Analysis of xx-top500-355-base.sdk
Contents
Original Sudoku
level: medium
position: ...35....8.......4...2.........1...7.2...5.........3..76.8.....1......5.......24. initial
Autosolve
position: 2.435..7.8531.7.24...24..3543..125.7.2.7354..5..48.3.2765824..3142..3758389571246 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B3: 1,9 => SOL * PRF # B6: 7 => SOL * DIS # G3: 8,9 => CTR => G3: 1 * PRF # G3: 1 => SOL * PRF # G3: 1,9 => SOL * DIS # G3: 8 => CTR => G3: 1,9 * PRF # C5: 6,8 => SOL * DIS # C5: 1 => CTR => C5: 6,8 * DIS # H4: 6,8 => CTR => H4: 9 * PRF # H4: 9 => SOL * DIS # H5: 6,9 => CTR => H5: 1,8 * DIS # H4: 8 => CTR => H4: 6,9 * PRF # H6: 6,9 => SOL * DIS # H6: 1 => CTR => H6: 6,9 * DIS # H5: 1,9 => CTR => H5: 6,8 * DIS # H6: 1,9 => CTR => H6: 6 * PRF # H6: 6 => SOL * PRF # G3: 1,9 => SOL * DIS # G3: 8 => CTR => G3: 1,9 * DIS # H5: 1,9 => CTR => H5: 6,8 * DIS # H6: 1,9 => CTR => H6: 6 * PRF # H6: 6 => SOL * CNT 22 HDP CHAINS / 28 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B3: 1,9 => SOL * STA B3: 1,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...35....8.......4...2.........1...7.2...5.........3..76.8.....1......5.......24. | initial |
| 2.435..7.8531.7.24...24..3543..125.7.2.7354..5..48.3.2765824..3142..3758389571246 | autosolve |
| 214356879853197624697248135438612597926735481571489362765824913142963758389571246 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) B1: 1,9 A3: 6,9 F1: 6,8 E2: 6,9 F3: 8,9 G1: 6,8 I1: 1,9 G2: 6,9 C4: 6,8 A5: 6,9 D4: 6,9 F6: 6,9 I5: 1,9 D8: 6,9 E8: 6,9 G7: 1,9 H7: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I1,G3: 1.. / I1 = 1 => 0 pairs (X) / G3 = 1 => 0 pairs (_) G7,H7: 1.. / G7 = 1 => 0 pairs (X) / H7 = 1 => 0 pairs (_) B1,I1: 1.. / B1 = 1 => 0 pairs (*) / I1 = 1 => 0 pairs (X) G3,G7: 1.. / G3 = 1 => 0 pairs (*) / G7 = 1 => 0 pairs (X) I1,I5: 1.. / I1 = 1 => 0 pairs (X) / I5 = 1 => 0 pairs (_) A3,C3: 6.. / A3 = 6 => 0 pairs (*) / C3 = 6 => 0 pairs (X) F1,E2: 6.. / F1 = 6 => 0 pairs (*) / E2 = 6 => 0 pairs (X) G1,G2: 6.. / G1 = 6 => 0 pairs (X) / G2 = 6 => 0 pairs (_) D4,F6: 6.. / D4 = 6 => 0 pairs (*) / F6 = 6 => 0 pairs (X) D8,E8: 6.. / D8 = 6 => 0 pairs (X) / E8 = 6 => 0 pairs (_) F1,G1: 6.. / F1 = 6 => 0 pairs (*) / G1 = 6 => 0 pairs (X) E2,G2: 6.. / E2 = 6 => 0 pairs (X) / G2 = 6 => 0 pairs (_) A3,A5: 6.. / A3 = 6 => 0 pairs (*) / A5 = 6 => 0 pairs (X) D4,D8: 6.. / D4 = 6 => 0 pairs (*) / D8 = 6 => 0 pairs (X) E2,E8: 6.. / E2 = 6 => 0 pairs (X) / E8 = 6 => 0 pairs (_) F1,F6: 6.. / F1 = 6 => 0 pairs (*) / F6 = 6 => 0 pairs (X) B3,C3: 7.. / B3 = 7 => 19 pairs (_) / C3 = 7 => 0 pairs (*) B6,C6: 7.. / B6 = 7 => 0 pairs (*) / C6 = 7 => 0 pairs (X) B3,B6: 7.. / B3 = 7 => 19 pairs (_) / B6 = 7 => 0 pairs (*) C3,C6: 7.. / C3 = 7 => 0 pairs (*) / C6 = 7 => 0 pairs (X) F1,F3: 8.. / F1 = 8 => 0 pairs (X) / F3 = 8 => 0 pairs (_) G1,G3: 8.. / G1 = 8 => 0 pairs (*) / G3 = 8 => 0 pairs (X) C4,C5: 8.. / C4 = 8 => 19 pairs (_) / C5 = 8 => 0 pairs (X) H4,H5: 8.. / H4 = 8 => 0 pairs (X) / H5 = 8 => 19 pairs (_) F1,G1: 8.. / F1 = 8 => 0 pairs (X) / G1 = 8 => 0 pairs (_) F3,G3: 8.. / F3 = 8 => 0 pairs (*) / G3 = 8 => 0 pairs (X) C4,H4: 8.. / C4 = 8 => 19 pairs (_) / H4 = 8 => 0 pairs (X) C5,H5: 8.. / C5 = 8 => 0 pairs (X) / H5 = 8 => 19 pairs (_) E2,F3: 9.. / E2 = 9 => 0 pairs (*) / F3 = 9 => 0 pairs (X) A5,B6: 9.. / A5 = 9 => 0 pairs (*) / B6 = 9 => 0 pairs (X) D4,F6: 9.. / D4 = 9 => 0 pairs (X) / F6 = 9 => 0 pairs (_) D8,E8: 9.. / D8 = 9 => 0 pairs (*) / E8 = 9 => 0 pairs (X) G7,H7: 9.. / G7 = 9 => 0 pairs (*) / H7 = 9 => 0 pairs (X) B1,I1: 9.. / B1 = 9 => 0 pairs (X) / I1 = 9 => 0 pairs (_) E2,G2: 9.. / E2 = 9 => 0 pairs (*) / G2 = 9 => 0 pairs (X) D4,H4: 9.. / D4 = 9 => 0 pairs (X) / H4 = 9 => 0 pairs (_) A3,A5: 9.. / A3 = 9 => 0 pairs (X) / A5 = 9 => 0 pairs (_) D4,D8: 9.. / D4 = 9 => 0 pairs (X) / D8 = 9 => 0 pairs (_) E2,E8: 9.. / E2 = 9 => 0 pairs (*) / E8 = 9 => 0 pairs (X) F3,F6: 9.. / F3 = 9 => 0 pairs (X) / F6 = 9 => 0 pairs (_) I1,I5: 9.. / I1 = 9 => 0 pairs (*) / I5 = 9 => 0 pairs (X) * DURATION: 0:01:10.360808 START: 14:53:10.940397 END: 14:54:21.301205 2017-05-04 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,B1,C4,D4,D8,E2,E8,F1,F3,F6,G1,G2,G7,H7,I1,I5) * 2.435..7.8531.7.24...24..3543..125.7.2.7354..5..48.3.2765824..3142..3758389571246 * PAIR B1: 1,9 BLK 1 B3: 1,9,7 # reduction candidate for 1,9 B3: 1,9 => SOLVED * 214356879853197624697248135438612597926735481571489362765824913142963758389571246 B3: 7 # 19 pairs * PAIR B1: 1,9 COL B B6: 1,9,7 # reduction candidate for 1,9 B6: 7 => SOLVED * 214356879853197624697248135438612597926735481571489362765824913142963758389571246 B6: 1,9 # 19 pairs * PAIR F3: 8,9 ROW 3 G3: 8,9,1 # reduction candidate for 8,9 G3: 8,9 => CTR * 2.435..718531.7.24...24..3543..125.7.2.7354.959.48.3.2765824..3142..3758389571246 G3: 1 => SOLVED * 214356879853197624697248135438612597926735481571489362765824913142963758389571246 * PAIR I1: 1,9 BLK 3 G3: 1,9,8 # reduction candidate for 1,9 G3: 1,9 => SOLVED * 214356879853197624697248135438612597926735481571489362765824913142963758389571246 G3: 8 => CTR * 2.435..718531.7924...24983543.9125.792.7354..5..48.3.2765824..3142..3758389571246 * PAIR C4: 6,8 BLK 4 C5: 6,8,1 # reduction candidate for 6,8 C5: 6,8 => SOLVED * 214356879853197624697248135438612597926735481571489362765824913142963758389571246 C5: 1 => CTR * 2.435..7.8531.7.24...24..35438.125.7.21735489597486312765824193142693758389571246 * PAIR C4: 6,8 ROW 4 H4: 6,8,9 # reduction candidate for 6,8 H4: 6,8 => CTR * 2.435867.853167924...24983543.9125.792.7354.15..4863.2765824..3142693758389571246 H4: 9 => SOLVED * 214356879853197624697248135438612597926735481571489362765824913142963758389571246 * PAIR A5: 6,9 ROW 5 H5: 6,9,1,8 # reduction candidate for 6,9 H5: 6,9 => CTR * 21435..79853197624...248135436912587.287354.15..48.3.2765824.13142..3758389571246 H5: 1,8 # 19 pairs * PAIR D4: 6,9 ROW 4 H4: 6,9,8 # reduction candidate for 6,9 H4: 8 => CTR * 2.435867.853167924...2498354369125879287354615..4863.2765824..3142693758389571246 H4: 6,9 # 19 pairs * PAIR F6: 6,9 ROW 6 H6: 6,9,1 # reduction candidate for 6,9 H6: 6,9 => SOLVED * 214356879853197624697248135438612597926735481571489362765824913142963758389571246 H6: 1 => CTR * 2.435..718531.7.24.1724..3543.9125.7.217354..5..48.312765824193142..3758389571246 * PAIR I5: 1,9 BLK 6 H5: 1,9,6,8 # reduction candidate for 1,9 H5: 1,9 => CTR * 2.435..7.8531.7.24...24..3543..12587.287354..5..48.362765824..3142..3758389571246 H5: 6,8 # 18 pairs H6: 1,9,6 # reduction candidate for 1,9 H6: 1,9 => CTR * 2.435867.853167924...24983543.9125.792.7354.15..4863.2765824..3142693758389571246 H6: 6 => SOLVED * 214356879853197624697248135438612597926735481571489362765824913142963758389571246 * PAIR G7: 1,9 COL G G3: 1,9,8 # reduction candidate for 1,9 G3: 1,9 => SOLVED * 214356879853197624697248135438612597926735481571489362765824913142963758389571246 G3: 8 => CTR * 2.435..718531.7924...24983543.9125.792.7354..5..48.3.2765824..3142..3758389571246 * PAIR H7: 1,9 COL H H5: 1,9,6,8 # reduction candidate for 1,9 H5: 1,9 => CTR * 2.435..7.8531.7.24...24..3543..12587.287354..5..48.362765824..3142..3758389571246 H5: 6,8 # 18 pairs H6: 1,9,6 # reduction candidate for 1,9 H6: 1,9 => CTR * 2.435867.853167924...24983543.9125.792.7354.15..4863.2765824..3142693758389571246 H6: 6 => SOLVED * 214356879853197624697248135438612597926735481571489362765824913142963758389571246 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-355-base-pr-000.dot * REASONING * PRF # B3: 1,9 => SOL * PRF # B6: 7 => SOL * DIS # G3: 8,9 => CTR => G3: 1 * PRF # G3: 1 => SOL * PRF # G3: 1,9 => SOL * DIS # G3: 8 => CTR => G3: 1,9 * PRF # C5: 6,8 => SOL * DIS # C5: 1 => CTR => C5: 6,8 * DIS # H4: 6,8 => CTR => H4: 9 * PRF # H4: 9 => SOL * DIS # H5: 6,9 => CTR => H5: 1,8 * DIS # H4: 8 => CTR => H4: 6,9 * PRF # H6: 6,9 => SOL * DIS # H6: 1 => CTR => H6: 6,9 * DIS # H5: 1,9 => CTR => H5: 6,8 * DIS # H6: 1,9 => CTR => H6: 6 * PRF # H6: 6 => SOL * PRF # G3: 1,9 => SOL * DIS # G3: 8 => CTR => G3: 1,9 * DIS # H5: 1,9 => CTR => H5: 6,8 * DIS # H6: 1,9 => CTR => H6: 6 * PRF # H6: 6 => SOL * CNT 22 HDP CHAINS / 28 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,B1,C4,D4,D8,E2,E8,F1,F3,F6,G1,G2,G7,H7,I1,I5) * 2.435..7.8531.7.24...24..3543..125.7.2.7354..5..48.3.2765824..3142..3758389571246 * PAIR B1: 1,9 BLK 1 B3: 1,9,7 # reduction candidate for 1,9 B3: 1,9 => SOLVED * 214356879853197624697248135438612597926735481571489362765824913142963758389571246 * DURATION: 0:00:02.101689 START: 14:54:53.294798 END: 14:54:55.396487 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-355-base-pr-001.dot * REASONING * PRF # B3: 1,9 => SOL * STA B3: 1,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 355 solution: 214356879853197624697248135438612597926735481571489362765824913142963758389571246 info: 4886 FNBTWX S8.f 41560 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 214356879853197624697248135438612597926735481571489362765824913142963758389571246 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 # B3: 1,9 => SOL * INC # B3: 7 => UNS * INC # B6: 1,9 => UNS * PRF # B6: 7 => SOL * DIS # G3: 8,9 => CTR => G3: 1 * PRF # G3: 1 => SOL * PRF # G3: 1,9 => SOL * DIS # G3: 8 => CTR => G3: 1,9 * PRF # C5: 6,8 => SOL * DIS # C5: 1 => CTR => C5: 6,8 * DIS # H4: 6,8 => CTR => H4: 9 * PRF # H4: 9 => SOL * DIS # H5: 6,9 => CTR => H5: 1,8 * INC # H5: 1,8 => UNS * INC # H4: 6,9 => UNS * DIS # H4: 8 => CTR => H4: 6,9 * PRF # H6: 6,9 => SOL * DIS # H6: 1 => CTR => H6: 6,9 * DIS # H5: 1,9 => CTR => H5: 6,8 * INC # H5: 6,8 => UNS * DIS # H6: 1,9 => CTR => H6: 6 * PRF # H6: 6 => SOL * PRF # G3: 1,9 => SOL * DIS # G3: 8 => CTR => G3: 1,9 * DIS # H5: 1,9 => CTR => H5: 6,8 * INC # H5: 6,8 => UNS * DIS # H6: 1,9 => CTR => H6: 6 * PRF # H6: 6 => SOL * CNT 28 HDP CHAINS / 28 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # B3: 1,9 => SOL * STA B3: 1,9 * CNT 1 HDP CHAINS / 1 HYP OPENED