Analysis of xx-top500-483-base.sdk
Contents
Original Sudoku
level: medium
position: 6..2...1..3.............7..2..1.6....7....3.5......9..8.1.........45........3.... initial
Autosolve
position: 6..2...1..3..1.....1....7..253196...1798..3654...7.9218.1......3..45........3.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A2: 5,9 => SOL * DIS # A2: 7 => CTR => A2: 5,9 * DIS # H3: 5,9 => CTR => H3: 3,4,8 * DIS # A9: 5,9 => CTR => A9: 7 * PRF # A9: 7 => SOL * DIS # E3: 6 => CTR => E3: 4,8 * PRF # B1: 4,8 => SOL * DIS # B1: 9 => CTR => B1: 4,8 * DIS # C1: 4,8 => CTR => C1: 5,7 * PRF # C1: 5,7 => SOL * DIS # G1: 4,8 => CTR => G1: 5 * PRF # G1: 5 => SOL * DIS # I1: 4,8 => CTR => I1: 3,9 * PRF # F1: 3,5 => SOL * DIS # F1: 4,7,9 => CTR => F1: 3,5 * DIS # F3: 3,5 => CTR => F3: 4,9 * DIS # G1: 4,8 => CTR => G1: 5 * PRF # G1: 5 => SOL * DIS # G2: 4,8 => CTR => G2: 2,5,6 * DIS # G9: 4,8 => CTR => G9: 1,2,6 * DIS # C9: 6,7 => CTR => C9: 4,5 * CNT 21 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 # A2: 5,9 => SOL * STA A2: 5,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6..2...1..3.............7..2..1.6....7....3.5......9..8.1.........45........3.... | initial |
| 6..2...1..3..1.....1....7..253196...1798..3654...7.9218.1......3..45........3.... | autosolve |
| 687243519932517648514689732253196874179824365468375921891762453326458197745931286 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) A3: 5,9 E1: 4,8 B6: 6,8 C6: 6,8 E5: 2,4 F5: 2,4 D6: 3,5 F6: 3,5 G4: 4,8 C8: 6,7 E7: 2,6 F8: 1,8 F9: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F8,F9: 1.. / F8 = 1 => 11 pairs (_) / F9 = 1 => 12 pairs (_) G8,G9: 1.. / G8 = 1 => 12 pairs (_) / G9 = 1 => 11 pairs (_) F8,G8: 1.. / F8 = 1 => 11 pairs (_) / G8 = 1 => 12 pairs (_) F9,G9: 1.. / F9 = 1 => 12 pairs (_) / G9 = 1 => 11 pairs (_) C2,C3: 2.. / C2 = 2 => 16 pairs (_) / C3 = 2 => 13 pairs (_) E5,F5: 2.. / E5 = 2 => 17 pairs (_) / F5 = 2 => 0 pairs (X) B8,B9: 2.. / B8 = 2 => 13 pairs (_) / B9 = 2 => 14 pairs (_) E7,F7: 2.. / E7 = 2 => 0 pairs (X) / F7 = 2 => 17 pairs (_) C3,I3: 2.. / C3 = 2 => 13 pairs (_) / I3 = 2 => 16 pairs (_) E5,E7: 2.. / E5 = 2 => 17 pairs (_) / E7 = 2 => 0 pairs (X) F5,F7: 2.. / F5 = 2 => 0 pairs (X) / F7 = 2 => 17 pairs (_) D6,F6: 3.. / D6 = 3 => 11 pairs (_) / F6 = 3 => 0 pairs (X) H7,I7: 3.. / H7 = 3 => 0 pairs (X) / I7 = 3 => 0 pairs (_) F1,I1: 3.. / F1 = 3 => 0 pairs (*) / I1 = 3 => 0 pairs (X) D3,D6: 3.. / D3 = 3 => 0 pairs (X) / D6 = 3 => 11 pairs (_) H3,H7: 3.. / H3 = 3 => 0 pairs (*) / H7 = 3 => 0 pairs (X) E5,F5: 4.. / E5 = 4 => 0 pairs (X) / F5 = 4 => 17 pairs (_) D6,F6: 5.. / D6 = 5 => 0 pairs (X) / F6 = 5 => 11 pairs (_) A9,C9: 5.. / A9 = 5 => 0 pairs (X) / C9 = 5 => 15 pairs (_) G7,H7: 5.. / G7 = 5 => 0 pairs (X) / H7 = 5 => 0 pairs (_) B6,C6: 6.. / B6 = 6 => 0 pairs (*) / C6 = 6 => 0 pairs (X) E3,E7: 6.. / E3 = 6 => 0 pairs (X) / E7 = 6 => 17 pairs (_) H4,I4: 7.. / H4 = 7 => 15 pairs (_) / I4 = 7 => 14 pairs (_) C1,F1: 7.. / C1 = 7 => 0 pairs (*) / F1 = 7 => 0 pairs (X) A2,A9: 7.. / A2 = 7 => 0 pairs (X) / A9 = 7 => 0 pairs (_) E1,E3: 8.. / E1 = 8 => 0 pairs (X) / E3 = 8 => 0 pairs (_) B6,C6: 8.. / B6 = 8 => 0 pairs (X) / C6 = 8 => 0 pairs (_) F8,F9: 8.. / F8 = 8 => 12 pairs (_) / F9 = 8 => 11 pairs (_) B1,B6: 8.. / B1 = 8 => 0 pairs (*) / B6 = 8 => 0 pairs (X) * DURATION: 0:00:44.078297 START: 19:08:40.514660 END: 19:09:24.592957 2017-05-04 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B6,C6,C8,D6,E1,E5,E7,F5,F6,F8,F9,G4) * 6..2...1..3..1.....1....7..253196...1798..3654...7.9218.1......3..45........3.... * PAIR A3: 5,9 BLK 1 A2: 5,9,7 # reduction candidate for 5,9 A2: 5,9 => SOLVED * 687243519932517648514689732253196874179824365468375921891762453326458197745931286 A2: 7 => CTR * 69.2.7.1373..1....51....7..253196...1798..365486.7.9218.1...53.3.745....9.5.3.... * PAIR A3: 5,9 ROW 3 D3: 5,9,3,6 # reduction candidate for 5,9 D3: 5,9 # 13 pairs F3: 5,9,3,4 # reduction candidate for 5,9 F3: 5,9 # 15 pairs H3: 5,9,3,4,8 # reduction candidate for 5,9 H3: 5,9 => CTR * 69.2...13.3..1....51....79.253196...1798..365486.7.9218.1...53.3.745........3.... H3: 3,4,8 # 13 pairs * PAIR A3: 5,9 COL A A9: 5,9,7 # reduction candidate for 5,9 A9: 5,9 => CTR * 69.2.7.1373..1....51....7..253196...1798..365486.7.9218.1...53.3.745....9.5.3.... A9: 7 => SOLVED * 687243519932517648514689732253196874179824365468375921891762453326458197745931286 * PAIR E1: 4,8 BLK 2 E3: 4,8,6 # reduction candidate for 4,8 E3: 6 => CTR * 69.287.1373..1....51..6.7..253196...179842365486.7.9218.1.2953.3.745....9.5.3.... E3: 4,8 # 17 pairs * PAIR E1: 4,8 ROW 1 B1: 4,8,9 # reduction candidate for 4,8 B1: 4,8 => SOLVED * 687243519932517648514689732253196874179824365468375921891762453326458197745931286 B1: 9 => CTR * 69.2.751373..1....51....7..253196...1798..365486.7.9218.1......3.745....9.5.3.... C1: 4,8,5,7 # reduction candidate for 4,8 C1: 4,8 => CTR * 6..2.7513.3..1.....1....7..253196...1798..3654...7.9218.1......3..45........3.... C1: 5,7 => SOLVED * 687243519932517648514689732253196874179824365468375921891762453326458197745931286 G1: 4,8,5 # reduction candidate for 4,8 G1: 4,8 => CTR * 69.2...13.3..1....51....7..253196...1798..365486.7.9218.1....3.3.745........3.... G1: 5 => SOLVED * 687243519932517648514689732253196874179824365468375921891762453326458197745931286 I1: 4,8,3,9 # reduction candidate for 4,8 I1: 4,8 => CTR * 6972.351.53..1.....1....7..253196...1798..3654..3759218.1......3..45........3.... I1: 3,9 # 14 pairs * PAIR D6: 3,5 COL D D3: 3,5,6,9 # reduction candidate for 3,5 D3: 6,9 # 16 pairs D3: 3,5 # 14 pairs * PAIR F6: 3,5 COL F F1: 3,5,4,7,9 # reduction candidate for 3,5 F1: 3,5 => SOLVED * 687243519932517648514689732253196874179824365468375921891762453326458197745931286 F1: 4,7,9 => CTR * 6.52.7.13.3..1....91....7..253196...1798..3654...7.9218.1...53.3..45....5...3.... F3: 3,5,4,9 # reduction candidate for 3,5 F3: 3,5 => CTR * 6.52.7.13.3..1....91....7..253196...1798..3654...7.9218.1...53.3..45....5...3.... F3: 4,9 # 14 pairs * PAIR G4: 4,8 BLK 6 H4: 4,8,7 # reduction candidate for 4,8 H4: 4,8 # 14 pairs I4: 4,8,7 # reduction candidate for 4,8 I4: 4,8 # 15 pairs * PAIR G4: 4,8 COL G G1: 4,8,5 # reduction candidate for 4,8 G1: 4,8 => CTR * 69.2...13.3..1....51....7..253196...1798..365486.7.9218.1....3.3.745........3.... G1: 5 => SOLVED * 687243519932517648514689732253196874179824365468375921891762453326458197745931286 G2: 4,8,2,5,6 # reduction candidate for 4,8 G2: 4,8 => CTR * 6.7283514.32.14896.1..6.732253196...1798..3654..375921841.2.6533..45.......63.... G2: 2,5,6 # 13 pairs G9: 4,8,1,2,6 # reduction candidate for 4,8 G9: 4,8 => CTR * 6.7283514.3..1.2.6.12.6.738253196...1798..3654..375921841.2.6533..4581.....631... G9: 1,2,6 # 13 pairs * PAIR C8: 6,7 BLK 7 C9: 6,7,4,5 # reduction candidate for 6,7 C9: 6,7 => CTR * 6..2.7.1.73..1....91....7..253196...1798..3654...7.9218.1......3..45....5...3.... C9: 4,5 # 14 pairs * PAIR C8: 6,7 ROW 8 I8: 6,7,2,8,9 # reduction candidate for 6,7 I8: 6,7 # 16 pairs I8: 2,8,9 # 13 pairs * PAIR F8: 1,8 ROW 8 G8: 1,8,2,6 # reduction candidate for 1,8 G8: 1,8 # 15 pairs G8: 2,6 # 12 pairs * PAIR F9: 1,8 ROW 9 G9: 1,8,2,4,6 # reduction candidate for 1,8 G9: 1,8 # 14 pairs G9: 2,4,6 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-483-base-pr-000.dot * REASONING * PRF # A2: 5,9 => SOL * DIS # A2: 7 => CTR => A2: 5,9 * DIS # H3: 5,9 => CTR => H3: 3,4,8 * DIS # A9: 5,9 => CTR => A9: 7 * PRF # A9: 7 => SOL * DIS # E3: 6 => CTR => E3: 4,8 * PRF # B1: 4,8 => SOL * DIS # B1: 9 => CTR => B1: 4,8 * DIS # C1: 4,8 => CTR => C1: 5,7 * PRF # C1: 5,7 => SOL * DIS # G1: 4,8 => CTR => G1: 5 * PRF # G1: 5 => SOL * DIS # I1: 4,8 => CTR => I1: 3,9 * PRF # F1: 3,5 => SOL * DIS # F1: 4,7,9 => CTR => F1: 3,5 * DIS # F3: 3,5 => CTR => F3: 4,9 * DIS # G1: 4,8 => CTR => G1: 5 * PRF # G1: 5 => SOL * DIS # G2: 4,8 => CTR => G2: 2,5,6 * DIS # G9: 4,8 => CTR => G9: 1,2,6 * DIS # C9: 6,7 => CTR => C9: 4,5 * CNT 21 HDP CHAINS / 40 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B6,C6,C8,D6,E1,E5,E7,F5,F6,F8,F9,G4) * 6..2...1..3..1.....1....7..253196...1798..3654...7.9218.1......3..45........3.... * PAIR A3: 5,9 BLK 1 A2: 5,9,7 # reduction candidate for 5,9 A2: 5,9 => SOLVED * 687243519932517648514689732253196874179824365468375921891762453326458197745931286 * DURATION: 0:00:02.483052 START: 19:09:59.673329 END: 19:10:02.156381 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-483-base-pr-001.dot * REASONING * PRF # A2: 5,9 => SOL * STA A2: 5,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 483 solution: 687243519932517648514689732253196874179824365468375921891762453326458197745931286 info: 95819 FNBHYK S8.f 34908 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 687243519932517648514689732253196874179824365468375921891762453326458197745931286 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 # A2: 5,9 => SOL * DIS # A2: 7 => CTR => A2: 5,9 * INC # D3: 5,9 => UNS * INC # F3: 5,9 => UNS * DIS # H3: 5,9 => CTR => H3: 3,4,8 * INC # H3: 3,4,8 => UNS * DIS # A9: 5,9 => CTR => A9: 7 * PRF # A9: 7 => SOL * INC # E3: 4,8 => UNS * DIS # E3: 6 => CTR => E3: 4,8 * PRF # B1: 4,8 => SOL * DIS # B1: 9 => CTR => B1: 4,8 * DIS # C1: 4,8 => CTR => C1: 5,7 * PRF # C1: 5,7 => SOL * DIS # G1: 4,8 => CTR => G1: 5 * PRF # G1: 5 => SOL * DIS # I1: 4,8 => CTR => I1: 3,9 * INC # I1: 3,9 => UNS * INC # D3: 3,5 => UNS * INC # D3: 6,9 => UNS * PRF # F1: 3,5 => SOL * DIS # F1: 4,7,9 => CTR => F1: 3,5 * DIS # F3: 3,5 => CTR => F3: 4,9 * INC # F3: 4,9 => UNS * INC # H4: 4,8 => UNS * INC # I4: 4,8 => UNS * DIS # G1: 4,8 => CTR => G1: 5 * PRF # G1: 5 => SOL * DIS # G2: 4,8 => CTR => G2: 2,5,6 * INC # G2: 2,5,6 => UNS * DIS # G9: 4,8 => CTR => G9: 1,2,6 * INC # G9: 1,2,6 => UNS * DIS # C9: 6,7 => CTR => C9: 4,5 * INC # C9: 4,5 => UNS * INC # I8: 6,7 => UNS * INC # I8: 2,8,9 => UNS * INC # G8: 1,8 => UNS * INC # G8: 2,6 => UNS * INC # G9: 1,8 => UNS * INC # G9: 2,4,6 => UNS * CNT 40 HDP CHAINS / 40 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A2: 5,9 => SOL * STA A2: 5,9 * CNT 1 HDP CHAINS / 1 HYP OPENED