNS * INC # B3: 8,9 => UNS * INC # E3: 8,9 => UNS * DIS # I4: 8,9 => CTR => I4: 4,5 * INC # I4: 4,5 => UNS * INC # I6: 8,9 => UNS * INC # F6: 8,9 => UNS * PRF # F6: 5 => SOL * INC # H4: 8,9 => UNS * DIS # I4: 8,9 => CTR => I4: 4,5 * INC # I4: 4,5 => UNS * INC # E2: 8,9 => UNS * INC # E3: 8,9 => UNS * PRF # F6: 5,9 => SOL * DIS # F6: 8 => CTR => F6: 5,9 * INC # A5: 5,9 => UNS * INC # B5: 5,9 => UNS * INC # C5: 5,9 => UNS * INC # H5: 5,9 => UNS * INC # I5: 5,9 => UNS * DIS # B7: 5,6 => CTR => B7: 1 * INC # B7: 1 => UNS * INC # C2: 5,6 => UNS * INC # C5: 5,6 => UNS * INC # B8: 5,9 => UNS * INC # B9: 5,9 => UNS * INC # D9: 5,9 => UNS * INC # D9: 8 => UNS * INC # C2: 5,9 => UNS * INC # C5: 5,9 => UNS * INC # D8: 5,7 => UNS * INC # D8: 8,9 => UNS * INC # I7: 5,7 => UNS * DIS # I7: 1 => CTR => I7: 5,7 * INC # I7: 5,7 => UNS * DIS # I7: 1 => CTR => I7: 5,7 * INC # D8: 5,7 => UNS * INC # D8: 8,9 => UNS * INC # H5: 5,7 => UNS * INC # H5: 6,9 => UNS * INC # I7: 1,5 => UNS * INC # I7: 7 => UNS * INC # B9: 1,5 => UNS * INC # B9: 4,9 => UNS * CNT 48 HDP CHAINS / 48 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D1: 8,9 => UNS * INC # F1: 8,9 => UNS * INC # H4: 8,9 => UNS * PRF # H6: 8,9 => SOL * STA H6: 8,9 * CNT 4 HDP CHAINS / 4 HYP OPENED