Analysis of xx-top500-220-base.sdk
Contents
Original Sudoku
level: medium
position: 4.2....7....6..3.......1...7...2.....5....6........1.....74..2..63.........8..... initial
Autosolve
position: 412....76.7.6.23..63.4712..7.612.4..154..76.232..641.7..1746.23.632..7..2478...6. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C2: 8,9 => SOL * PRF # E2: 5 => SOL * DIS # A7: 8,9 => CTR => A7: 5 * DIS # I8: 1,4 => CTR => I8: 5,8,9 * DIS # H4: 8,9 => CTR => H4: 3,5 * PRF # I4: 8,9 => SOL * DIS # H6: 5 => CTR => H6: 8,9 * PRF # C2: 8,9 => SOL * PRF # F4: 3,9 => SOL * DIS # E5: 3,9 => CTR => E5: 8 * PRF # E5: 8 => SOL * PRF # H5: 3,9 => SOL * DIS # H5: 8 => CTR => H5: 3,9 * DIS # D1: 5 => CTR => D1: 3,9 * DIS # F4: 5,9 => CTR => F4: 3,8 * DIS # H6: 5,9 => CTR => H6: 8 * PRF # H6: 8 => SOL * DIS # A7: 8,9 => CTR => A7: 5 * DIS # G7: 5 => CTR => G7: 8,9 * DIS # E8: 5,9 => CTR => E8: 1 * DIS # A8: 5,9 => CTR => A8: 8 * PRF # A8: 8 => SOL * PRF # I8: 5,9 => SOL * DIS # F1: 5,9 => CTR => F1: 3,8 * DIS # F4: 5,9 => CTR => F4: 3,8 * DIS # I8: 1,4 => CTR => I8: 5,8,9 * DIS # G7: 5,9 => CTR => G7: 8 * PRF # G7: 8 => SOL * PRF # I8: 5,9 => SOL * DIS # I9: 5,9 => CTR => I9: 1 * PRF # G1: 5,9 => SOL * DIS # G1: 8 => CTR => G1: 5,9 * CNT 32 HDP CHAINS / 63 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C2: 8,9 => SOL * STA C2: 8,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 4.2....7....6..3.......1...7...2.....5....6........1.....74..2..63.........8..... | initial |
| 412....76.7.6.23..63.4712..7.612.4..154..76.232..641.7..1746.23.632..7..2478...6. | autosolve |
| 412398576978652314635471298786123459154987632329564187591746823863219745247835961 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) A2: 8,9 H2: 1,4 I2: 1,4 B4: 8,9 C6: 8,9 D5: 3,9 D6: 5,9 B7: 8,9 F8: 5,9 H8: 1,4 G9: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H2,I2: 1.. / H2 = 1 => 8 pairs (_) / I2 = 1 => 0 pairs (X) E8,E9: 1.. / E8 = 1 => 8 pairs (_) / E9 = 1 => 0 pairs (X) E9,I9: 1.. / E9 = 1 => 0 pairs (X) / I9 = 1 => 8 pairs (_) H2,H8: 1.. / H2 = 1 => 8 pairs (_) / H8 = 1 => 0 pairs (X) H4,H5: 3.. / H4 = 3 => 12 pairs (_) / H5 = 3 => 0 pairs (*) E9,F9: 3.. / E9 = 3 => 14 pairs (_) / F9 = 3 => 12 pairs (_) F4,H4: 3.. / F4 = 3 => 0 pairs (*) / H4 = 3 => 0 pairs (X) D1,D5: 3.. / D1 = 3 => 13 pairs (_) / D5 = 3 => 13 pairs (_) H2,I2: 4.. / H2 = 4 => 0 pairs (X) / I2 = 4 => 8 pairs (_) H8,I8: 4.. / H8 = 4 => 8 pairs (_) / I8 = 4 => 0 pairs (X) H2,H8: 4.. / H2 = 4 => 0 pairs (X) / H8 = 4 => 8 pairs (_) I2,I8: 4.. / I2 = 4 => 8 pairs (_) / I8 = 4 => 0 pairs (X) C2,C3: 5.. / C2 = 5 => 15 pairs (_) / C3 = 5 => 0 pairs (*) F4,D6: 5.. / F4 = 5 => 0 pairs (X) / D6 = 5 => 12 pairs (_) A7,A8: 5.. / A7 = 5 => 13 pairs (_) / A8 = 5 => 0 pairs (X) C2,E2: 5.. / C2 = 5 => 15 pairs (_) / E2 = 5 => 0 pairs (*) D6,H6: 5.. / D6 = 5 => 12 pairs (_) / H6 = 5 => 0 pairs (X) A7,G7: 5.. / A7 = 5 => 13 pairs (_) / G7 = 5 => 0 pairs (X) D1,D6: 5.. / D1 = 5 => 0 pairs (X) / D6 = 5 => 12 pairs (_) B4,C6: 8.. / B4 = 8 => 0 pairs (*) / C6 = 8 => 0 pairs (X) F4,E5: 8.. / F4 = 8 => 0 pairs (X) / E5 = 8 => 0 pairs (_) G7,I8: 8.. / G7 = 8 => 0 pairs (*) / I8 = 8 => 0 pairs (X) E5,H5: 8.. / E5 = 8 => 0 pairs (*) / H5 = 8 => 0 pairs (X) C6,H6: 8.. / C6 = 8 => 0 pairs (X) / H6 = 8 => 0 pairs (_) A8,I8: 8.. / A8 = 8 => 0 pairs (*) / I8 = 8 => 0 pairs (X) B4,B7: 8.. / B4 = 8 => 0 pairs (*) / B7 = 8 => 0 pairs (X) F1,F4: 8.. / F1 = 8 => 0 pairs (*) / F4 = 8 => 0 pairs (X) G1,G7: 8.. / G1 = 8 => 0 pairs (X) / G7 = 8 => 0 pairs (_) B4,C6: 9.. / B4 = 9 => 0 pairs (X) / C6 = 9 => 0 pairs (_) B4,B7: 9.. / B4 = 9 => 0 pairs (X) / B7 = 9 => 0 pairs (_) * DURATION: 0:01:14.008003 START: 10:17:31.750219 END: 10:18:45.758222 2017-05-04 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B4,B7,C6,D5,D6,F8,G9,H2,H8,I2) * 412....76.7.6.23..63.4712..7.612.4..154..76.232..641.7..1746.23.632..7..2478...6. * PAIR A2: 8,9 BLK 1 C2: 8,9,5 # reduction candidate for 8,9 C2: 8,9 => SOLVED * 412398576978652314635471298786123459154987632329564187591746823863219745247835961 C2: 5 # 15 pairs C3: 8,9,5 # reduction candidate for 8,9 C3: 8,9 # 15 pairs * PAIR A2: 8,9 ROW 2 E2: 8,9,5 # reduction candidate for 8,9 E2: 5 => SOLVED * 412398576978652314635471298786123459154987632329564187591746823863219745247835961 E2: 8,9 # 15 pairs * PAIR A2: 8,9 COL A A7: 8,9,5 # reduction candidate for 8,9 A7: 8,9 => CTR * 412...876.7.6823146384712..78612.4..154..76823295641.7..17465235632.97.82478..961 A7: 5 # 13 pairs A8: 8,9,5 # reduction candidate for 8,9 A8: 8,9 # 13 pairs * PAIR I2: 1,4 COL I I8: 1,4,5,8,9 # reduction candidate for 1,4 I8: 1,4 => CTR * 412..8.769786523..63547129878612.4591549876323295641875917468238632.57..2478.956. I8: 5,8,9 # 8 pairs * PAIR B4: 8,9 ROW 4 F4: 8,9,3,5 # reduction candidate for 8,9 F4: 8,9 # 19 pairs H4: 8,9,3,5 # reduction candidate for 8,9 H4: 8,9 => CTR * 4123.8.76.7.6.231463.4712587.61234.515498763232.5641.7..1746823863215749247839561 H4: 3,5 # 12 pairs I4: 8,9,5 # reduction candidate for 8,9 I4: 8,9 => SOLVED * 412398576978652314635471298786123459154987632329564187591746823863219745247835961 I4: 5 # 17 pairs * PAIR C6: 8,9 ROW 6 H6: 8,9,5 # reduction candidate for 8,9 H6: 5 => CTR * 412....76.7.6.23..63.4712..7.612.4..154..76.2328964157.81746.23.632..7.82478...6. H6: 8,9 # 12 pairs * PAIR C6: 8,9 COL C C2: 8,9,5 # reduction candidate for 8,9 C2: 8,9 => SOLVED * 412398576978652314635471298786123459154987632329564187591746823863219745247835961 C2: 5 # 15 pairs C3: 8,9,5 # reduction candidate for 8,9 C3: 8,9 # 15 pairs * PAIR D5: 3,9 BLK 5 F4: 3,9,5,8 # reduction candidate for 3,9 F4: 3,9 => SOLVED * 412398576978652314635471298786123459154987632329564187591746823863219745247835961 F4: 5,8 # 13 pairs E5: 3,9,8 # reduction candidate for 3,9 E5: 3,9 => CTR * 412....76.7.6.23..63.4712..7.6128435154..7682328564197.81746.23.632..7.82478...6. E5: 8 => SOLVED * 412398576978652314635471298786123459154987632329564187591746823863219745247835961 * PAIR D5: 3,9 ROW 5 H5: 3,9,8 # reduction candidate for 3,9 H5: 3,9 => SOLVED * 412398576978652314635471298786123459154987632329564187591746823863219745247835961 H5: 8 => CTR * 412....76.7.6.23..63.4712..7.612.43.154..7682328.641.7.81746.23.632..7.82478...6. * PAIR D5: 3,9 COL D D1: 3,9,5 # reduction candidate for 3,9 D1: 5 => CTR * 4125389768756923..639471285796125438154387692328964157981746.23.632.97..2478.3.6. D1: 3,9 # 12 pairs * PAIR D6: 5,9 BLK 5 F4: 5,9,3,8 # reduction candidate for 5,9 F4: 5,9 => CTR * 412.38.769786523..63547128.7.612.43.154.8769232..641.7..17468238632..7..2478.3.6. F4: 3,8 # 14 pairs * PAIR D6: 5,9 ROW 6 H6: 5,9,8 # reduction candidate for 5,9 H6: 5,9 => CTR * 412...87687.6.23.463.4712..796128435154..7682328564197.81746.23.632..7482478...61 H6: 8 => SOLVED * 412398576978652314635471298786123459154987632329564187591746823863219745247835961 * PAIR D6: 5,9 COL D D1: 5,9,3 # reduction candidate for 5,9 D1: 5,9 # 13 pairs D1: 3 # 13 pairs * PAIR B7: 8,9 BLK 7 A7: 8,9,5 # reduction candidate for 8,9 A7: 8,9 => CTR * 412...876.7.6823146384712..78612.4..154..76823295641.7..17465235632.97.82478..961 A7: 5 # 13 pairs A8: 8,9,5 # reduction candidate for 8,9 A8: 8,9 # 13 pairs * PAIR B7: 8,9 ROW 7 G7: 8,9,5 # reduction candidate for 8,9 G7: 5 => CTR * 412...876.7.6823..6384712..78612.4..154..76823295641.7..1746.23.632..7..2478...6. G7: 8,9 # 13 pairs * PAIR F8: 5,9 BLK 8 E8: 5,9,1 # reduction candidate for 5,9 E8: 5,9 => CTR * 412....7697.6.23..63.4712..78612.43.154.876923295641875917468238632..7..247813.6. E8: 1 # 8 pairs E9: 5,9,1,3 # reduction candidate for 5,9 E9: 5,9 # 10 pairs F9: 5,9,3 # reduction candidate for 5,9 F9: 5,9 # 14 pairs * PAIR F8: 5,9 ROW 8 A8: 5,9,8 # reduction candidate for 5,9 A8: 5,9 => CTR * 412...876.7.6823.46384712..78612.4..154..76823295641.7..1746.23.632..7.82478...6. A8: 8 => SOLVED * 412398576978652314635471298786123459154987632329564187591746823863219745247835961 I8: 5,9,1,4,8 # reduction candidate for 5,9 I8: 5,9 => SOLVED * 412398576978652314635471298786123459154987632329564187591746823863219745247835961 I8: 1,4,8 # 11 pairs * PAIR F8: 5,9 COL F F1: 5,9,3,8 # reduction candidate for 5,9 F1: 5,9 => CTR * 412....76.7.6.23..63.4712..7.6128435154..7682328564197.81746.23.632..7.82478.3.6. F1: 3,8 # 12 pairs F4: 5,9,3,8 # reduction candidate for 5,9 F4: 5,9 => CTR * 412.38.769786523..63547128.7.612.43.154.8769232..641.7..17468238632..7..2478.3.6. F4: 3,8 # 14 pairs * PAIR H8: 1,4 BLK 9 I8: 1,4,5,8,9 # reduction candidate for 1,4 I8: 1,4 => CTR * 412..8.769786523..63547129878612.4591549876323295641875917468238632.57..2478.956. I8: 5,8,9 # 8 pairs * PAIR G9: 5,9 BLK 9 G7: 5,9,8 # reduction candidate for 5,9 G7: 5,9 => CTR * 412...876.7.6823..6384712..78612.4..154..76823295641.7..1746.23.632..7..2478...6. G7: 8 => SOLVED * 412398576978652314635471298786123459154987632329564187591746823863219745247835961 I8: 5,9,1,4,8 # reduction candidate for 5,9 I8: 5,9 => SOLVED * 412398576978652314635471298786123459154987632329564187591746823863219745247835961 I8: 1,4,8 # 11 pairs I9: 5,9,1 # reduction candidate for 5,9 I9: 5,9 => CTR * 412....7697.6.23..63.4712..78612.43.154.876923295641875917468238632..7..247813.6. I9: 1 # 8 pairs * PAIR G9: 5,9 ROW 9 E9: 5,9,1,3 # reduction candidate for 5,9 E9: 5,9 # 10 pairs F9: 5,9,3 # reduction candidate for 5,9 F9: 5,9 # 14 pairs * PAIR G9: 5,9 COL G G1: 5,9,8 # reduction candidate for 5,9 G1: 5,9 => SOLVED * 412398576978652314635471298786123459154987632329564187591746823863219745247835961 G1: 8 => CTR * 412...876.7.6823..6384712..78612.4..154..76823295641.7..1746.23.632..7..2478...6. * INCONCLUSIVE * SAVE PR GRAPH xx-top500-220-base-pr-000.dot * REASONING * PRF # C2: 8,9 => SOL * PRF # E2: 5 => SOL * DIS # A7: 8,9 => CTR => A7: 5 * DIS # I8: 1,4 => CTR => I8: 5,8,9 * DIS # H4: 8,9 => CTR => H4: 3,5 * PRF # I4: 8,9 => SOL * DIS # H6: 5 => CTR => H6: 8,9 * PRF # C2: 8,9 => SOL * PRF # F4: 3,9 => SOL * DIS # E5: 3,9 => CTR => E5: 8 * PRF # E5: 8 => SOL * PRF # H5: 3,9 => SOL * DIS # H5: 8 => CTR => H5: 3,9 * DIS # D1: 5 => CTR => D1: 3,9 * DIS # F4: 5,9 => CTR => F4: 3,8 * DIS # H6: 5,9 => CTR => H6: 8 * PRF # H6: 8 => SOL * DIS # A7: 8,9 => CTR => A7: 5 * DIS # G7: 5 => CTR => G7: 8,9 * DIS # E8: 5,9 => CTR => E8: 1 * DIS # A8: 5,9 => CTR => A8: 8 * PRF # A8: 8 => SOL * PRF # I8: 5,9 => SOL * DIS # F1: 5,9 => CTR => F1: 3,8 * DIS # F4: 5,9 => CTR => F4: 3,8 * DIS # I8: 1,4 => CTR => I8: 5,8,9 * DIS # G7: 5,9 => CTR => G7: 8 * PRF # G7: 8 => SOL * PRF # I8: 5,9 => SOL * DIS # I9: 5,9 => CTR => I9: 1 * PRF # G1: 5,9 => SOL * DIS # G1: 8 => CTR => G1: 5,9 * CNT 32 HDP CHAINS / 63 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B4,B7,C6,D5,D6,F8,G9,H2,H8,I2) * 412....76.7.6.23..63.4712..7.612.4..154..76.232..641.7..1746.23.632..7..2478...6. * PAIR A2: 8,9 BLK 1 C2: 8,9,5 # reduction candidate for 8,9 C2: 8,9 => SOLVED * 412398576978652314635471298786123459154987632329564187591746823863219745247835961 * DURATION: 0:00:02.556231 START: 10:20:14.535349 END: 10:20:17.091580 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-220-base-pr-001.dot * REASONING * PRF # C2: 8,9 => SOL * STA C2: 8,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 220 solution: 412398576978652314635471298786123459154987632329564187591746823863219745247835961 info: 1960 FNBTHWX S8.f 31293 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 412398576978652314635471298786123459154987632329564187591746823863219745247835961 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 # C2: 8,9 => SOL * INC # C2: 5 => UNS * INC # C3: 8,9 => UNS * INC # E2: 8,9 => UNS * PRF # E2: 5 => SOL * DIS # A7: 8,9 => CTR => A7: 5 * INC # A7: 5 => UNS * INC # A8: 8,9 => UNS * DIS # I8: 1,4 => CTR => I8: 5,8,9 * INC # I8: 5,8,9 => UNS * INC # F4: 8,9 => UNS * DIS # H4: 8,9 => CTR => H4: 3,5 * INC # H4: 3,5 => UNS * PRF # I4: 8,9 => SOL * INC # I4: 5 => UNS * INC # H6: 8,9 => UNS * DIS # H6: 5 => CTR => H6: 8,9 * PRF # C2: 8,9 => SOL * INC # C2: 5 => UNS * INC # C3: 8,9 => UNS * PRF # F4: 3,9 => SOL * INC # F4: 5,8 => UNS * DIS # E5: 3,9 => CTR => E5: 8 * PRF # E5: 8 => SOL * PRF # H5: 3,9 => SOL * DIS # H5: 8 => CTR => H5: 3,9 * INC # D1: 3,9 => UNS * DIS # D1: 5 => CTR => D1: 3,9 * DIS # F4: 5,9 => CTR => F4: 3,8 * INC # F4: 3,8 => UNS * DIS # H6: 5,9 => CTR => H6: 8 * PRF # H6: 8 => SOL * INC # D1: 5,9 => UNS * INC # D1: 3 => UNS * DIS # A7: 8,9 => CTR => A7: 5 * INC # A7: 5 => UNS * INC # A8: 8,9 => UNS * INC # G7: 8,9 => UNS * DIS # G7: 5 => CTR => G7: 8,9 * DIS # E8: 5,9 => CTR => E8: 1 * INC # E8: 1 => UNS * INC # E9: 5,9 => UNS * INC # F9: 5,9 => UNS * DIS # A8: 5,9 => CTR => A8: 8 * PRF # A8: 8 => SOL * PRF # I8: 5,9 => SOL * INC # I8: 1,4,8 => UNS * DIS # F1: 5,9 => CTR => F1: 3,8 * INC # F1: 3,8 => UNS * DIS # F4: 5,9 => CTR => F4: 3,8 * INC # F4: 3,8 => UNS * DIS # I8: 1,4 => CTR => I8: 5,8,9 * INC # I8: 5,8,9 => UNS * DIS # G7: 5,9 => CTR => G7: 8 * PRF # G7: 8 => SOL * PRF # I8: 5,9 => SOL * INC # I8: 1,4,8 => UNS * DIS # I9: 5,9 => CTR => I9: 1 * INC # I9: 1 => UNS * INC # E9: 5,9 => UNS * INC # F9: 5,9 => UNS * PRF # G1: 5,9 => SOL * DIS # G1: 8 => CTR => G1: 5,9 * CNT 63 HDP CHAINS / 63 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C2: 8,9 => SOL * STA C2: 8,9 * CNT 1 HDP CHAINS / 1 HYP OPENED