Analysis of xx-top500-043-base.sdk
Contents
Original Sudoku
level: medium
position: .3.5.............4.......6.6.4...1.....3..7..2............64.2.....1.3...8......5 initial
Autosolve
position: .3.5.............4.......6.6.4...1.....3..7..2.3......3...64.2.....153...8......5 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 2,6 => CTR => C1: 1,7,8,9 * PRF # C1: 1,7,8,9 => SOL * DIS # C2: 2,6 => CTR => C2: 1,5,7,8,9 * DIS # F2: 2,6 => CTR => F2: 1,3,7,8,9 * DIS # B8: 2,6 => CTR => B8: 4 * PRF # B8: 4 => SOL * DIS # E3: 2,4 => CTR => E3: 3,7,8,9 * PRF # B8: 2,4 => SOL * DIS # B8: 6 => CTR => B8: 2,4 * PRF # F1: 1,6 => SOL * DIS # F1: 2,7,8,9 => CTR => F1: 1,6 * DIS # F2: 1,6 => CTR => F2: 2,3,7,8,9 * DIS # C2: 1,6 => CTR => C2: 2,5,7,8,9 * PRF # D6: 1,6 => SOL * DIS # D6: 4 => CTR => D6: 1,6 * DIS # A3: 1,4 => CTR => A3: 5,7,8,9 * DIS # D6: 1,4 => CTR => D6: 6 * PRF # D6: 6 => SOL * DIS # D6: 1 => CTR => D6: 4,6 * DIS # I8: 8,9 => CTR => I8: 6,7 * CNT 20 HDP CHAINS / 35 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 2,6 => CTR => C1: 1,7,8,9 * PRF C1: 1,7,8,9 => SOL * STA C1: 1,7,8,9 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .3.5.............4.......6.6.4...1.....3..7..2............64.2.....1.3...8......5 | initial |
| .3.5.............4.......6.6.4...1.....3..7..2.3......3...64.2.....153...8......5 | autosolve |
| 438576219569123874721489563694758132815342796273691458357864921946215387182937645 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) B2: 2,6 B3: 2,4 D2: 1,6 D3: 1,4 G6: 4,6 G7: 8,9 G9: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I7,H9: 1.. / I7 = 1 => 8 pairs (_) / H9 = 1 => 9 pairs (_) I4,I5: 2.. / I4 = 2 => 9 pairs (_) / I5 = 2 => 0 pairs (X) H2,I3: 3.. / H2 = 3 => 0 pairs (X) / I3 = 3 => 7 pairs (_) H4,I4: 3.. / H4 = 3 => 7 pairs (_) / I4 = 3 => 0 pairs (X) E9,F9: 3.. / E9 = 3 => 7 pairs (_) / F9 = 3 => 7 pairs (_) H2,H4: 3.. / H2 = 3 => 0 pairs (X) / H4 = 3 => 7 pairs (_) I3,I4: 3.. / I3 = 3 => 7 pairs (_) / I4 = 3 => 0 pairs (X) A1,E1: 4.. / A1 = 4 => 0 pairs (*) / E1 = 4 => 0 pairs (X) E5,H5: 4.. / E5 = 4 => 0 pairs (*) / H5 = 4 => 0 pairs (X) B3,B8: 4.. / B3 = 4 => 0 pairs (X) / B8 = 4 => 0 pairs (_) D3,D6: 4.. / D3 = 4 => 0 pairs (*) / D6 = 4 => 0 pairs (X) G6,G9: 4.. / G6 = 4 => 0 pairs (*) / G9 = 4 => 0 pairs (X) G2,G3: 5.. / G2 = 5 => 7 pairs (_) / G3 = 5 => 7 pairs (_) B7,C7: 5.. / B7 = 5 => 12 pairs (_) / C7 = 5 => 8 pairs (_) I8,G9: 6.. / I8 = 6 => 0 pairs (X) / G9 = 6 => 0 pairs (_) C1,F1: 6.. / C1 = 6 => 0 pairs (X) / F1 = 6 => 0 pairs (_) F5,I5: 6.. / F5 = 6 => 0 pairs (X) / I5 = 6 => 0 pairs (_) C9,G9: 6.. / C9 = 6 => 0 pairs (X) / G9 = 6 => 0 pairs (_) B2,B8: 6.. / B2 = 6 => 0 pairs (*) / B8 = 6 => 0 pairs (X) D2,D6: 6.. / D2 = 6 => 0 pairs (X) / D6 = 6 => 0 pairs (_) G6,G9: 6.. / G6 = 6 => 0 pairs (X) / G9 = 6 => 0 pairs (_) B4,B6: 7.. / B4 = 7 => 8 pairs (_) / B6 = 7 => 8 pairs (_) A5,C5: 8.. / A5 = 8 => 7 pairs (_) / C5 = 8 => 7 pairs (_) D7,D8: 8.. / D7 = 8 => 9 pairs (_) / D8 = 8 => 8 pairs (_) * DURATION: 0:00:38.607219 START: 04:08:40.904343 END: 04:09:19.511562 2017-05-04 * CP COUNT: (24) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B3,D2,D3,G6,G7,G9) * .3.5.............4.......6.6.4...1.....3..7..2.3......3...64.2.....153...8......5 * PAIR B2: 2,6 BLK 1 C1: 2,6,1,7,8,9 # reduction candidate for 2,6 C1: 2,6 => CTR * .32546...........4.4.1...6.6.4...1.....3..7..2.34..6..3...64.2.....153.6.86...4.5 C1: 1,7,8,9 => SOLVED * 438576219569123874721489563694758132815342796273691458357864921946215387182937645 C2: 2,6,1,5,7,8,9 # reduction candidate for 2,6 C2: 2,6 => CTR * .3.5.6......1....4.4.....6.6.4...1.....3..7..2.3......3...64.2.....153...8......5 C2: 1,5,7,8,9 # 7 pairs * PAIR B2: 2,6 ROW 2 F2: 2,6,1,3,7,8,9 # reduction candidate for 2,6 F2: 2,6 => CTR * 43.5...1..6.1.2..4.2.4...6.6.4...1.....34.7..2.36..4..3...64.2..4..153...8....645 F2: 1,3,7,8,9 # 7 pairs * PAIR B2: 2,6 COL B B8: 2,6,4 # reduction candidate for 2,6 B8: 2,6 => CTR * .3.546...........4.4.1...6.6.4...1.....3..7..2.34..6..3...64.2.....153.6.86...4.5 B8: 4 => SOLVED * 438576219569123874721489563694758132815342796273691458357864921946215387182937645 * PAIR B3: 2,4 ROW 3 E3: 2,4,3,7,8,9 # reduction candidate for 2,4 E3: 2,4 => CTR * .3.5.6...........4...1...6.6.4...1.....3..7..2.34..6..3...64.2.....153.6.86...4.5 E3: 3,7,8,9 # 7 pairs * PAIR B3: 2,4 COL B B8: 2,4,6 # reduction candidate for 2,4 B8: 2,4 => SOLVED * 438576219569123874721489563694758132815342796273691458357864921946215387182937645 B8: 6 => CTR * .3.5.............4.4.1...6.6.4...1.....3..7..2.34..6..3...64.2..6..153...8....4.5 * PAIR D2: 1,6 BLK 2 F1: 1,6,2,7,8,9 # reduction candidate for 1,6 F1: 1,6 => SOLVED * 438576219569123874721489563694758132815342796273691458357864921946215387182937645 F1: 2,7,8,9 => CTR * .365......2......4.4.1...6.6.4...1.....3..7..2.34..6..3...64.2.....153...8......5 F2: 1,6,2,3,7,8,9 # reduction candidate for 1,6 F2: 1,6 => CTR * .365......2......4.4.....6.6.4...1.....3..7..2.3......3...64.2.....153...8......5 F2: 2,3,7,8,9 # 7 pairs * PAIR D2: 1,6 ROW 2 C2: 1,6,2,5,7,8,9 # reduction candidate for 1,6 C2: 1,6 => CTR * .3.5......2......4.4.1...6.6.4...1.....3..7..2.34..6..3...64.2..6..153...8....4.5 C2: 2,5,7,8,9 # 7 pairs * PAIR D2: 1,6 COL D D6: 1,6,4 # reduction candidate for 1,6 D6: 1,6 => SOLVED * 438576219569123874721489563694758132815342796273691458357864921946215387182937645 D6: 4 => CTR * .3.5........6....4...1...6.6.4...1.....3..7..2.34..6..3...64.2..6..153...8....4.5 * PAIR D3: 1,4 ROW 3 A3: 1,4,5,7,8,9 # reduction candidate for 1,4 A3: 1,4 => CTR * 43.5.6.1..6.1....412.4...6.6.4...1.....34.7.62.36..4..3...64.21.462153...8....645 A3: 5,7,8,9 # 7 pairs * PAIR D3: 1,4 COL D D6: 1,4,6 # reduction candidate for 1,4 D6: 1,4 => CTR * .365......2.6....4.4.1...6.6.4...1.....3..7..2.34.....3...64.2..6..153...8....6.5 D6: 6 => SOLVED * 438576219569123874721489563694758132815342796273691458357864921946215387182937645 * PAIR G6: 4,6 ROW 6 D6: 4,6,1 # reduction candidate for 4,6 D6: 1 => CTR * .3.5........6....4...4...6.6.4...1.....3..7..2.31.....3...64.2.....153...8......5 D6: 4,6 # 9 pairs * PAIR G7: 8,9 BLK 9 I7: 8,9,1,7 # reduction candidate for 8,9 I7: 8,9 # 17 pairs H8: 8,9,4,7 # reduction candidate for 8,9 H8: 8,9 # 10 pairs I8: 8,9,6,7 # reduction candidate for 8,9 I8: 8,9 => CTR * 43.5.6.17.6.1...94.214...636.4...132.193427562.36.14.9357864921946215378182...645 I8: 6,7 # 8 pairs * PAIR G7: 8,9 ROW 7 D7: 8,9,7 # reduction candidate for 8,9 D7: 8,9 # 10 pairs D7: 7 # 9 pairs * PAIR G7: 8,9 COL G G1: 8,9,2 # reduction candidate for 8,9 G1: 8,9 # 10 pairs G2: 8,9,2,5 # reduction candidate for 8,9 G2: 8,9 # 8 pairs G3: 8,9,2,5 # reduction candidate for 8,9 G3: 8,9 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-043-base-pr-000.dot * REASONING * DIS # C1: 2,6 => CTR => C1: 1,7,8,9 * PRF # C1: 1,7,8,9 => SOL * DIS # C2: 2,6 => CTR => C2: 1,5,7,8,9 * DIS # F2: 2,6 => CTR => F2: 1,3,7,8,9 * DIS # B8: 2,6 => CTR => B8: 4 * PRF # B8: 4 => SOL * DIS # E3: 2,4 => CTR => E3: 3,7,8,9 * PRF # B8: 2,4 => SOL * DIS # B8: 6 => CTR => B8: 2,4 * PRF # F1: 1,6 => SOL * DIS # F1: 2,7,8,9 => CTR => F1: 1,6 * DIS # F2: 1,6 => CTR => F2: 2,3,7,8,9 * DIS # C2: 1,6 => CTR => C2: 2,5,7,8,9 * PRF # D6: 1,6 => SOL * DIS # D6: 4 => CTR => D6: 1,6 * DIS # A3: 1,4 => CTR => A3: 5,7,8,9 * DIS # D6: 1,4 => CTR => D6: 6 * PRF # D6: 6 => SOL * DIS # D6: 1 => CTR => D6: 4,6 * DIS # I8: 8,9 => CTR => I8: 6,7 * CNT 20 HDP CHAINS / 35 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B3,D2,D3,G6,G7,G9) * .3.5.............4.......6.6.4...1.....3..7..2.3......3...64.2.....153...8......5 * PAIR B2: 2,6 BLK 1 C1: 2,6,1,7,8,9 # reduction candidate for 2,6 C1: 2,6 => CTR * .32546...........4.4.1...6.6.4...1.....3..7..2.34..6..3...64.2.....153.6.86...4.5 C1: 1,7,8,9 => SOLVED * 438576219569123874721489563694758132815342796273691458357864921946215387182937645 * DURATION: 0:00:01.892583 START: 04:09:50.440293 END: 04:09:52.332876 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-043-base-pr-001.dot * REASONING * DIS # C1: 2,6 => CTR => C1: 1,7,8,9 * PRF C1: 1,7,8,9 => SOL * STA C1: 1,7,8,9 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 043 solution: 438576219569123874721489563694758132815342796273691458357864921946215387182937645 info: 1375 FNBHX S8.f 17956 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 438576219569123874721489563694758132815342796273691458357864921946215387182937645 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:
* DIS # C1: 2,6 => CTR => C1: 1,7,8,9 * PRF # C1: 1,7,8,9 => SOL * DIS # C2: 2,6 => CTR => C2: 1,5,7,8,9 * INC # C2: 1,5,7,8,9 => UNS * DIS # F2: 2,6 => CTR => F2: 1,3,7,8,9 * INC # F2: 1,3,7,8,9 => UNS * DIS # B8: 2,6 => CTR => B8: 4 * PRF # B8: 4 => SOL * DIS # E3: 2,4 => CTR => E3: 3,7,8,9 * INC # E3: 3,7,8,9 => UNS * PRF # B8: 2,4 => SOL * DIS # B8: 6 => CTR => B8: 2,4 * PRF # F1: 1,6 => SOL * DIS # F1: 2,7,8,9 => CTR => F1: 1,6 * DIS # F2: 1,6 => CTR => F2: 2,3,7,8,9 * INC # F2: 2,3,7,8,9 => UNS * DIS # C2: 1,6 => CTR => C2: 2,5,7,8,9 * INC # C2: 2,5,7,8,9 => UNS * PRF # D6: 1,6 => SOL * DIS # D6: 4 => CTR => D6: 1,6 * DIS # A3: 1,4 => CTR => A3: 5,7,8,9 * INC # A3: 5,7,8,9 => UNS * DIS # D6: 1,4 => CTR => D6: 6 * PRF # D6: 6 => SOL * INC # D6: 4,6 => UNS * DIS # D6: 1 => CTR => D6: 4,6 * INC # I7: 8,9 => UNS * INC # H8: 8,9 => UNS * DIS # I8: 8,9 => CTR => I8: 6,7 * INC # I8: 6,7 => UNS * INC # D7: 8,9 => UNS * INC # D7: 7 => UNS * INC # G1: 8,9 => UNS * INC # G2: 8,9 => UNS * INC # G3: 8,9 => UNS * CNT 35 HDP CHAINS / 35 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C1: 2,6 => CTR => C1: 1,7,8,9 * PRF C1: 1,7,8,9 => SOL * STA C1: 1,7,8,9 * CNT 2 HDP CHAINS / 1 HYP OPENED