Analysis of xx-top500-318-base.sdk
Contents
Original Sudoku
level: medium
position: ..2.9.3..8.1......5.........9..6..4........18........5.7....2..3..5........1..... initial
Autosolve
position: 7.2.9.3..8.1......5.9.......9..6.74........18........5.7....2..3..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 * DIS # A6: 1,2 => CTR => A6: 4,6 * PRF # B6: 1,2 => SOL * DIS # B6: 8 => CTR => B6: 1,2 * DIS # F4: 1,2 => CTR => F4: 3,5,8 * PRF # F4: 3,5,8 => SOL * PRF # F5: 2,5 => SOL * PRF # B9: 8 => 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 * CNT 18 HDP CHAINS / 32 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..3..5........1..... | initial |
| 7.2.9.3..8.1......5.9.......9..6.74........18........5.7....2..3..5........1..... | autosolve |
| 742891356831657429569234187198365742653742918427918635975483261316529874284176593 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) B1: 4,6 G2: 4,5 A4: 1,2 B5: 2,5 I4: 2,3 G5: 6,9 G6: 6,9 H6: 2,3 -------------------------------------------------- * 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 => 0 pairs (*) / H6 = 2 => 0 pairs (X) B2,B3: 3.. / B2 = 3 => 9 pairs (_) / B3 = 3 => 9 pairs (_) I4,H6: 3.. / I4 = 3 => 15 pairs (_) / H6 = 3 => 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 (_) G5,G6: 6.. / G5 = 6 => 7 pairs (_) / G6 = 6 => 6 pairs (_) C5,C6: 7.. / C5 = 7 => 9 pairs (_) / C6 = 7 => 8 pairs (_) H2,I2: 9.. / H2 = 9 => 8 pairs (_) / I2 = 9 => 8 pairs (_) G5,G6: 9.. / G5 = 9 => 6 pairs (_) / G6 = 9 => 7 pairs (_) A7,A9: 9.. / A7 = 9 => 0 pairs (*) / A9 = 9 => 0 pairs (X) * DURATION: 0:00:32.339160 START: 13:50:34.292640 END: 13:51:06.631800 2017-05-04 * CP COUNT: (21) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B1,B5,G2,G5,G6,H6,I4) * 7.2.9.3..8.1......5.9.......9..6.74........18........5.7....2..3..5........1..... * PAIR B1: 4,6 BLK 1 B2: 4,6,3 # reduction candidate for 4,6 B2: 4,6 # 9 pairs B3: 4,6,3 # reduction candidate for 4,6 B3: 4,6 # 9 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......29..61743.5.....18.1.....2517....2..3..5..1..9..1..... D1: 8 => SOLVED * 742891356831657429569234187198365742653742918427918635975483261316529874284176593 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..3..5..1..9..1..5.. F1: 1,5,8 # 8 pairs I1: 4,6,1 # reduction candidate for 4,6 I1: 4,6 => SOLVED * 742891356831657429569234187198365742653742918427918635975483261316529874284176593 I1: 1 => CTR * 7.2.9.3.18.1......5.9......29..61743.5.....18.1.....2517....2..3..5..1..9..1..... * PAIR G2: 4,5 ROW 2 E2: 4,5,2,3,7 # reduction candidate for 4,5 E2: 4,5 # 10 pairs F2: 4,5,2,3,6,7 # reduction candidate for 4,5 F2: 4,5 => CTR * 7.2.953.18.1..45..5.9......195.6.74..2..5..18........5.7....25.3..5.....25.1..... F2: 2,3,6,7 # 8 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........517....2..3..5......5.1..8.. G9: 4,5 # 11 pairs * PAIR A4: 1,2 BLK 4 A6: 1,2,4,6 # reduction candidate for 1,2 A6: 1,2 => CTR * 7.2.9135.8.1.5.4..5.9...18.193865742.5.....1828..1..35.75...2.131.5..8.4.281..5.3 A6: 4,6 # 9 pairs B6: 1,2,8 # reduction candidate for 1,2 B6: 1,2 => SOLVED * 742891356831657429569234187198365742653742918427918635975483261316529874284176593 B6: 8 => CTR * 7.28913568.1...4..5.9...18.193.6.74........18.8..1...5.75...2.131.5..8...281..5.. * PAIR A4: 1,2 ROW 4 F4: 1,2,3,5,8 # reduction candidate for 1,2 F4: 1,2 => CTR * 7.2.953818.1...5..5.9...4..19586.743.2.....18.......25.7....25.3..5.....25.1...3. F4: 3,5,8 => SOLVED * 742891356831657429569234187198365742653742918427918635975483261316529874284176593 * PAIR B5: 2,5 ROW 5 E5: 2,5,3,4,7 # reduction candidate for 2,5 E5: 2,5 # 10 pairs F5: 2,5,3,4,7,9 # reduction candidate for 2,5 F5: 2,5 => SOLVED * 742891356831657429569234187198365742653742918427918635975483261316529874284176593 F5: 3,4,7,9 # 8 pairs * PAIR B5: 2,5 COL B B9: 2,5,8 # reduction candidate for 2,5 B9: 8 => SOLVED * 742891356831657429569234187198365742653742918427918635975483261316529874284176593 B9: 2,5 # 11 pairs * PAIR I4: 2,3 ROW 4 D4: 2,3,8 # reduction candidate for 2,3 D4: 2,3 => SOLVED * 742891356831657429569234187198365742653742918427918635975483261316529874284176593 D4: 8 => CTR * 7.2.9.3.18.1......5.9......29.861743.5.....18........517....2..3..5..1..9..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....25131.5.....25.1..... F4: 1,5,8 # 8 pairs * PAIR H6: 2,3 ROW 6 D6: 2,3,4,7,8,9 # reduction candidate for 2,3 D6: 2,3 # 10 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....29..61743.5.....18.1.....2517....2..3..5..1..9..1..... E6: 1,4,7,8 # 8 pairs F6: 2,3,1,4,7,8,9 # reduction candidate for 2,3 F6: 2,3 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-318-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 * DIS # A6: 1,2 => CTR => A6: 4,6 * PRF # B6: 1,2 => SOL * DIS # B6: 8 => CTR => B6: 1,2 * DIS # F4: 1,2 => CTR => F4: 3,5,8 * PRF # F4: 3,5,8 => SOL * PRF # F5: 2,5 => SOL * PRF # B9: 8 => 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 * CNT 18 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B1,B5,G2,G5,G6,H6,I4) * 7.2.9.3..8.1......5.9.......9..6.74........18........5.7....2..3..5........1..... * PAIR B1: 4,6 BLK 1 B2: 4,6,3 # reduction candidate for 4,6 B2: 4,6 # 9 pairs B3: 4,6,3 # reduction candidate for 4,6 B3: 4,6 # 9 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......29..61743.5.....18.1.....2517....2..3..5..1..9..1..... D1: 8 => SOLVED * 742891356831657429569234187198365742653742918427918635975483261316529874284176593 * DURATION: 0:00:02.951496 START: 13:51:32.455573 END: 13:51:35.407069 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-318-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 17 318 solution: 742891356831657429569234187198365742653742918427918635975483261316529874284176593 info: 2914 FNBTHWY S8.f 13276 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 742891356831657429569234187198365742653742918427918635975483261316529874284176593 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 * DIS # A6: 1,2 => CTR => A6: 4,6 * INC # A6: 4,6 => UNS * PRF # B6: 1,2 => SOL * DIS # B6: 8 => CTR => B6: 1,2 * DIS # F4: 1,2 => CTR => F4: 3,5,8 * PRF # F4: 3,5,8 => SOL * 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 * 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 # 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 * CNT 32 HDP CHAINS / 32 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