Analysis of xx-top500-144-base.sdk
Contents
Original Sudoku
level: medium
position: .....28..4..5.......1.........71..4.32...............51.....2...8..4.......6..3.. initial
Autosolve
position: 63.4.28514.2581..38513.642.5.8713.4232.95418..14268.351..83.2.428314.5...4.62.318 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C7: 7,9 => CTR => C7: 5,6 * DIS # C9: 7,9 => CTR => C9: 5 * PRF # H2: 7,9 => SOL * DIS # H2: 6 => CTR => H2: 7,9 * PRF # B7: 7,9 => SOL * DIS # B7: 6 => CTR => B7: 7,9 * DIS # H2: 6,7 => CTR => H2: 9 * PRF # H2: 9 => SOL * PRF # H2: 7,9 => SOL * DIS # H2: 6 => CTR => H2: 7,9 * PRF # I8: 7,9 => SOL * DIS # I8: 6 => CTR => I8: 7,9 * PRF # B7: 6,9 => SOL * DIS # B7: 7 => CTR => B7: 6,9 * PRF # C7: 6,7 => SOL * DIS # C7: 5,9 => CTR => C7: 6,7 * DIS # I8: 6,7 => CTR => I8: 9 * PRF # I8: 9 => SOL * PRF # B7: 7,9 => SOL * DIS # B7: 6 => CTR => B7: 7,9 * DIS # C7: 7,9 => CTR => C7: 5,6 * DIS # C9: 7,9 => CTR => C9: 5 * DIS # F9: 5 => CTR => F9: 7,9 * DIS # F7: 7,9 => CTR => F7: 5 * DIS # H8: 7,9 => CTR => H8: 6 * PRF # H8: 6 => SOL * PRF # I8: 7,9 => SOL * DIS # I8: 6 => CTR => I8: 7,9 * DIS # H8: 7,9 => CTR => H8: 6 * PRF # H8: 6 => SOL * PRF # I8: 7,9 => SOL * DIS # I8: 6 => CTR => I8: 7,9 * PRF # B7: 7,9 => SOL * DIS # B7: 6 => CTR => B7: 7,9 * DIS # C7: 7,9 => CTR => C7: 5,6 * DIS # F7: 7,9 => CTR => F7: 5 * PRF # H2: 7,9 => SOL * DIS # H2: 6 => CTR => H2: 7,9 * CNT 38 HDP CHAINS / 47 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C7: 7,9 => CTR => C7: 5,6 * DIS C7: 5,6 # C9: 7,9 => CTR => C9: 5 * PRF C7: 5,6 + C9: 5 => SOL * STA C7: 5,6 + C9: 5 * CNT 3 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....28..4..5.......1.........71..4.32...............51.....2...8..4.......6..3.. | initial |
| 63.4.28514.2581..38513.642.5.8713.4232.95418..14268.351..83.2.428314.5...4.62.318 | autosolve |
| 639472851472581693851396427568713942327954186914268735196835274283147569745629318 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) C1: 7,9 B2: 7,9 E1: 7,9 E3: 7,9 G2: 6,7 I3: 7,9 B4: 6,9 C5: 6,7 A6: 7,9 G4: 6,9 I5: 6,7 G6: 7,9 A9: 7,9 F8: 7,9 H7: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C7,C9: 5.. / C7 = 5 => 0 pairs (X) / C9 = 5 => 16 pairs (_) F7,F9: 5.. / F7 = 5 => 16 pairs (_) / F9 = 5 => 0 pairs (X) C7,F7: 5.. / C7 = 5 => 0 pairs (X) / F7 = 5 => 16 pairs (_) C9,F9: 5.. / C9 = 5 => 16 pairs (_) / F9 = 5 => 0 pairs (X) G2,H2: 6.. / G2 = 6 => 0 pairs (*) / H2 = 6 => 0 pairs (X) B4,C5: 6.. / B4 = 6 => 0 pairs (*) / C5 = 6 => 0 pairs (X) G4,I5: 6.. / G4 = 6 => 0 pairs (X) / I5 = 6 => 0 pairs (_) B7,C7: 6.. / B7 = 6 => 0 pairs (X) / C7 = 6 => 0 pairs (_) H8,I8: 6.. / H8 = 6 => 0 pairs (*) / I8 = 6 => 0 pairs (X) B4,G4: 6.. / B4 = 6 => 0 pairs (*) / G4 = 6 => 0 pairs (X) C5,I5: 6.. / C5 = 6 => 0 pairs (X) / I5 = 6 => 0 pairs (_) B4,B7: 6.. / B4 = 6 => 0 pairs (*) / B7 = 6 => 0 pairs (X) C5,C7: 6.. / C5 = 6 => 0 pairs (X) / C7 = 6 => 0 pairs (_) G2,G4: 6.. / G2 = 6 => 0 pairs (*) / G4 = 6 => 0 pairs (X) H2,H8: 6.. / H2 = 6 => 0 pairs (X) / H8 = 6 => 0 pairs (_) I5,I8: 6.. / I5 = 6 => 0 pairs (*) / I8 = 6 => 0 pairs (X) C1,B2: 7.. / C1 = 7 => 0 pairs (X) / B2 = 7 => 0 pairs (_) E1,E3: 7.. / E1 = 7 => 0 pairs (*) / E3 = 7 => 0 pairs (X) C5,A6: 7.. / C5 = 7 => 0 pairs (*) / A6 = 7 => 0 pairs (X) I5,G6: 7.. / I5 = 7 => 0 pairs (X) / G6 = 7 => 0 pairs (_) C1,E1: 7.. / C1 = 7 => 0 pairs (X) / E1 = 7 => 0 pairs (_) E3,I3: 7.. / E3 = 7 => 0 pairs (X) / I3 = 7 => 0 pairs (_) C5,I5: 7.. / C5 = 7 => 0 pairs (*) / I5 = 7 => 0 pairs (X) A6,G6: 7.. / A6 = 7 => 0 pairs (X) / G6 = 7 => 0 pairs (_) A6,A9: 7.. / A6 = 7 => 0 pairs (X) / A9 = 7 => 0 pairs (_) B2,B7: 7.. / B2 = 7 => 0 pairs (*) / B7 = 7 => 0 pairs (X) G2,G6: 7.. / G2 = 7 => 0 pairs (X) / G6 = 7 => 0 pairs (_) C1,B2: 9.. / C1 = 9 => 0 pairs (*) / B2 = 9 => 0 pairs (X) E1,E3: 9.. / E1 = 9 => 0 pairs (X) / E3 = 9 => 0 pairs (_) H2,I3: 9.. / H2 = 9 => 0 pairs (*) / I3 = 9 => 0 pairs (X) B4,A6: 9.. / B4 = 9 => 0 pairs (X) / A6 = 9 => 0 pairs (_) G4,G6: 9.. / G4 = 9 => 0 pairs (*) / G6 = 9 => 0 pairs (X) C1,E1: 9.. / C1 = 9 => 0 pairs (*) / E1 = 9 => 0 pairs (X) B2,H2: 9.. / B2 = 9 => 0 pairs (X) / H2 = 9 => 0 pairs (_) E3,I3: 9.. / E3 = 9 => 0 pairs (*) / I3 = 9 => 0 pairs (X) B4,G4: 9.. / B4 = 9 => 0 pairs (X) / G4 = 9 => 0 pairs (_) A6,G6: 9.. / A6 = 9 => 0 pairs (*) / G6 = 9 => 0 pairs (X) A6,A9: 9.. / A6 = 9 => 0 pairs (*) / A9 = 9 => 0 pairs (X) I3,I8: 9.. / I3 = 9 => 0 pairs (X) / I8 = 9 => 0 pairs (_) * DURATION: 0:01:04.121364 START: 07:39:17.492098 END: 07:40:21.613462 2017-05-04 * CP COUNT: (39) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A9,B2,B4,C1,C5,E1,E3,F8,G2,G4,G6,H7,I3,I5) * 63.4.28514.2581..38513.642.5.8713.4232.95418..14268.351..83.2.428314.5...4.62.318 * PAIR C1: 7,9 COL C C7: 7,9,5,6 # reduction candidate for 7,9 C7: 7,9 => CTR * 6394728514.2581..38513.642.5.8713.4232695418771426893516.8352.428314.5.6945627318 C7: 5,6 # 16 pairs C9: 7,9,5 # reduction candidate for 7,9 C9: 7,9 => CTR * 6394728514.2581..38513.642.5.8713.4232695418771426893516583.2.428314.5.6947625318 C9: 5 # 16 pairs * PAIR B2: 7,9 ROW 2 H2: 7,9,6 # reduction candidate for 7,9 H2: 7,9 => SOLVED * 639472851472581693851396427568713942327954186914268735196835274283147569745629318 H2: 6 => CTR * 63.4.2851492581763851376429568713.4232.95418..14268.351..83.2.428314.5...4.62.318 * PAIR B2: 7,9 COL B B7: 7,9,6 # reduction candidate for 7,9 B7: 7,9 => SOLVED * 639472851472581693851396427568713942327954186914268735196835274283147569745629318 B7: 6 => CTR * 63.4.28514725816938513964275.8713.4232.95418..14268.351..83.2.428314.5...4.62.318 * PAIR G2: 6,7 BLK 3 H2: 6,7,9 # reduction candidate for 6,7 H2: 6,7 => CTR * 63.4.2851492581..38513.642956871394232795418..14268.351..83.2.428314.5...4.62.318 H2: 9 => SOLVED * 639472851472581693851396427568713942327954186914268735196835274283147569745629318 * PAIR I3: 7,9 BLK 3 H2: 7,9,6 # reduction candidate for 7,9 H2: 7,9 => SOLVED * 639472851472581693851396427568713942327954186914268735196835274283147569745629318 H2: 6 => CTR * 63.4.2851492581763851376429568713.4232.95418..14268.351..83.2.428314.5...4.62.318 * PAIR I3: 7,9 COL I I8: 7,9,6 # reduction candidate for 7,9 I8: 7,9 => SOLVED * 639472851472581693851396427568713942327954186914268735196835274283147569745629318 I8: 6 => CTR * 6394728514.2581..38513.64295.8713.4232.9541877142689351..83.2.428314.5.694.62.318 * PAIR B4: 6,9 COL B B7: 6,9,7 # reduction candidate for 6,9 B7: 6,9 => SOLVED * 639472851472581693851396427568713942327954186914268735196835274283147569745629318 B7: 7 => CTR * 63.4.28514.2581..38513.642.56871394232795418691426873517.83.2.428314.5...4.62.318 * PAIR C5: 6,7 COL C C7: 6,7,5,9 # reduction candidate for 6,7 C7: 6,7 => SOLVED * 639472851472581693851396427568713942327954186914268735196835274283147569745629318 C7: 5,9 => CTR * 6394728514.2581..38513.642.5.8713.4232695418771426893516.83.2.428314.5.6947625318 * PAIR I5: 6,7 COL I I8: 6,7,9 # reduction candidate for 6,7 I8: 6,7 => CTR * 63.492851492581..385137642956871394232795418..14268.351..83.2.428314.5...4.62.318 I8: 9 => SOLVED * 639472851472581693851396427568713942327954186914268735196835274283147569745629318 * PAIR A9: 7,9 BLK 7 B7: 7,9,6 # reduction candidate for 7,9 B7: 7,9 => SOLVED * 639472851472581693851396427568713942327954186914268735196835274283147569745629318 B7: 6 => CTR * 63.4.28514725816938513964275.8713.4232.95418..14268.351..83.2.428314.5...4.62.318 C7: 7,9,5,6 # reduction candidate for 7,9 C7: 7,9 => CTR * 6394728514.2581..38513.642.5.8713.4232695418771426893516.8352.428314.5.6945627318 C7: 5,6 # 16 pairs C9: 7,9,5 # reduction candidate for 7,9 C9: 7,9 => CTR * 6394728514.2581..38513.642.5.8713.4232695418771426893516583.2.428314.5.6947625318 C9: 5 # 16 pairs * PAIR A9: 7,9 ROW 9 F9: 7,9,5 # reduction candidate for 7,9 F9: 5 => CTR * 6394728514.2581..38513.642.5.8713.4232695418771426893516583.2.428314.5.6947625318 F9: 7,9 # 16 pairs * PAIR F8: 7,9 BLK 8 F7: 7,9,5 # reduction candidate for 7,9 F7: 7,9 => CTR * 6394728514.2581..38513.642.5.8713.4232695418771426893516583.2.428314.5.6947625318 F7: 5 # 16 pairs F9: 7,9,5 # reduction candidate for 7,9 F9: 7,9 # 16 pairs * PAIR F8: 7,9 ROW 8 H8: 7,9,6 # reduction candidate for 7,9 H8: 7,9 => CTR * 63.4.28514.2581.638513.64295.871364232695418771426893516.83.2.428314.5.694.62.318 H8: 6 => SOLVED * 639472851472581693851396427568713942327954186914268735196835274283147569745629318 I8: 7,9,6 # reduction candidate for 7,9 I8: 7,9 => SOLVED * 639472851472581693851396427568713942327954186914268735196835274283147569745629318 I8: 6 => CTR * 6394728514.2581..38513.64295.8713.4232.9541877142689351..83.2.428314.5.694.62.318 * PAIR H7: 7,9 BLK 9 H8: 7,9,6 # reduction candidate for 7,9 H8: 7,9 => CTR * 63.4.28514.2581.638513.64295.871364232695418771426893516.83.2.428314.5.694.62.318 H8: 6 => SOLVED * 639472851472581693851396427568713942327954186914268735196835274283147569745629318 I8: 7,9,6 # reduction candidate for 7,9 I8: 7,9 => SOLVED * 639472851472581693851396427568713942327954186914268735196835274283147569745629318 I8: 6 => CTR * 6394728514.2581..38513.64295.8713.4232.9541877142689351..83.2.428314.5.694.62.318 * PAIR H7: 7,9 ROW 7 B7: 7,9,6 # reduction candidate for 7,9 B7: 7,9 => SOLVED * 639472851472581693851396427568713942327954186914268735196835274283147569745629318 B7: 6 => CTR * 63.4.28514725816938513964275.8713.4232.95418..14268.351..83.2.428314.5...4.62.318 C7: 7,9,5,6 # reduction candidate for 7,9 C7: 7,9 => CTR * 6394728514.2581..38513.642.5.8713.4232695418771426893516.8352.428314.5.6945627318 C7: 5,6 # 16 pairs F7: 7,9,5 # reduction candidate for 7,9 F7: 7,9 => CTR * 6394728514.2581..38513.642.5.8713.4232695418771426893516583.2.428314.5.6947625318 F7: 5 # 16 pairs * PAIR H7: 7,9 COL H H2: 7,9,6 # reduction candidate for 7,9 H2: 7,9 => SOLVED * 639472851472581693851396427568713942327954186914268735196835274283147569745629318 H2: 6 => CTR * 63.4.2851492581763851376429568713.4232.95418..14268.351..83.2.428314.5...4.62.318 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-144-base-pr-000.dot * REASONING * DIS # C7: 7,9 => CTR => C7: 5,6 * DIS # C9: 7,9 => CTR => C9: 5 * PRF # H2: 7,9 => SOL * DIS # H2: 6 => CTR => H2: 7,9 * PRF # B7: 7,9 => SOL * DIS # B7: 6 => CTR => B7: 7,9 * DIS # H2: 6,7 => CTR => H2: 9 * PRF # H2: 9 => SOL * PRF # H2: 7,9 => SOL * DIS # H2: 6 => CTR => H2: 7,9 * PRF # I8: 7,9 => SOL * DIS # I8: 6 => CTR => I8: 7,9 * PRF # B7: 6,9 => SOL * DIS # B7: 7 => CTR => B7: 6,9 * PRF # C7: 6,7 => SOL * DIS # C7: 5,9 => CTR => C7: 6,7 * DIS # I8: 6,7 => CTR => I8: 9 * PRF # I8: 9 => SOL * PRF # B7: 7,9 => SOL * DIS # B7: 6 => CTR => B7: 7,9 * DIS # C7: 7,9 => CTR => C7: 5,6 * DIS # C9: 7,9 => CTR => C9: 5 * DIS # F9: 5 => CTR => F9: 7,9 * DIS # F7: 7,9 => CTR => F7: 5 * DIS # H8: 7,9 => CTR => H8: 6 * PRF # H8: 6 => SOL * PRF # I8: 7,9 => SOL * DIS # I8: 6 => CTR => I8: 7,9 * DIS # H8: 7,9 => CTR => H8: 6 * PRF # H8: 6 => SOL * PRF # I8: 7,9 => SOL * DIS # I8: 6 => CTR => I8: 7,9 * PRF # B7: 7,9 => SOL * DIS # B7: 6 => CTR => B7: 7,9 * DIS # C7: 7,9 => CTR => C7: 5,6 * DIS # F7: 7,9 => CTR => F7: 5 * PRF # H2: 7,9 => SOL * DIS # H2: 6 => CTR => H2: 7,9 * CNT 38 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A9,B2,B4,C1,C5,E1,E3,F8,G2,G4,G6,H7,I3,I5) * 63.4.28514.2581..38513.642.5.8713.4232.95418..14268.351..83.2.428314.5...4.62.318 * PAIR C1: 7,9 COL C C7: 7,9,5,6 # reduction candidate for 7,9 C7: 7,9 => CTR * 6394728514.2581..38513.642.5.8713.4232695418771426893516.8352.428314.5.6945627318 C9: 7,9,5 # reduction candidate for 7,9 C9: 7,9 => CTR * 6394728514.2581..38513.642.5.8713.4232695418771426893516583.2.428314.5.6947625318 C9: 5 => SOLVED * 639472851472581693851396427568713942327954186914268735196835274283147569745629318 * DURATION: 0:00:02.834715 START: 07:41:11.396276 END: 07:41:14.230991 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-144-base-pr-001.dot * REASONING * DIS # C7: 7,9 => CTR => C7: 5,6 * DIS C7: 5,6 # C9: 7,9 => CTR => C9: 5 * PRF C7: 5,6 + C9: 5 => SOL * STA C7: 5,6 + C9: 5 * CNT 3 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 144 solution: 639472851472581693851396427568713942327954186914268735196835274283147569745629318 info: 1814 FNBWY S8.f 39723 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 639472851472581693851396427568713942327954186914268735196835274283147569745629318 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 # C7: 7,9 => CTR => C7: 5,6 * INC # C7: 5,6 => UNS * DIS # C9: 7,9 => CTR => C9: 5 * INC # C9: 5 => UNS * PRF # H2: 7,9 => SOL * DIS # H2: 6 => CTR => H2: 7,9 * PRF # B7: 7,9 => SOL * DIS # B7: 6 => CTR => B7: 7,9 * DIS # H2: 6,7 => CTR => H2: 9 * PRF # H2: 9 => SOL * PRF # H2: 7,9 => SOL * DIS # H2: 6 => CTR => H2: 7,9 * PRF # I8: 7,9 => SOL * DIS # I8: 6 => CTR => I8: 7,9 * PRF # B7: 6,9 => SOL * DIS # B7: 7 => CTR => B7: 6,9 * PRF # C7: 6,7 => SOL * DIS # C7: 5,9 => CTR => C7: 6,7 * DIS # I8: 6,7 => CTR => I8: 9 * PRF # I8: 9 => SOL * PRF # B7: 7,9 => SOL * DIS # B7: 6 => CTR => B7: 7,9 * DIS # C7: 7,9 => CTR => C7: 5,6 * INC # C7: 5,6 => UNS * DIS # C9: 7,9 => CTR => C9: 5 * INC # C9: 5 => UNS * INC # F9: 7,9 => UNS * DIS # F9: 5 => CTR => F9: 7,9 * DIS # F7: 7,9 => CTR => F7: 5 * INC # F7: 5 => UNS * INC # F9: 7,9 => UNS * DIS # H8: 7,9 => CTR => H8: 6 * PRF # H8: 6 => SOL * PRF # I8: 7,9 => SOL * DIS # I8: 6 => CTR => I8: 7,9 * DIS # H8: 7,9 => CTR => H8: 6 * PRF # H8: 6 => SOL * PRF # I8: 7,9 => SOL * DIS # I8: 6 => CTR => I8: 7,9 * PRF # B7: 7,9 => SOL * DIS # B7: 6 => CTR => B7: 7,9 * DIS # C7: 7,9 => CTR => C7: 5,6 * INC # C7: 5,6 => UNS * DIS # F7: 7,9 => CTR => F7: 5 * INC # F7: 5 => UNS * PRF # H2: 7,9 => SOL * DIS # H2: 6 => CTR => H2: 7,9 * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C7: 7,9 => CTR => C7: 5,6 * DIS C7: 5,6 # C9: 7,9 => CTR => C9: 5 * PRF C7: 5,6 + C9: 5 => SOL * STA C7: 5,6 + C9: 5 * CNT 3 HDP CHAINS / 2 HYP OPENED