Analysis of xx-top500-266-base.sdk
Contents
Original Sudoku
level: medium
position: ....38.6..24...................7.2...1.4.....8......3....6..4.1..6...5..3........ initial
Autosolve
position: 1..238.64.241..385.38....12.6.371248.1348.65.84....13..8.6.34.14.681.5.33.1...8.6 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F2: 6,9 => CTR => F2: 7 * DIS # E3: 6,9 => CTR => E3: 4,5 * DIS # F3: 6,9 => CTR => F3: 4,5,7 * DIS # A2: 7 => CTR => A2: 6,9 * DIS # A3: 7,9 => CTR => A3: 6 * DIS # F3: 7,9 => CTR => F3: 4,5,6 * DIS # A7: 5,9 => CTR => A7: 2,7 * DIS # C7: 5,9 => CTR => C7: 2,7 * DIS # A7: 5,9 => CTR => A7: 2,7 * DIS # C7: 5,9 => CTR => C7: 2,7 * DIS # F6: 2,9 => CTR => F6: 5,6 * DIS # F9: 2,9 => CTR => F9: 4,5,7 * DIS # E6: 5,9 => CTR => E6: 2,6 * DIS # F6: 5,9 => CTR => F6: 2,6 * DIS # D9: 5,9 => CTR => D9: 7 * DIS # C7: 7,9 => CTR => C7: 2,5 * PRF # H8: 7,9 => SOL * DIS # D9: 5,9 => CTR => D9: 7 * PRF # E9: 5,9 => SOL * DIS # F9: 5,9 => CTR => F9: 2,4,7 * DIS # A7: 5,9 => CTR => A7: 2,7 * DIS # C7: 5,9 => CTR => C7: 2,7 * DIS # E3: 5,9 => CTR => E3: 4,6 * DIS # E6: 5,9 => CTR => E6: 2,6 * PRF # H8: 7,9 => SOL * DIS # C7: 7,9 => CTR => C7: 2,5 * CNT 26 HDP CHAINS / 68 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F2: 6,9 => CTR => F2: 7 * DIS F2: 7 # E3: 6,9 => CTR => E3: 4,5 * DIS F2: 7 + E3: 4,5 # E6: 6,9 => CTR => E6: 2,5 * PRF F2: 7 + E3: 4,5 + E6: 2,5 => SOL * STA F2: 7 + E3: 4,5 + E6: 2,5 * CNT 4 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....38.6..24...................7.2...1.4.....8......3....6..4.1..6...5..3........ | initial |
| 1..238.64.241..385.38....12.6.371248.1348.65.84....13..8.6.34.14.681.5.33.1...8.6 | autosolve |
| 175238964924167385638945712569371248213489657847526139782653491496812573351794826 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) E2: 6,9 G1: 7,9 G3: 7,9 A4: 5,9 C4: 5,9 A5: 2,7 C6: 2,7 F5: 2,9 D6: 5,9 I5: 7,9 I6: 7,9 B8: 7,9 E7: 5,9 H7: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A5,C6: 2.. / A5 = 2 => 19 pairs (_) / C6 = 2 => 0 pairs (X) A7,C7: 2.. / A7 = 2 => 0 pairs (X) / C7 = 2 => 19 pairs (_) H8,H9: 2.. / H8 = 2 => 18 pairs (_) / H9 = 2 => 0 pairs (*) A5,F5: 2.. / A5 = 2 => 19 pairs (_) / F5 = 2 => 0 pairs (X) F8,H8: 2.. / F8 = 2 => 0 pairs (*) / H8 = 2 => 0 pairs (X) A5,A7: 2.. / A5 = 2 => 19 pairs (_) / A7 = 2 => 0 pairs (X) C6,C7: 2.. / C6 = 2 => 0 pairs (X) / C7 = 2 => 19 pairs (_) E6,E9: 2.. / E6 = 2 => 0 pairs (*) / E9 = 2 => 0 pairs (X) E3,F3: 4.. / E3 = 4 => 14 pairs (_) / F3 = 4 => 0 pairs (X) E9,F9: 4.. / E9 = 4 => 0 pairs (X) / F9 = 4 => 14 pairs (_) E3,E9: 4.. / E3 = 4 => 14 pairs (_) / E9 = 4 => 0 pairs (X) F3,F9: 4.. / F3 = 4 => 0 pairs (X) / F9 = 4 => 14 pairs (_) B1,C1: 5.. / B1 = 5 => 26 pairs (_) / C1 = 5 => 14 pairs (_) A4,C4: 5.. / A4 = 5 => 13 pairs (_) / C4 = 5 => 0 pairs (X) A4,A7: 5.. / A4 = 5 => 13 pairs (_) / A7 = 5 => 0 pairs (X) B1,B9: 5.. / B1 = 5 => 26 pairs (_) / B9 = 5 => 14 pairs (_) A2,A3: 6.. / A2 = 6 => 0 pairs (X) / A3 = 6 => 15 pairs (_) E6,F6: 6.. / E6 = 6 => 18 pairs (_) / F6 = 6 => 17 pairs (_) G1,G3: 7.. / G1 = 7 => 0 pairs (X) / G3 = 7 => 21 pairs (_) A5,C6: 7.. / A5 = 7 => 0 pairs (X) / C6 = 7 => 19 pairs (_) I5,I6: 7.. / I5 = 7 => 19 pairs (_) / I6 = 7 => 0 pairs (X) A2,F2: 7.. / A2 = 7 => 0 pairs (X) / F2 = 7 => 21 pairs (_) A5,I5: 7.. / A5 = 7 => 0 pairs (X) / I5 = 7 => 19 pairs (_) C6,I6: 7.. / C6 = 7 => 19 pairs (_) / I6 = 7 => 0 pairs (X) D3,D9: 7.. / D3 = 7 => 0 pairs (X) / D9 = 7 => 21 pairs (_) G1,G3: 9.. / G1 = 9 => 21 pairs (_) / G3 = 9 => 0 pairs (X) A4,C4: 9.. / A4 = 9 => 0 pairs (X) / C4 = 9 => 13 pairs (_) I5,I6: 9.. / I5 = 9 => 0 pairs (X) / I6 = 9 => 19 pairs (_) F5,I5: 9.. / F5 = 9 => 19 pairs (_) / I5 = 9 => 0 pairs (X) * DURATION: 0:00:51.819398 START: 11:57:55.176272 END: 11:58:46.995670 2017-05-04 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,B8,C4,C6,D6,E2,E7,F5,G1,G3,H7,I5,I6) * 1..238.64.241..385.38....12.6.371248.1348.65.84....13..8.6.34.14.681.5.33.1...8.6 * PAIR E2: 6,9 BLK 2 F2: 6,9,7 # reduction candidate for 6,9 F2: 6,9 => CTR * 1..2387647241963856387..912.6.37124821348965784756213998265347147681.5.33.1...8.6 F2: 7 # 21 pairs E3: 6,9,4,5 # reduction candidate for 6,9 E3: 6,9 => CTR * 1..238.64.241..385.385.4.12.6.371248.1348.65.84.92.13..8.6.34.14.681.5.33.1.4.8.6 E3: 4,5 # 15 pairs F3: 6,9,4,5,7 # reduction candidate for 6,9 F3: 6,9 => CTR * 19.238.64.241.7385.38546.12.6.37124871348265984296513728.6.34.14.68195233.1724896 F3: 4,5,7 # 14 pairs * PAIR E2: 6,9 ROW 2 A2: 6,9,7 # reduction candidate for 6,9 A2: 7 => CTR * 1..2387647241963856387..912.6.37124821348965784756213998265347147681.5.33.1...8.6 A2: 6,9 # 21 pairs * PAIR E2: 6,9 COL E E6: 6,9,2,5 # reduction candidate for 6,9 E6: 2,5 # 18 pairs E6: 6,9 # 17 pairs * PAIR G1: 7,9 ROW 1 B1: 7,9,5 # reduction candidate for 7,9 B1: 7,9 # 14 pairs C1: 7,9,5 # reduction candidate for 7,9 C1: 7,9 # 26 pairs * PAIR G3: 7,9 ROW 3 A3: 7,9,6 # reduction candidate for 7,9 A3: 7,9 => CTR * 1.5238.64624197385.385...125693712487134826598429651372876534914.681.5.33517..8.6 A3: 6 # 15 pairs D3: 7,9,5 # reduction candidate for 7,9 D3: 7,9 # 18 pairs F3: 7,9,4,5,6 # reduction candidate for 7,9 F3: 7,9 => CTR * 1..238.64.241.6385638547912.6.37124871348265984296513728.6.34.14.68195233.1724896 F3: 4,5,6 # 14 pairs * PAIR A4: 5,9 COL A A7: 5,9,2,7 # reduction candidate for 5,9 A7: 5,9 => CTR * 1..238764.2419.385.387..912.6.371248213489657847526139.826.34714.681.5.33.19..826 A7: 2,7 # 21 pairs * PAIR C4: 5,9 COL C C1: 5,9,7 # reduction candidate for 5,9 C1: 5,9 # 16 pairs C7: 5,9,2,7 # reduction candidate for 5,9 C7: 5,9 => CTR * 1.7238964.241.7385.38.4.712569371248713482659842...1372856.34714.681.5.33.1.24896 C7: 2,7 # 16 pairs * PAIR A5: 2,7 COL A A7: 2,7,5,9 # reduction candidate for 2,7 A7: 5,9 => CTR * 1..238764.2419.385.387..912.6.371248213489657847526139.826.34714.681.5.33.19..826 A7: 2,7 # 21 pairs * PAIR C6: 2,7 COL C C7: 2,7,5,9 # reduction candidate for 2,7 C7: 5,9 => CTR * 1.7238964.241.7385.38.4.712569371248713482659842...1372856.34714.681.5.33.1.24896 C7: 2,7 # 16 pairs * PAIR F5: 2,9 BLK 5 E6: 2,9,5,6 # reduction candidate for 2,9 E6: 2,9 # 20 pairs F6: 2,9,5,6 # reduction candidate for 2,9 F6: 2,9 => CTR * 1.5238.64.24196385638745912569371248.1348.65.84.56.13.98.6534.14.681.523351924876 F6: 5,6 # 15 pairs * PAIR F5: 2,9 COL F F8: 2,9,7 # reduction candidate for 2,9 F8: 2,9 # 19 pairs F9: 2,9,4,5,7 # reduction candidate for 2,9 F9: 2,9 => CTR * 1..238.64.241..385.38..4.12.6.371248.1348.65.84...513..8.6.34.14.681.5.33.1.4.8.6 F9: 4,5,7 # 14 pairs * PAIR D6: 5,9 BLK 5 E6: 5,9,2,6 # reduction candidate for 5,9 E6: 5,9 => CTR * 1..238.6492416738563894571256937124871348265984259613728.65349147681.5233.1.248.6 E6: 2,6 # 15 pairs F6: 5,9,2,6 # reduction candidate for 5,9 F6: 5,9 => CTR * 1.5238.64.2419.385.38.4..12569371248713482659842.6.137287653491496817523351924876 F6: 2,6 # 17 pairs * PAIR D6: 5,9 COL D D3: 5,9,7 # reduction candidate for 5,9 D3: 5,9 # 21 pairs D9: 5,9,7 # reduction candidate for 5,9 D9: 5,9 => CTR * 1..2387647241963856387..912.6.3712482134896578475..139.826.34714.681.5.33.19..826 D9: 7 # 21 pairs * PAIR B8: 7,9 BLK 7 A7: 7,9,2,5 # reduction candidate for 7,9 A7: 7,9 # 16 pairs C7: 7,9,2,5 # reduction candidate for 7,9 C7: 7,9 => CTR * 1.5238.64.241..385.38.4..12569371248713482659842...137287653491496817523351924876 C7: 2,5 # 15 pairs B9: 7,9,5 # reduction candidate for 7,9 B9: 7,9 # 26 pairs * PAIR B8: 7,9 ROW 8 F8: 7,9,2 # reduction candidate for 7,9 F8: 7,9 # 18 pairs H8: 7,9,2 # reduction candidate for 7,9 H8: 7,9 => SOLVED * 175238964924167385638945712569371248213489657847526139782653491496812573351794826 H8: 2 # 18 pairs * PAIR B8: 7,9 COL B B1: 7,9,5 # reduction candidate for 7,9 B1: 5 # 26 pairs B1: 7,9 # 14 pairs * PAIR E7: 5,9 BLK 8 D9: 5,9,7 # reduction candidate for 5,9 D9: 5,9 => CTR * 1..2387647241963856387..912.6.3712482134896578475..139.826.34714.681.5.33.19..826 D9: 7 # 21 pairs E9: 5,9,2,4 # reduction candidate for 5,9 E9: 5,9 => SOLVED * 175238964924167385638945712569371248213489657847526139782653491496812573351794826 E9: 2,4 # 15 pairs F9: 5,9,2,4,7 # reduction candidate for 5,9 F9: 5,9 => CTR * 15.238.64.241.7385.38.54.12.653712482134896578475261395826.34.14.68125.33.1745826 F9: 2,4,7 # 14 pairs * PAIR E7: 5,9 ROW 7 A7: 5,9,2,7 # reduction candidate for 5,9 A7: 5,9 => CTR * 1..238764.2419.385.387..912.6.371248213489657847526139.826.34714.681.5.33.19..826 A7: 2,7 # 21 pairs C7: 5,9,2,7 # reduction candidate for 5,9 C7: 5,9 => CTR * 1.7238964.241.7385.38.4.712569371248713482659842...1372856.34714.681.5.33.1.24896 C7: 2,7 # 16 pairs * PAIR E7: 5,9 COL E E3: 5,9,4,6 # reduction candidate for 5,9 E3: 5,9 => CTR * 15.238.64.2416.385638.54.12.653712482134896578475261395826.34.14.681.5.33.1.45826 E3: 4,6 # 15 pairs E6: 5,9,2,6 # reduction candidate for 5,9 E6: 5,9 => CTR * 1..238.6492416738563894571256937124871348265984259613728.65349147681.5233.1.248.6 E6: 2,6 # 15 pairs * PAIR H7: 7,9 BLK 9 H8: 7,9,2 # reduction candidate for 7,9 H8: 7,9 => SOLVED * 175238964924167385638945712569371248213489657847526139782653491496812573351794826 H8: 2 # 18 pairs H9: 7,9,2 # reduction candidate for 7,9 H9: 7,9 # 18 pairs * PAIR H7: 7,9 ROW 7 A7: 7,9,2,5 # reduction candidate for 7,9 A7: 7,9 # 16 pairs C7: 7,9,2,5 # reduction candidate for 7,9 C7: 7,9 => CTR * 1.5238.64.241..385.38.4..12569371248713482659842...137287653491496817523351924876 C7: 2,5 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-266-base-pr-000.dot * REASONING * DIS # F2: 6,9 => CTR => F2: 7 * DIS # E3: 6,9 => CTR => E3: 4,5 * DIS # F3: 6,9 => CTR => F3: 4,5,7 * DIS # A2: 7 => CTR => A2: 6,9 * DIS # A3: 7,9 => CTR => A3: 6 * DIS # F3: 7,9 => CTR => F3: 4,5,6 * DIS # A7: 5,9 => CTR => A7: 2,7 * DIS # C7: 5,9 => CTR => C7: 2,7 * DIS # A7: 5,9 => CTR => A7: 2,7 * DIS # C7: 5,9 => CTR => C7: 2,7 * DIS # F6: 2,9 => CTR => F6: 5,6 * DIS # F9: 2,9 => CTR => F9: 4,5,7 * DIS # E6: 5,9 => CTR => E6: 2,6 * DIS # F6: 5,9 => CTR => F6: 2,6 * DIS # D9: 5,9 => CTR => D9: 7 * DIS # C7: 7,9 => CTR => C7: 2,5 * PRF # H8: 7,9 => SOL * DIS # D9: 5,9 => CTR => D9: 7 * PRF # E9: 5,9 => SOL * DIS # F9: 5,9 => CTR => F9: 2,4,7 * DIS # A7: 5,9 => CTR => A7: 2,7 * DIS # C7: 5,9 => CTR => C7: 2,7 * DIS # E3: 5,9 => CTR => E3: 4,6 * DIS # E6: 5,9 => CTR => E6: 2,6 * PRF # H8: 7,9 => SOL * DIS # C7: 7,9 => CTR => C7: 2,5 * CNT 26 HDP CHAINS / 68 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,B8,C4,C6,D6,E2,E7,F5,G1,G3,H7,I5,I6) * 1..238.64.241..385.38....12.6.371248.1348.65.84....13..8.6.34.14.681.5.33.1...8.6 * PAIR E2: 6,9 BLK 2 F2: 6,9,7 # reduction candidate for 6,9 F2: 6,9 => CTR * 1..2387647241963856387..912.6.37124821348965784756213998265347147681.5.33.1...8.6 E3: 6,9,4,5 # reduction candidate for 6,9 E3: 6,9 => CTR * 1..238.64.241.7385.38..4.12.6.371248.1348.65.84...613..8.6.34.14.681.5.33.1745826 * RESTART * PAIR E2: 6,9 COL E E6: 6,9,2,5 # reduction candidate for 6,9 E6: 6,9 => CTR * 1952387646241.7385.38....12.6.371248.13482659842...13728.6.34.14.68195233.1724896 E6: 2,5 => SOLVED * 175238964924167385638945712569371248213489657847526139782653491496812573351794826 * DURATION: 0:00:05.419167 START: 11:59:51.159795 END: 11:59:56.578962 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-266-base-pr-001.dot * REASONING * DIS # F2: 6,9 => CTR => F2: 7 * DIS F2: 7 # E3: 6,9 => CTR => E3: 4,5 * DIS F2: 7 + E3: 4,5 # E6: 6,9 => CTR => E6: 2,5 * PRF F2: 7 + E3: 4,5 + E6: 2,5 => SOL * STA F2: 7 + E3: 4,5 + E6: 2,5 * CNT 4 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 266 solution: 175238964924167385638945712569371248213489657847526139782653491496812573351794826 info: 2139 FNBTHWY S8.f 4125 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 175238964924167385638945712569371248213489657847526139782653491496812573351794826 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 # F2: 6,9 => CTR => F2: 7 * INC # F2: 7 => UNS * DIS # E3: 6,9 => CTR => E3: 4,5 * INC # E3: 4,5 => UNS * DIS # F3: 6,9 => CTR => F3: 4,5,7 * INC # F3: 4,5,7 => UNS * INC # A2: 6,9 => UNS * DIS # A2: 7 => CTR => A2: 6,9 * INC # E6: 6,9 => UNS * INC # E6: 2,5 => UNS * INC # B1: 7,9 => UNS * INC # C1: 7,9 => UNS * DIS # A3: 7,9 => CTR => A3: 6 * INC # A3: 6 => UNS * INC # D3: 7,9 => UNS * DIS # F3: 7,9 => CTR => F3: 4,5,6 * INC # F3: 4,5,6 => UNS * DIS # A7: 5,9 => CTR => A7: 2,7 * INC # A7: 2,7 => UNS * INC # C1: 5,9 => UNS * DIS # C7: 5,9 => CTR => C7: 2,7 * INC # C7: 2,7 => UNS * INC # A7: 2,7 => UNS * DIS # A7: 5,9 => CTR => A7: 2,7 * INC # C7: 2,7 => UNS * DIS # C7: 5,9 => CTR => C7: 2,7 * INC # E6: 2,9 => UNS * DIS # F6: 2,9 => CTR => F6: 5,6 * INC # F6: 5,6 => UNS * INC # F8: 2,9 => UNS * DIS # F9: 2,9 => CTR => F9: 4,5,7 * INC # F9: 4,5,7 => UNS * DIS # E6: 5,9 => CTR => E6: 2,6 * INC # E6: 2,6 => UNS * DIS # F6: 5,9 => CTR => F6: 2,6 * INC # F6: 2,6 => UNS * INC # D3: 5,9 => UNS * DIS # D9: 5,9 => CTR => D9: 7 * INC # D9: 7 => UNS * INC # A7: 7,9 => UNS * DIS # C7: 7,9 => CTR => C7: 2,5 * INC # C7: 2,5 => UNS * INC # B9: 7,9 => UNS * INC # F8: 7,9 => UNS * PRF # H8: 7,9 => SOL * INC # H8: 2 => UNS * INC # B1: 7,9 => UNS * INC # B1: 5 => UNS * DIS # D9: 5,9 => CTR => D9: 7 * INC # D9: 7 => UNS * PRF # E9: 5,9 => SOL * INC # E9: 2,4 => UNS * DIS # F9: 5,9 => CTR => F9: 2,4,7 * INC # F9: 2,4,7 => UNS * DIS # A7: 5,9 => CTR => A7: 2,7 * INC # A7: 2,7 => UNS * DIS # C7: 5,9 => CTR => C7: 2,7 * INC # C7: 2,7 => UNS * DIS # E3: 5,9 => CTR => E3: 4,6 * INC # E3: 4,6 => UNS * DIS # E6: 5,9 => CTR => E6: 2,6 * INC # E6: 2,6 => UNS * PRF # H8: 7,9 => SOL * INC # H8: 2 => UNS * INC # H9: 7,9 => UNS * INC # A7: 7,9 => UNS * DIS # C7: 7,9 => CTR => C7: 2,5 * INC # C7: 2,5 => UNS * CNT 68 HDP CHAINS / 68 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # F2: 6,9 => CTR => F2: 7 * DIS F2: 7 # E3: 6,9 => CTR => E3: 4,5 * DIS F2: 7 + E3: 4,5 # E6: 6,9 => CTR => E6: 2,5 * PRF F2: 7 + E3: 4,5 + E6: 2,5 => SOL * STA F2: 7 + E3: 4,5 + E6: 2,5 * CNT 4 HDP CHAINS / 3 HYP OPENED