Analysis of xx-top500-330-base.sdk
Contents
Original Sudoku
level: medium
position: ..2.9.3..8.1......5.........9..6..4........18........5.7....2..4..5........1..... initial
Autosolve
position: 7.2.9.3..8.1......5.9.......9..6.74........18........5.7....2..4..5........1..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D1: 4,6 => CTR => D1: 8 * PRF # D1: 8 => SOL * DIS # F1: 4,6 => CTR => F1: 1,5,8 * PRF # I1: 4,6 => SOL * DIS # I1: 1 => CTR => I1: 4,6 * DIS # F2: 4,5 => CTR => F2: 2,3,6,7 * DIS # G9: 8 => CTR => G9: 4,5 * PRF # F5: 2,5 => SOL * PRF # B9: 8 => SOL * PRF # E5: 4,7 => SOL * DIS # E6: 4,7 => CTR => E6: 1,2,3,8 * DIS # A4: 2,3 => CTR => A4: 1 * PRF # A4: 1 => SOL * PRF # D4: 2,3 => SOL * DIS # D4: 8 => CTR => D4: 2,3 * DIS # F4: 2,3 => CTR => F4: 1,5,8 * DIS # E6: 2,3 => CTR => E6: 1,4,7,8 * DIS # B8: 2 => CTR => B8: 1,8 * DIS # G3: 4 => CTR => G3: 1,8 * CNT 19 HDP CHAINS / 41 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D1: 4,6 => CTR => D1: 8 * PRF D1: 8 => SOL * STA D1: 8 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..2.9.3..8.1......5.........9..6..4........18........5.7....2..4..5........1..... | initial |
| 7.2.9.3..8.1......5.9.......9..6.74........18........5.7....2..4..5........1..... | autosolve |
| 742891356831657429569234187198365742357942618624718935975483261416529873283176594 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) B1: 4,6 G2: 4,5 B5: 2,5 C5: 4,7 C6: 4,7 I4: 2,3 G5: 6,9 G6: 6,9 H6: 2,3 G8: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A7,B8: 1.. / A7 = 1 => 0 pairs (X) / B8 = 1 => 0 pairs (_) F1,I1: 1.. / F1 = 1 => 0 pairs (*) / I1 = 1 => 0 pairs (X) A4,F4: 1.. / A4 = 1 => 0 pairs (*) / F4 = 1 => 0 pairs (X) A7,I7: 1.. / A7 = 1 => 0 pairs (X) / I7 = 1 => 0 pairs (_) B6,B8: 1.. / B6 = 1 => 0 pairs (X) / B8 = 1 => 0 pairs (_) E3,E6: 1.. / E3 = 1 => 0 pairs (X) / E6 = 1 => 0 pairs (_) G3,G8: 1.. / G3 = 1 => 0 pairs (*) / G8 = 1 => 0 pairs (X) I4,H6: 2.. / I4 = 2 => 10 pairs (_) / H6 = 2 => 16 pairs (_) B2,B3: 3.. / B2 = 3 => 11 pairs (_) / B3 = 3 => 11 pairs (_) I4,H6: 3.. / I4 = 3 => 16 pairs (_) / H6 = 3 => 10 pairs (_) C5,C6: 4.. / C5 = 4 => 8 pairs (_) / C6 = 4 => 8 pairs (_) C4,B5: 5.. / C4 = 5 => 0 pairs (X) / B5 = 5 => 0 pairs (_) F1,H1: 5.. / F1 = 5 => 0 pairs (X) / H1 = 5 => 0 pairs (_) C4,F4: 5.. / C4 = 5 => 0 pairs (X) / F4 = 5 => 0 pairs (_) C7,H7: 5.. / C7 = 5 => 0 pairs (*) / H7 = 5 => 0 pairs (X) B5,B9: 5.. / B5 = 5 => 0 pairs (*) / B9 = 5 => 0 pairs (X) E2,E5: 5.. / E2 = 5 => 0 pairs (*) / E5 = 5 => 0 pairs (X) G2,G9: 5.. / G2 = 5 => 0 pairs (X) / G9 = 5 => 0 pairs (_) A5,A6: 6.. / A5 = 6 => 9 pairs (_) / A6 = 6 => 9 pairs (_) G5,G6: 6.. / G5 = 6 => 9 pairs (_) / G6 = 6 => 9 pairs (_) A5,G5: 6.. / A5 = 6 => 9 pairs (_) / G5 = 6 => 9 pairs (_) A6,G6: 6.. / A6 = 6 => 9 pairs (_) / G6 = 6 => 9 pairs (_) C5,C6: 7.. / C5 = 7 => 8 pairs (_) / C6 = 7 => 8 pairs (_) C4,B6: 8.. / C4 = 8 => 0 pairs (*) / B6 = 8 => 0 pairs (X) H2,I2: 9.. / H2 = 9 => 10 pairs (_) / I2 = 9 => 10 pairs (_) G5,G6: 9.. / G5 = 9 => 9 pairs (_) / G6 = 9 => 9 pairs (_) A7,A9: 9.. / A7 = 9 => 0 pairs (*) / A9 = 9 => 0 pairs (X) * DURATION: 0:00:41.820179 START: 14:05:36.431016 END: 14:06:18.251195 2017-05-04 * CP COUNT: (27) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B5,C5,C6,G2,G5,G6,G8,H6,I4) * 7.2.9.3..8.1......5.9.......9..6.74........18........5.7....2..4..5........1..... * PAIR B1: 4,6 BLK 1 B2: 4,6,3 # reduction candidate for 4,6 B2: 4,6 # 11 pairs B3: 4,6,3 # reduction candidate for 4,6 B3: 4,6 # 11 pairs * PAIR B1: 4,6 ROW 1 D1: 4,6,8 # reduction candidate for 4,6 D1: 4,6 => CTR * 7.2.9.3.18.1......5.9.......9..6174........18.1......517....2..4..5..1..9..1..... D1: 8 => SOLVED * 742891356831657429569234187198365742357942618624718935975483261416529873283176594 F1: 4,6,1,5,8 # reduction candidate for 4,6 F1: 4,6 => CTR * 7.2.9.3518.1...4..5.9...8...9..6.74........18........5175...2..4..5..1..9..1..5.. F1: 1,5,8 # 10 pairs I1: 4,6,1 # reduction candidate for 4,6 I1: 4,6 => SOLVED * 742891356831657429569234187198365742357942618624718935975483261416529873283176594 I1: 1 => CTR * 7.2.9.3.18.1......5.9.......9..6174........18.1......517....2..4..5..1..9..1..... * PAIR G2: 4,5 ROW 2 E2: 4,5,2,3,7 # reduction candidate for 4,5 E2: 4,5 # 12 pairs F2: 4,5,2,3,6,7 # reduction candidate for 4,5 F2: 4,5 => CTR * 7.2.953.18.1...5..5.9.......95.6.74..2..5..18.8......5.7....25.41.5..8..25.1..4.. F2: 2,3,6,7 # 10 pairs * PAIR G2: 4,5 COL G G9: 4,5,8 # reduction candidate for 4,5 G9: 8 => CTR * 7.2.953.18.1...5..5.9...4...95.6.74..2..5..18........5.7....2..4..5..1...5.1..8.. G9: 4,5 # 12 pairs * PAIR B5: 2,5 ROW 5 E5: 2,5,3,4,7 # reduction candidate for 2,5 E5: 2,5 # 12 pairs F5: 2,5,3,4,7,9 # reduction candidate for 2,5 F5: 2,5 => SOLVED * 742891356831657429569234187198365742357942618624718935975483261416529873283176594 F5: 3,4,7,9 # 10 pairs * PAIR B5: 2,5 COL B B9: 2,5,8 # reduction candidate for 2,5 B9: 8 => SOLVED * 742891356831657429569234187198365742357942618624718935975483261416529873283176594 B9: 2,5 # 14 pairs * PAIR C5: 4,7 ROW 5 D5: 4,7,2,3,9 # reduction candidate for 4,7 D5: 4,7 # 11 pairs E5: 4,7,2,3,5 # reduction candidate for 4,7 E5: 4,7 => SOLVED * 742891356831657429569234187198365742357942618624718935975483261416529873283176594 E5: 2,3,5 # 10 pairs F5: 4,7,2,3,5,9 # reduction candidate for 4,7 F5: 4,7 # 11 pairs * PAIR C6: 4,7 ROW 6 D6: 4,7,2,3,8,9 # reduction candidate for 4,7 D6: 4,7 # 11 pairs E6: 4,7,1,2,3,8 # reduction candidate for 4,7 E6: 4,7 => CTR * 7.2.9.3.18.1......5.9.1.....98.6.74........18.1......517....2..4..5..1..9..1..... E6: 1,2,3,8 # 10 pairs F6: 4,7,1,2,3,8,9 # reduction candidate for 4,7 F6: 4,7 # 11 pairs * PAIR I4: 2,3 ROW 4 A4: 2,3,1 # reduction candidate for 2,3 A4: 2,3 => CTR * 7.2.9.3.18.1......5.9.1.....9586174..2.....18.8......517....2..4..5........1..... A4: 1 => SOLVED * 742891356831657429569234187198365742357942618624718935975483261416529873283176594 D4: 2,3,8 # reduction candidate for 2,3 D4: 2,3 => SOLVED * 742891356831657429569234187198365742357942618624718935975483261416529873283176594 D4: 8 => CTR * 7.2.913..8.1......5.9...1...9.86.74........18.8..1...5.7....2.141.5..8.....1..... F4: 2,3,1,5,8 # reduction candidate for 2,3 F4: 2,3 => CTR * 7.2.9.3..8.1......5.9......19586.74..2.....18.8......5.7....25141.5..8..25.1..4.. F4: 1,5,8 # 10 pairs * PAIR H6: 2,3 ROW 6 A6: 2,3,1,6 # reduction candidate for 2,3 A6: 2,3 # 11 pairs D6: 2,3,4,7,8,9 # reduction candidate for 2,3 D6: 2,3 # 13 pairs E6: 2,3,1,4,7,8 # reduction candidate for 2,3 E6: 2,3 => CTR * 7.2.9.3.18.1......5.9.1.....98.6.74........18.1......517....2..4..5..1..9..1..... E6: 1,4,7,8 # 10 pairs F6: 2,3,1,4,7,8,9 # reduction candidate for 2,3 F6: 2,3 # 13 pairs * PAIR G8: 1,8 ROW 8 B8: 1,8,2 # reduction candidate for 1,8 B8: 2 => CTR * 7.2.9.3..8.1......5.9.1.....98.6.74........18.1......517....2..42.5.....98.1..... B8: 1,8 # 12 pairs * PAIR G8: 1,8 COL G G3: 1,8,4 # reduction candidate for 1,8 G3: 4 => CTR * 7.2.9.3..8.1...5..5.9...4...9..6.74.....5..18.1......517....2..48.5..1..9..1..8.. G3: 1,8 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-330-base-pr-000.dot * REASONING * DIS # D1: 4,6 => CTR => D1: 8 * PRF # D1: 8 => SOL * DIS # F1: 4,6 => CTR => F1: 1,5,8 * PRF # I1: 4,6 => SOL * DIS # I1: 1 => CTR => I1: 4,6 * DIS # F2: 4,5 => CTR => F2: 2,3,6,7 * DIS # G9: 8 => CTR => G9: 4,5 * PRF # F5: 2,5 => SOL * PRF # B9: 8 => SOL * PRF # E5: 4,7 => SOL * DIS # E6: 4,7 => CTR => E6: 1,2,3,8 * DIS # A4: 2,3 => CTR => A4: 1 * PRF # A4: 1 => SOL * PRF # D4: 2,3 => SOL * DIS # D4: 8 => CTR => D4: 2,3 * DIS # F4: 2,3 => CTR => F4: 1,5,8 * DIS # E6: 2,3 => CTR => E6: 1,4,7,8 * DIS # B8: 2 => CTR => B8: 1,8 * DIS # G3: 4 => CTR => G3: 1,8 * CNT 19 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B5,C5,C6,G2,G5,G6,G8,H6,I4) * 7.2.9.3..8.1......5.9.......9..6.74........18........5.7....2..4..5........1..... * PAIR B1: 4,6 BLK 1 B2: 4,6,3 # reduction candidate for 4,6 B2: 4,6 # 11 pairs B3: 4,6,3 # reduction candidate for 4,6 B3: 4,6 # 11 pairs * PAIR B1: 4,6 ROW 1 D1: 4,6,8 # reduction candidate for 4,6 D1: 4,6 => CTR * 7.2.9.3.18.1......5.9.......9..6174........18.1......517....2..4..5..1..9..1..... D1: 8 => SOLVED * 742891356831657429569234187198365742357942618624718935975483261416529873283176594 * DURATION: 0:00:03.135710 START: 14:06:52.075832 END: 14:06:55.211542 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-330-base-pr-001.dot * REASONING * DIS # D1: 4,6 => CTR => D1: 8 * PRF D1: 8 => SOL * STA D1: 8 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 330 solution: 742891356831657429569234187198365742357942618624718935975483261416529873283176594 info: 2985 FNBTHWY S8.f 13277 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 742891356831657429569234187198365742357942618624718935975483261416529873283176594 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 # B2: 4,6 => UNS * INC # B3: 4,6 => UNS * DIS # D1: 4,6 => CTR => D1: 8 * PRF # D1: 8 => SOL * DIS # F1: 4,6 => CTR => F1: 1,5,8 * INC # F1: 1,5,8 => UNS * PRF # I1: 4,6 => SOL * DIS # I1: 1 => CTR => I1: 4,6 * INC # E2: 4,5 => UNS * DIS # F2: 4,5 => CTR => F2: 2,3,6,7 * INC # F2: 2,3,6,7 => UNS * INC # G9: 4,5 => UNS * DIS # G9: 8 => CTR => G9: 4,5 * INC # E5: 2,5 => UNS * PRF # F5: 2,5 => SOL * INC # F5: 3,4,7,9 => UNS * INC # B9: 2,5 => UNS * PRF # B9: 8 => SOL * INC # D5: 4,7 => UNS * PRF # E5: 4,7 => SOL * INC # E5: 2,3,5 => UNS * INC # F5: 4,7 => UNS * INC # D6: 4,7 => UNS * DIS # E6: 4,7 => CTR => E6: 1,2,3,8 * INC # E6: 1,2,3,8 => UNS * INC # F6: 4,7 => UNS * DIS # A4: 2,3 => CTR => A4: 1 * PRF # A4: 1 => SOL * PRF # D4: 2,3 => SOL * DIS # D4: 8 => CTR => D4: 2,3 * DIS # F4: 2,3 => CTR => F4: 1,5,8 * INC # F4: 1,5,8 => UNS * INC # A6: 2,3 => UNS * INC # D6: 2,3 => UNS * DIS # E6: 2,3 => CTR => E6: 1,4,7,8 * INC # E6: 1,4,7,8 => UNS * INC # F6: 2,3 => UNS * INC # B8: 1,8 => UNS * DIS # B8: 2 => CTR => B8: 1,8 * INC # G3: 1,8 => UNS * DIS # G3: 4 => CTR => G3: 1,8 * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 4,6 => UNS * INC # B3: 4,6 => UNS * DIS # D1: 4,6 => CTR => D1: 8 * PRF D1: 8 => SOL * STA D1: 8 * CNT 4 HDP CHAINS / 3 HYP OPENED