Analysis of xx-top500-163-base.sdk
Contents
Original Sudoku
level: medium
position: 7..5....4...1..3......7....61.....7....3....8.....2.......1.25.4.3............... initial
Autosolve
position: 72.53.814..512.3.713..7.5.26128459735..3916283..762145...41325.4.325.781251.8743. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 6,9 => CTR => B2: 4,8 * PRF # B2: 4,8 => SOL * DIS # C7: 6,9 => CTR => C7: 7,8 * PRF # C7: 7,8 => SOL * DIS # B2: 8,9 => CTR => B2: 4,6 * PRF # B2: 4,8 => SOL * DIS # B2: 6,9 => CTR => B2: 4,8 * PRF # B2: 4,8 => SOL * DIS # B2: 6,9 => CTR => B2: 4,8 * DIS # B2: 6,9 => CTR => B2: 4,8 * PRF # B2: 4,8 => SOL * DIS # B2: 8,9 => CTR => B2: 4,6 * DIS # B7: 8,9 => CTR => B7: 6,7 * DIS # C7: 8,9 => CTR => C7: 6,7 * DIS # B7: 8,9 => CTR => B7: 6,7 * DIS # C7: 8,9 => CTR => C7: 6,7 * PRF # B7: 6,9 => SOL * DIS # C7: 6,9 => CTR => C7: 7,8 * PRF # C7: 7,8 => SOL * DIS # B2: 6,9 => CTR => B2: 4,8 * PRF # B2: 4,8 => SOL * PRF # B7: 6,9 => SOL * DIS # C7: 6,9 => CTR => C7: 7,8 * PRF # C7: 7,8 => SOL * CNT 24 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 # B2: 6,9 => CTR => B2: 4,8 * PRF B2: 4,8 => SOL * STA B2: 4,8 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 7..5....4...1..3......7....61.....7....3....8.....2.......1.25.4.3............... | initial |
| 72.53.814..512.3.713..7.5.26128459735..3916283..762145...41325.4.325.781251.8743. | autosolve |
| 726539814945128367138674592612845973574391628389762145867413259493256781251987436 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) C1: 6,9 A2: 8,9 C3: 4,8 F1: 6,9 F2: 4,8 D3: 6,9 F3: 4,8 H2: 6,9 H3: 6,9 B5: 4,7 C5: 4,7 B6: 8,9 C6: 8,9 A7: 8,9 B8: 6,9 F8: 6,9 D9: 6,9 I7: 6,9 I9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,C3: 4.. / B2 = 4 => 0 pairs (*) / C3 = 4 => 0 pairs (X) F2,F3: 4.. / F2 = 4 => 14 pairs (_) / F3 = 4 => 0 pairs (*) B5,C5: 4.. / B5 = 4 => 14 pairs (_) / C5 = 4 => 0 pairs (*) B2,F2: 4.. / B2 = 4 => 0 pairs (*) / F2 = 4 => 0 pairs (X) C3,F3: 4.. / C3 = 4 => 14 pairs (_) / F3 = 4 => 0 pairs (*) B2,B5: 4.. / B2 = 4 => 0 pairs (*) / B5 = 4 => 0 pairs (X) C3,C5: 4.. / C3 = 4 => 14 pairs (_) / C5 = 4 => 0 pairs (*) C1,B2: 6.. / C1 = 6 => 0 pairs (*) / B2 = 6 => 0 pairs (X) F1,D3: 6.. / F1 = 6 => 0 pairs (X) / D3 = 6 => 0 pairs (_) H2,H3: 6.. / H2 = 6 => 0 pairs (*) / H3 = 6 => 0 pairs (X) F8,D9: 6.. / F8 = 6 => 0 pairs (*) / D9 = 6 => 0 pairs (X) I7,I9: 6.. / I7 = 6 => 0 pairs (X) / I9 = 6 => 0 pairs (_) C1,F1: 6.. / C1 = 6 => 0 pairs (*) / F1 = 6 => 0 pairs (X) B2,H2: 6.. / B2 = 6 => 0 pairs (X) / H2 = 6 => 0 pairs (_) D3,H3: 6.. / D3 = 6 => 0 pairs (*) / H3 = 6 => 0 pairs (X) B8,F8: 6.. / B8 = 6 => 0 pairs (X) / F8 = 6 => 0 pairs (_) D9,I9: 6.. / D9 = 6 => 0 pairs (X) / I9 = 6 => 0 pairs (_) C1,C7: 6.. / C1 = 6 => 0 pairs (*) / C7 = 6 => 0 pairs (X) D3,D9: 6.. / D3 = 6 => 0 pairs (*) / D9 = 6 => 0 pairs (X) F1,F8: 6.. / F1 = 6 => 0 pairs (X) / F8 = 6 => 0 pairs (_) B5,C5: 7.. / B5 = 7 => 0 pairs (*) / C5 = 7 => 0 pairs (X) B7,C7: 7.. / B7 = 7 => 14 pairs (_) / C7 = 7 => 0 pairs (*) B5,B7: 7.. / B5 = 7 => 0 pairs (*) / B7 = 7 => 0 pairs (X) C5,C7: 7.. / C5 = 7 => 14 pairs (_) / C7 = 7 => 0 pairs (*) F2,F3: 8.. / F2 = 8 => 0 pairs (*) / F3 = 8 => 0 pairs (X) B6,C6: 8.. / B6 = 8 => 0 pairs (*) / C6 = 8 => 0 pairs (X) C3,F3: 8.. / C3 = 8 => 0 pairs (*) / F3 = 8 => 0 pairs (X) A2,A7: 8.. / A2 = 8 => 0 pairs (X) / A7 = 8 => 0 pairs (_) F1,D3: 9.. / F1 = 9 => 0 pairs (*) / D3 = 9 => 0 pairs (X) H2,H3: 9.. / H2 = 9 => 0 pairs (X) / H3 = 9 => 0 pairs (_) B6,C6: 9.. / B6 = 9 => 0 pairs (X) / C6 = 9 => 0 pairs (_) F8,D9: 9.. / F8 = 9 => 0 pairs (X) / D9 = 9 => 0 pairs (_) I7,I9: 9.. / I7 = 9 => 0 pairs (*) / I9 = 9 => 0 pairs (X) C1,F1: 9.. / C1 = 9 => 0 pairs (X) / F1 = 9 => 0 pairs (_) D3,H3: 9.. / D3 = 9 => 0 pairs (X) / H3 = 9 => 0 pairs (_) B8,F8: 9.. / B8 = 9 => 0 pairs (*) / F8 = 9 => 0 pairs (X) D9,I9: 9.. / D9 = 9 => 0 pairs (*) / I9 = 9 => 0 pairs (X) A2,A7: 9.. / A2 = 9 => 0 pairs (*) / A7 = 9 => 0 pairs (X) D3,D9: 9.. / D3 = 9 => 0 pairs (X) / D9 = 9 => 0 pairs (_) F1,F8: 9.. / F1 = 9 => 0 pairs (*) / F8 = 9 => 0 pairs (X) * DURATION: 0:01:08.763876 START: 08:19:06.068829 END: 08:20:14.832705 2017-05-04 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,B5,B6,B8,C1,C3,C5,C6,D3,D9,F1,F2,F3,F8,H2,H3,I7,I9) * 72.53.814..512.3.713..7.5.26128459735..3916283..762145...41325.4.325.781251.8743. * PAIR C1: 6,9 BLK 1 B2: 6,9,4,8 # reduction candidate for 6,9 B2: 6,9 => CTR * 72.53.8148.51243.7134.785.2612845973547391628389762145978413256463259781251.8743. B2: 4,8 => SOLVED * 726539814945128367138674592612845973574391628389762145867413259493256781251987436 * PAIR C1: 6,9 COL C C7: 6,9,7,8 # reduction candidate for 6,9 C7: 6,9 => CTR * 72.53.8149851243671346785926128459735473916283987621458794132564.325.781251.8743. C7: 7,8 => SOLVED * 726539814945128367138674592612845973574391628389762145867413259493256781251987436 * PAIR A2: 8,9 BLK 1 B2: 8,9,4,6 # reduction candidate for 8,9 B2: 8,9 => CTR * 726539814..51243671346785926128459735473916283..762145.7.4132564.325.781251.8743. B2: 4,6 # 20 pairs * PAIR C3: 4,8 BLK 1 B2: 4,8,6,9 # reduction candidate for 4,8 B2: 4,8 => SOLVED * 726539814945128367138674592612845973574391628389762145867413259493256781251987436 B2: 6,9 => CTR * 72.53.8148.51243.7134.785.2612845973547391628389762145978413256463259781251.8743. * PAIR F2: 4,8 ROW 2 B2: 4,8,6,9 # reduction candidate for 4,8 B2: 4,8 => SOLVED * 726539814945128367138674592612845973574391628389762145867413259493256781251987436 B2: 6,9 => CTR * 72.53.8148.51243.7134.785.2612845973547391628389762145978413256463259781251.8743. * PAIR H2: 6,9 ROW 2 B2: 6,9,4,8 # reduction candidate for 6,9 B2: 6,9 => CTR * 72.53.8148.51243.7134.785.2612845973547391628389762145978413256463259781251.8743. B2: 4,8 => SOLVED * 726539814945128367138674592612845973574391628389762145867413259493256781251987436 * PAIR B6: 8,9 COL B B2: 8,9,4,6 # reduction candidate for 8,9 B2: 8,9 => CTR * 726539814..51243671346785926128459735473916283..762145.7.4132564.325.781251.8743. B2: 4,6 # 20 pairs B7: 8,9,6,7 # reduction candidate for 8,9 B7: 8,9 => CTR * 72.53.814..512.3.713..7.5.26128459735743916283..762145..7413256463259781251687439 B7: 6,7 # 20 pairs * PAIR C6: 8,9 COL C C7: 8,9,6,7 # reduction candidate for 8,9 C7: 8,9 => CTR * 726539814..512.36713.67.5926128459735.73916283..762145.7.4132564.325.781251.8743. C7: 6,7 # 20 pairs * PAIR A7: 8,9 BLK 7 B7: 8,9,6,7 # reduction candidate for 8,9 B7: 8,9 => CTR * 72.53.814..512.3.713..7.5.26128459735743916283..762145..7413256463259781251687439 B7: 6,7 # 20 pairs C7: 8,9,6,7 # reduction candidate for 8,9 C7: 8,9 => CTR * 726539814..512.36713.67.5926128459735.73916283..762145.7.4132564.325.781251.8743. C7: 6,7 # 20 pairs * PAIR B8: 6,9 BLK 7 B7: 6,9,7,8 # reduction candidate for 6,9 B7: 6,9 => SOLVED * 726539814945128367138674592612845973574391628389762145867413259493256781251987436 B7: 7,8 # 20 pairs C7: 6,9,7,8 # reduction candidate for 6,9 C7: 6,9 => CTR * 72.53.8149851243671346785926128459735473916283987621458794132564.325.781251.8743. C7: 7,8 => SOLVED * 726539814945128367138674592612845973574391628389762145867413259493256781251987436 * PAIR B8: 6,9 COL B B2: 6,9,4,8 # reduction candidate for 6,9 B2: 6,9 => CTR * 72.53.8148.51243.7134.785.2612845973547391628389762145978413256463259781251.8743. B2: 4,8 => SOLVED * 726539814945128367138674592612845973574391628389762145867413259493256781251987436 * PAIR I7: 6,9 ROW 7 B7: 6,9,7,8 # reduction candidate for 6,9 B7: 6,9 => SOLVED * 726539814945128367138674592612845973574391628389762145867413259493256781251987436 B7: 7,8 # 20 pairs C7: 6,9,7,8 # reduction candidate for 6,9 C7: 6,9 => CTR * 72.53.8149851243671346785926128459735473916283987621458794132564.325.781251.8743. C7: 7,8 => SOLVED * 726539814945128367138674592612845973574391628389762145867413259493256781251987436 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-163-base-pr-000.dot * REASONING * DIS # B2: 6,9 => CTR => B2: 4,8 * PRF # B2: 4,8 => SOL * DIS # C7: 6,9 => CTR => C7: 7,8 * PRF # C7: 7,8 => SOL * DIS # B2: 8,9 => CTR => B2: 4,6 * PRF # B2: 4,8 => SOL * DIS # B2: 6,9 => CTR => B2: 4,8 * PRF # B2: 4,8 => SOL * DIS # B2: 6,9 => CTR => B2: 4,8 * DIS # B2: 6,9 => CTR => B2: 4,8 * PRF # B2: 4,8 => SOL * DIS # B2: 8,9 => CTR => B2: 4,6 * DIS # B7: 8,9 => CTR => B7: 6,7 * DIS # C7: 8,9 => CTR => C7: 6,7 * DIS # B7: 8,9 => CTR => B7: 6,7 * DIS # C7: 8,9 => CTR => C7: 6,7 * PRF # B7: 6,9 => SOL * DIS # C7: 6,9 => CTR => C7: 7,8 * PRF # C7: 7,8 => SOL * DIS # B2: 6,9 => CTR => B2: 4,8 * PRF # B2: 4,8 => SOL * PRF # B7: 6,9 => SOL * DIS # C7: 6,9 => CTR => C7: 7,8 * PRF # C7: 7,8 => SOL * CNT 24 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,B5,B6,B8,C1,C3,C5,C6,D3,D9,F1,F2,F3,F8,H2,H3,I7,I9) * 72.53.814..512.3.713..7.5.26128459735..3916283..762145...41325.4.325.781251.8743. * PAIR C1: 6,9 BLK 1 B2: 6,9,4,8 # reduction candidate for 6,9 B2: 6,9 => CTR * 72.53.8148.51243.7134.785.2612845973547391628389762145978413256463259781251.8743. B2: 4,8 => SOLVED * 726539814945128367138674592612845973574391628389762145867413259493256781251987436 * DURATION: 0:00:03.080462 START: 08:20:51.361767 END: 08:20:54.442229 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-163-base-pr-001.dot * REASONING * DIS # B2: 6,9 => CTR => B2: 4,8 * PRF B2: 4,8 => SOL * STA B2: 4,8 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 163 solution: 726539814945128367138674592612845973574391628389762145867413259493256781251987436 info: 1821 FNTWX S8.f 37007 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 726539814945128367138674592612845973574391628389762145867413259493256781251987436 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 # B2: 6,9 => CTR => B2: 4,8 * PRF # B2: 4,8 => SOL * DIS # C7: 6,9 => CTR => C7: 7,8 * PRF # C7: 7,8 => SOL * DIS # B2: 8,9 => CTR => B2: 4,6 * INC # B2: 4,6 => UNS * PRF # B2: 4,8 => SOL * DIS # B2: 6,9 => CTR => B2: 4,8 * PRF # B2: 4,8 => SOL * DIS # B2: 6,9 => CTR => B2: 4,8 * DIS # B2: 6,9 => CTR => B2: 4,8 * PRF # B2: 4,8 => SOL * DIS # B2: 8,9 => CTR => B2: 4,6 * INC # B2: 4,6 => UNS * DIS # B7: 8,9 => CTR => B7: 6,7 * INC # B7: 6,7 => UNS * DIS # C7: 8,9 => CTR => C7: 6,7 * INC # C7: 6,7 => UNS * DIS # B7: 8,9 => CTR => B7: 6,7 * INC # B7: 6,7 => UNS * DIS # C7: 8,9 => CTR => C7: 6,7 * INC # C7: 6,7 => UNS * PRF # B7: 6,9 => SOL * INC # B7: 7,8 => UNS * DIS # C7: 6,9 => CTR => C7: 7,8 * PRF # C7: 7,8 => SOL * DIS # B2: 6,9 => CTR => B2: 4,8 * PRF # B2: 4,8 => SOL * PRF # B7: 6,9 => SOL * INC # B7: 7,8 => UNS * DIS # C7: 6,9 => CTR => C7: 7,8 * PRF # C7: 7,8 => SOL * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B2: 6,9 => CTR => B2: 4,8 * PRF B2: 4,8 => SOL * STA B2: 4,8 * CNT 2 HDP CHAINS / 1 HYP OPENED