Analysis of xx-top500-472-base.sdk
Contents
Original Sudoku
level: medium
position: ......3.4.....2......6.......1.4.......5...2.......68....13.5..26......78........ initial
Autosolve
position: ......3.4.....21.6...6..2.8..1.4.73....5..42.......68....138562263...817815...943 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 3,4 => CTR => A3: 1,5,7,9 * PRF # B1: 5,7,9 => SOL * DIS # E5: 6,9 => CTR => E5: 1,7,8 * PRF # E5: 1,7,8 => SOL * DIS # F5: 6,9 => CTR => F5: 1,3,7 * DIS # A4: 5 => CTR => A4: 6,9 * PRF # A4: 5,9 => SOL * DIS # A4: 6 => CTR => A4: 5,9 * DIS # I6: 5 => CTR => I6: 1,9 * PRF # E5: 1,9 => SOL * DIS # E9: 2,7 => CTR => E9: 6 * PRF # E9: 6 => SOL * PRF # D6: 2,7 => SOL * PRF # E9: 6,7 => SOL * DIS # E9: 2 => CTR => E9: 6,7 * DIS # F5: 6,7 => CTR => F5: 1,3,9 * CNT 16 HDP CHAINS / 37 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 3,4 => CTR => A3: 1,5,7,9 * PRF A3: 1,5,7,9 # B1: 5,7,9 => SOL * STA A3: 1,5,7,9 + B1: 5,7,9 * CNT 2 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ......3.4.....2......6.......1.4.......5...2.......68....13.5..26......78........ | initial |
| ......3.4.....21.6...6..2.8..1.4.73....5..42.......68....138562263...817815...943 | autosolve |
| 672981354548372196139654278921846735786513429354729681497138562263495817815267943 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) D2: 3,4 F3: 3,4 B4: 2,8 D4: 2,8 F4: 6,9 I4: 5,9 I5: 1,9 D8: 4,9 E8: 5,9 D9: 2,7 F9: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A3: 1.. / A1 = 1 => 0 pairs (X) / A3 = 1 => 11 pairs (_) I5,I6: 1.. / I5 = 1 => 11 pairs (_) / I6 = 1 => 10 pairs (_) A3,E3: 1.. / A3 = 1 => 11 pairs (_) / E3 = 1 => 0 pairs (X) B1,C1: 2.. / B1 = 2 => 0 pairs (X) / C1 = 2 => 0 pairs (_) D9,E9: 2.. / D9 = 2 => 0 pairs (*) / E9 = 2 => 0 pairs (X) B4,D4: 2.. / B4 = 2 => 0 pairs (*) / D4 = 2 => 0 pairs (X) C1,C6: 2.. / C1 = 2 => 0 pairs (*) / C6 = 2 => 0 pairs (X) E6,E9: 2.. / E6 = 2 => 0 pairs (*) / E9 = 2 => 0 pairs (X) D2,F3: 3.. / D2 = 3 => 10 pairs (_) / F3 = 3 => 10 pairs (_) D2,D6: 3.. / D2 = 3 => 10 pairs (_) / D6 = 3 => 10 pairs (_) D2,F3: 4.. / D2 = 4 => 10 pairs (_) / F3 = 4 => 10 pairs (_) D8,F8: 4.. / D8 = 4 => 10 pairs (_) / F8 = 4 => 10 pairs (_) D2,D8: 4.. / D2 = 4 => 10 pairs (_) / D8 = 4 => 10 pairs (_) F3,F8: 4.. / F3 = 4 => 10 pairs (_) / F8 = 4 => 10 pairs (_) I4,I6: 5.. / I4 = 5 => 12 pairs (_) / I6 = 5 => 0 pairs (X) E8,F8: 5.. / E8 = 5 => 12 pairs (_) / F8 = 5 => 9 pairs (_) A4,I4: 5.. / A4 = 5 => 0 pairs (X) / I4 = 5 => 12 pairs (_) F1,F8: 5.. / F1 = 5 => 12 pairs (_) / F8 = 5 => 9 pairs (_) A1,C1: 6.. / A1 = 6 => 0 pairs (*) / C1 = 6 => 0 pairs (X) E9,F9: 6.. / E9 = 6 => 0 pairs (*) / F9 = 6 => 0 pairs (X) A4,F4: 6.. / A4 = 6 => 0 pairs (X) / F4 = 6 => 0 pairs (_) C1,C5: 6.. / C1 = 6 => 0 pairs (X) / C5 = 6 => 0 pairs (_) E5,E9: 6.. / E5 = 6 => 0 pairs (X) / E9 = 6 => 0 pairs (_) D4,E5: 8.. / D4 = 8 => 0 pairs (*) / E5 = 8 => 0 pairs (X) B4,D4: 8.. / B4 = 8 => 0 pairs (X) / D4 = 8 => 0 pairs (_) D1,D4: 8.. / D1 = 8 => 0 pairs (X) / D4 = 8 => 0 pairs (_) * DURATION: 0:00:40.842077 START: 18:48:31.429774 END: 18:49:12.271851 2017-05-04 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,D2,D4,D8,D9,E8,F3,F4,F9,I4,I5) * ......3.4.....21.6...6..2.8..1.4.73....5..42.......68....138562263...817815...943 * PAIR D2: 3,4 ROW 2 A2: 3,4,5,7,9 # reduction candidate for 3,4 A2: 3,4 # 12 pairs B2: 3,4,5,7,8,9 # reduction candidate for 3,4 B2: 3,4 # 12 pairs * PAIR F3: 3,4 ROW 3 A3: 3,4,1,5,7,9 # reduction candidate for 3,4 A3: 3,4 => CTR * 126...3.4.....21.6...61.2.868124.73....5..42...2...68....138562263...817815.26943 A3: 1,5,7,9 # 11 pairs B3: 3,4,5,7,9 # reduction candidate for 3,4 B3: 3,4 # 13 pairs * PAIR B4: 2,8 COL B B1: 2,8,5,7,9 # reduction candidate for 2,8 B1: 5,7,9 => SOLVED * 672981354548372196139654278921846735786513429354729681497138562263495817815267943 B1: 2,8 # 12 pairs * PAIR F4: 6,9 BLK 5 E5: 6,9,1,7,8 # reduction candidate for 6,9 E5: 6,9 => CTR * 6.2..53.4..8.721.6...6..2.8.2184.73...659.421......68....138562263.5.817815.67943 E5: 1,7,8 => SOLVED * 672981354548372196139654278921846735786513429354729681497138562263495817815267943 F5: 6,9,1,3,7 # reduction candidate for 6,9 F5: 6,9 => CTR * 6.2.153.4..8..21.61..6.32.8.2184673..86579421...32168....138562263.54817815267943 F5: 1,3,7 # 11 pairs * PAIR F4: 6,9 ROW 4 A4: 6,9,5 # reduction candidate for 6,9 A4: 5 => CTR * 6.2.1.3.4..8..21.61..6..2.8521846739.865..421....21685...138562263...817815267943 A4: 6,9 # 12 pairs * PAIR I4: 5,9 BLK 6 I6: 5,9,1 # reduction candidate for 5,9 I6: 5,9 # 11 pairs I6: 1 # 10 pairs * PAIR I4: 5,9 ROW 4 A4: 5,9,6 # reduction candidate for 5,9 A4: 5,9 => SOLVED * 672981354548372196139654278921846735786513429354729681497138562263495817815267943 A4: 6 => CTR * .26...3.4.....21.6...6..2.8681249735...5..42...2...68....138562263...817815.26943 * PAIR I5: 1,9 BLK 6 I6: 1,9,5 # reduction candidate for 1,9 I6: 5 => CTR * 6.2.1.3.4..8..21.61..6..2.8521846739.865..421....21685...138562263...817815267943 I6: 1,9 # 12 pairs * PAIR I5: 1,9 ROW 5 E5: 1,9,6,7,8 # reduction candidate for 1,9 E5: 1,9 => SOLVED * 672981354548372196139654278921846735786513429354729681497138562263495817815267943 E5: 6,7,8 # 11 pairs F5: 1,9,3,6,7 # reduction candidate for 1,9 F5: 1,9 # 12 pairs * PAIR D8: 4,9 BLK 8 F8: 4,9,5 # reduction candidate for 4,9 F8: 4,9 # 12 pairs F8: 5 # 9 pairs * PAIR E8: 5,9 BLK 8 F8: 5,9,4 # reduction candidate for 5,9 F8: 5,9 # 10 pairs F8: 4 # 10 pairs * PAIR E8: 5,9 COL E E1: 5,9,1,7,8 # reduction candidate for 5,9 E1: 5,9 # 21 pairs E2: 5,9,7,8 # reduction candidate for 5,9 E2: 5,9 # 13 pairs E3: 5,9,1,7 # reduction candidate for 5,9 E3: 5,9 # 13 pairs * PAIR D9: 2,7 BLK 8 E9: 2,7,6 # reduction candidate for 2,7 E9: 2,7 => CTR * ..6...3.4.....21.6...6..2.86.1849735...56.42...2...68....138562263...817815..6943 E9: 6 => SOLVED * 672981354548372196139654278921846735786513429354729681497138562263495817815267943 * PAIR D9: 2,7 COL D D6: 2,7,3,9 # reduction candidate for 2,7 D6: 2,7 => SOLVED * 672981354548372196139654278921846735786513429354729681497138562263495817815267943 D6: 3,9 # 12 pairs * PAIR F9: 6,7 BLK 8 E9: 6,7,2 # reduction candidate for 6,7 E9: 6,7 => SOLVED * 672981354548372196139654278921846735786513429354729681497138562263495817815267943 E9: 2 => CTR * ..6...3.4.....21.6...6..2.86.1849735...56.42...2...68....138562263...817815.26943 * PAIR F9: 6,7 COL F F5: 6,7,1,3,9 # reduction candidate for 6,7 F5: 6,7 => CTR * .26...3.4.....21.6...6..2.8681249735...5..42...2...68....138562263...817815.26943 F5: 1,3,9 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-472-base-pr-000.dot * REASONING * DIS # A3: 3,4 => CTR => A3: 1,5,7,9 * PRF # B1: 5,7,9 => SOL * DIS # E5: 6,9 => CTR => E5: 1,7,8 * PRF # E5: 1,7,8 => SOL * DIS # F5: 6,9 => CTR => F5: 1,3,7 * DIS # A4: 5 => CTR => A4: 6,9 * PRF # A4: 5,9 => SOL * DIS # A4: 6 => CTR => A4: 5,9 * DIS # I6: 5 => CTR => I6: 1,9 * PRF # E5: 1,9 => SOL * DIS # E9: 2,7 => CTR => E9: 6 * PRF # E9: 6 => SOL * PRF # D6: 2,7 => SOL * PRF # E9: 6,7 => SOL * DIS # E9: 2 => CTR => E9: 6,7 * DIS # F5: 6,7 => CTR => F5: 1,3,9 * CNT 16 HDP CHAINS / 37 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,D2,D4,D8,D9,E8,F3,F4,F9,I4,I5) * ......3.4.....21.6...6..2.8..1.4.73....5..42.......68....138562263...817815...943 * PAIR D2: 3,4 ROW 2 A2: 3,4,5,7,9 # reduction candidate for 3,4 A2: 3,4 # 12 pairs B2: 3,4,5,7,8,9 # reduction candidate for 3,4 B2: 3,4 # 12 pairs * PAIR F3: 3,4 ROW 3 A3: 3,4,1,5,7,9 # reduction candidate for 3,4 A3: 3,4 => CTR * 126...3.4.....21.6...61.2.868124.73....5..42...2...68....138562263...817815.26943 B3: 3,4,5,7,9 # reduction candidate for 3,4 B3: 3,4 # 13 pairs * RESTART * PAIR F3: 3,4 ROW 3 B3: 3,4,5,7,9 # reduction candidate for 3,4 B3: 3,4 # 13 pairs B3: 5,7,9 # 11 pairs * PAIR RESTART * PAIR F3: 3,4 ROW 3 B3: 3,4,5,7,9 # reduction candidate for 3,4 B3: 3,4 # 13 pairs B3: 5,7,9 # 11 pairs * PAIR B4: 2,8 COL B B1: 2,8,5,7,9 # reduction candidate for 2,8 B1: 5,7,9 => SOLVED * 672981354548372196139654278921846735786513429354729681497138562263495817815267943 * DURATION: 0:00:09.634179 START: 18:49:46.656177 END: 18:49:56.290356 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-472-base-pr-001.dot * REASONING * DIS # A3: 3,4 => CTR => A3: 1,5,7,9 * PRF A3: 1,5,7,9 # B1: 5,7,9 => SOL * STA A3: 1,5,7,9 + B1: 5,7,9 * CNT 2 HDP CHAINS / 10 HYP OPENED
Header Info
Top 500 Minimum 17 472 solution: 672981354548372196139654278921846735786513429354729681497138562263495817815267943 info: 95681 FNHYK S8.f 1153 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 672981354548372196139654278921846735786513429354729681497138562263495817815267943 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 # A2: 3,4 => UNS * INC # B2: 3,4 => UNS * DIS # A3: 3,4 => CTR => A3: 1,5,7,9 * INC # A3: 1,5,7,9 => UNS * INC # B3: 3,4 => UNS * INC # B1: 2,8 => UNS * PRF # B1: 5,7,9 => SOL * DIS # E5: 6,9 => CTR => E5: 1,7,8 * PRF # E5: 1,7,8 => SOL * DIS # F5: 6,9 => CTR => F5: 1,3,7 * INC # F5: 1,3,7 => UNS * INC # A4: 6,9 => UNS * DIS # A4: 5 => CTR => A4: 6,9 * INC # I6: 5,9 => UNS * INC # I6: 1 => UNS * PRF # A4: 5,9 => SOL * DIS # A4: 6 => CTR => A4: 5,9 * INC # I6: 1,9 => UNS * DIS # I6: 5 => CTR => I6: 1,9 * PRF # E5: 1,9 => SOL * INC # E5: 6,7,8 => UNS * INC # F5: 1,9 => UNS * INC # F8: 4,9 => UNS * INC # F8: 5 => UNS * INC # F8: 5,9 => UNS * INC # F8: 4 => UNS * INC # E1: 5,9 => UNS * INC # E2: 5,9 => UNS * INC # E3: 5,9 => UNS * DIS # E9: 2,7 => CTR => E9: 6 * PRF # E9: 6 => SOL * PRF # D6: 2,7 => SOL * INC # D6: 3,9 => UNS * PRF # E9: 6,7 => SOL * DIS # E9: 2 => CTR => E9: 6,7 * DIS # F5: 6,7 => CTR => F5: 1,3,9 * INC # F5: 1,3,9 => UNS * CNT 37 HDP CHAINS / 37 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A2: 3,4 => UNS * INC # B2: 3,4 => UNS * DIS # A3: 3,4 => CTR => A3: 1,5,7,9 * INC A3: 1,5,7,9 # B3: 3,4 => UNS * INC A3: 1,5,7,9 # B3: 3,4 => UNS * INC A3: 1,5,7,9 # B3: 5,7,9 => UNS * INC A3: 1,5,7,9 # B3: 3,4 => UNS * INC A3: 1,5,7,9 # B3: 5,7,9 => UNS * INC A3: 1,5,7,9 # B1: 2,8 => UNS * PRF A3: 1,5,7,9 # B1: 5,7,9 => SOL * STA A3: 1,5,7,9 + B1: 5,7,9 * CNT 10 HDP CHAINS / 10 HYP OPENED