Analysis of xx-top500-456-base.sdk
Original Sudoku
level: deep
position: .7......14..2........5.....2.5...3......41...6.........1..7......8....2.......56. initial
Autosolve
position: .7......14..21....1..5.....2.57..31.....41...6.1.......1..7......8...12....1..56. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F7: 3,4,6,8,9 => CTR => F7: 2,5 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F7: 3,4,6,8,9 => CTR => F7: 2,5 * STA F7: 2,5 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction Position
position: .7......14..21....1..5.....2.57..31.....41...6.1.......1..7......8...12....1..56. pair_reduction
See section Pair Reduction for the HDP chains leading to this result.
Deep Constraint Pair Analysis
Time used: 0:00:00.000016
List of important HDP chains detected for A8,I8: 7..:
* DIS # A8: 7 # A7: 3,9 => CTR => A7: 5 * DIS # A8: 7 + A7: 5 => CTR => A8: 3,5,9 * STA A8: 3,5,9 * CNT 2 HDP CHAINS / 3 HYP OPENED
List of important HDP chains detected for I8,I9: 7..:
* DIS # I9: 7 # A7: 3,9 => CTR => A7: 5 * DIS # I9: 7 + A7: 5 => CTR => I9: 3,4,8,9 * STA I9: 3,4,8,9 * CNT 2 HDP CHAINS / 3 HYP OPENED
List of important HDP chains detected for C5,C9: 7..:
* DIS # C9: 7 => CTR => C9: 2,3,4,9 * STA C9: 2,3,4,9 * CNT 1 HDP CHAINS / 2 HYP OPENED
List of important HDP chains detected for A5,C5: 7..:
* DIS # A5: 7 => CTR => A5: 3,8,9 * STA A5: 3,8,9 * CNT 1 HDP CHAINS / 2 HYP OPENED
List of important HDP chains detected for B4,I4: 4..:
* DIS # I4: 4 => CTR => I4: 6,8,9 * STA I4: 6,8,9 * CNT 1 HDP CHAINS / 2 HYP OPENED
List of important HDP chains detected for C7,C9: 4..:
* DIS # C7: 4 => CTR => C7: 2,3,6,9 * STA C7: 2,3,6,9 * CNT 1 HDP CHAINS / 2 HYP OPENED
List of important HDP chains detected for B4,B6: 4..:
* DIS # B6: 4 => CTR => B6: 3,8,9 * STA B6: 3,8,9 * CNT 1 HDP CHAINS / 2 HYP OPENED
List of important HDP chains detected for B6,D6: 3..:
* DIS # B6: 3 => CTR => B6: 4,8,9 * STA B6: 4,8,9 * CNT 1 HDP CHAINS / 2 HYP OPENED
List of important HDP chains detected for D5,D6: 3..:
* DIS # D5: 3 => CTR => D5: 6,8,9 * STA D5: 6,8,9 * CNT 1 HDP CHAINS / 2 HYP OPENED
List of important HDP chains detected for A1,A5: 8..:
* PRF # A1: 8 => SOL * STA A1: 8 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
This sudoku is deep. Here is some information that may be helpful on how to proceed.
Positions
| .7......14..2........5.....2.5...3......41...6.........1..7......8....2.......56. | initial |
| .7......14..21....1..5.....2.57..31.....41...6.1.......1..7......8...12....1..56. | autosolve |
| .7......14..21....1..5.....2.57..31.....41...6.1.......1..7......8...12....1..56. | pair_reduction |
Classification
level: deep
Pairing Analysis
-------------------------------------------------- * PAIRS (2) E6: 2,5 F6: 2,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E6,F6: 2.. / E6 = 2 => 0 pairs (*) / F6 = 2 => 0 pairs (X) G5,I5: 2.. / G5 = 2 => 0 pairs (*) / I5 = 2 => 0 pairs (X) C1,G1: 2.. / C1 = 2 => 0 pairs (*) / G1 = 2 => 0 pairs (X) C7,F7: 2.. / C7 = 2 => 0 pairs (X) / F7 = 2 => 0 pairs (_) B3,B9: 2.. / B3 = 2 => 0 pairs (X) / B9 = 2 => 0 pairs (_) E6,E9: 2.. / E6 = 2 => 0 pairs (*) / E9 = 2 => 0 pairs (X) I3,I5: 2.. / I3 = 2 => 0 pairs (*) / I5 = 2 => 0 pairs (X) D5,D6: 3.. / D5 = 3 => 0 pairs (X) / D6 = 3 => 2 pairs (_) B6,D6: 3.. / B6 = 3 => 0 pairs (X) / D6 = 3 => 2 pairs (_) B4,B6: 4.. / B4 = 4 => 2 pairs (_) / B6 = 4 => 0 pairs (X) C7,C9: 4.. / C7 = 4 => 0 pairs (X) / C9 = 4 => 2 pairs (_) B4,I4: 4.. / B4 = 4 => 2 pairs (_) / I4 = 4 => 0 pairs (X) A1,B2: 5.. / A1 = 5 => 0 pairs (X) / B2 = 5 => 0 pairs (_) E6,F6: 5.. / E6 = 5 => 0 pairs (X) / F6 = 5 => 0 pairs (_) H5,I5: 5.. / H5 = 5 => 0 pairs (X) / I5 = 5 => 0 pairs (_) A1,H1: 5.. / A1 = 5 => 0 pairs (X) / H1 = 5 => 0 pairs (_) A7,F7: 5.. / A7 = 5 => 0 pairs (*) / F7 = 5 => 0 pairs (X) B2,B8: 5.. / B2 = 5 => 0 pairs (*) / B8 = 5 => 0 pairs (X) E6,E8: 5.. / E6 = 5 => 0 pairs (X) / E8 = 5 => 0 pairs (_) I2,I5: 5.. / I2 = 5 => 0 pairs (X) / I5 = 5 => 0 pairs (_) C7,B8: 6.. / C7 = 6 => 0 pairs (*) / B8 = 6 => 0 pairs (X) F2,F3: 7.. / F2 = 7 => 2 pairs (_) / F3 = 7 => 2 pairs (_) A5,C5: 7.. / A5 = 7 => 0 pairs (X) / C5 = 7 => 2 pairs (_) G6,H6: 7.. / G6 = 7 => 2 pairs (_) / H6 = 7 => 2 pairs (_) I8,I9: 7.. / I8 = 7 => 2 pairs (_) / I9 = 7 => 3 pairs (_) A8,I8: 7.. / A8 = 7 => 3 pairs (_) / I8 = 7 => 2 pairs (_) C5,C9: 7.. / C5 = 7 => 2 pairs (_) / C9 = 7 => 0 pairs (X) A1,A5: 8.. / A1 = 8 => 0 pairs (*) / A5 = 8 => 0 pairs (X) * DURATION: 0:00:46.652795 START: 18:19:25.440539 END: 18:20:12.093334 2017-05-04 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * DEEP CONSTRAINT PAIRS (PAIR REDUCTION) A8,I8: 7.. / A8 = 7 ==> 0 pairs (X) / I8 = 7 => 3 pairs (_) I8,I9: 7.. / I8 = 7 => 3 pairs (_) / I9 = 7 ==> 0 pairs (X) G6,H6: 7.. / G6 = 7 ==> 3 pairs (_) / H6 = 7 ==> 3 pairs (_) F2,F3: 7.. / F2 = 7 ==> 3 pairs (_) / F3 = 7 ==> 3 pairs (_) C5,C9: 7.. / C5 = 7 ==> 3 pairs (_) / C9 = 7 => 0 pairs (X) A5,C5: 7.. / A5 = 7 => 0 pairs (X) / C5 = 7 ==> 3 pairs (_) B4,I4: 4.. / B4 = 4 ==> 3 pairs (_) / I4 = 4 => 0 pairs (X) C7,C9: 4.. / C7 = 4 => 0 pairs (X) / C9 = 4 ==> 3 pairs (_) B4,B6: 4.. / B4 = 4 ==> 3 pairs (_) / B6 = 4 => 0 pairs (X) B6,D6: 3.. / B6 = 3 => 0 pairs (X) / D6 = 3 ==> 3 pairs (_) D5,D6: 3.. / D5 = 3 => 0 pairs (X) / D6 = 3 ==> 3 pairs (_) A1,A5: 8.. / A1 = 8 => 0 pairs (*) / A5 = 8 => 0 pairs (X) * DURATION: 0:01:24.133138 START: 18:20:20.141827 END: 18:21:44.274965 2017-05-04 * REASONING A8,I8: 7.. * DIS # A8: 7 # A7: 3,9 => CTR => A7: 5 * DIS # A8: 7 + A7: 5 => CTR => A8: 3,5,9 * STA A8: 3,5,9 * CNT 2 HDP CHAINS / 3 HYP OPENED * REASONING I8,I9: 7.. * DIS # I9: 7 # A7: 3,9 => CTR => A7: 5 * DIS # I9: 7 + A7: 5 => CTR => I9: 3,4,8,9 * STA I9: 3,4,8,9 * CNT 2 HDP CHAINS / 3 HYP OPENED * REASONING C5,C9: 7.. * DIS # C9: 7 => CTR => C9: 2,3,4,9 * STA C9: 2,3,4,9 * CNT 1 HDP CHAINS / 2 HYP OPENED * REASONING A5,C5: 7.. * DIS # A5: 7 => CTR => A5: 3,8,9 * STA A5: 3,8,9 * CNT 1 HDP CHAINS / 2 HYP OPENED * REASONING B4,I4: 4.. * DIS # I4: 4 => CTR => I4: 6,8,9 * STA I4: 6,8,9 * CNT 1 HDP CHAINS / 2 HYP OPENED * REASONING C7,C9: 4.. * DIS # C7: 4 => CTR => C7: 2,3,6,9 * STA C7: 2,3,6,9 * CNT 1 HDP CHAINS / 2 HYP OPENED * REASONING B4,B6: 4.. * DIS # B6: 4 => CTR => B6: 3,8,9 * STA B6: 3,8,9 * CNT 1 HDP CHAINS / 2 HYP OPENED * REASONING B6,D6: 3.. * DIS # B6: 3 => CTR => B6: 4,8,9 * STA B6: 4,8,9 * CNT 1 HDP CHAINS / 2 HYP OPENED * REASONING D5,D6: 3.. * DIS # D5: 3 => CTR => D5: 6,8,9 * STA D5: 6,8,9 * CNT 1 HDP CHAINS / 2 HYP OPENED * REASONING A1,A5: 8.. * PRF # A1: 8 => SOL * STA A1: 8 * CNT 1 HDP CHAINS / 1 HYP OPENED * DCP COUNT: (12) * SOLUTION FOUND
Header Info
Top 500 Minimum 17 456 solution: 872963451453217689169584732245798316387641295691325874516872943938456127724139568 info: 95499 FNBHYK S8.f 22009 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Appendix: Full HDP Chains
A1. Pair Reduction Analysis
Full list of HDP chains traversed:
* INC # F7: 2,5 => UNS * DIS # F7: 3,4,6,8,9 => CTR => F7: 2,5 * CNT 2 HDP CHAINS / 2 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F7: 2,5 => UNS * DIS # F7: 3,4,6,8,9 => CTR => F7: 2,5 * STA F7: 2,5 * CNT 2 HDP CHAINS / 2 HYP OPENED
A3. Deep Constraint Pair Analysis
Full list of HDP chains traversed for A8,I8: 7..:
* DIS # A8: 7 # A7: 3,9 => CTR => A7: 5 * DIS # A8: 7 + A7: 5 => CTR => A8: 3,5,9 * INC A8: 3,5,9 # I8: 7 => UNS * STA A8: 3,5,9 * CNT 3 HDP CHAINS / 3 HYP OPENED
Full list of HDP chains traversed for I8,I9: 7..:
* DIS # I9: 7 # A7: 3,9 => CTR => A7: 5 * DIS # I9: 7 + A7: 5 => CTR => I9: 3,4,8,9 * INC I9: 3,4,8,9 # I8: 7 => UNS * STA I9: 3,4,8,9 * CNT 3 HDP CHAINS / 3 HYP OPENED
Full list of HDP chains traversed for G6,H6: 7..:
* INC # G6: 7 => UNS * INC # H6: 7 => UNS * CNT 2 HDP CHAINS / 2 HYP OPENED
Full list of HDP chains traversed for F2,F3: 7..:
* INC # F2: 7 => UNS * INC # F3: 7 => UNS * CNT 2 HDP CHAINS / 2 HYP OPENED
Full list of HDP chains traversed for C5,C9: 7..:
* INC # C5: 7 => UNS * DIS # C9: 7 => CTR => C9: 2,3,4,9 * STA C9: 2,3,4,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
Full list of HDP chains traversed for A5,C5: 7..:
* INC # C5: 7 => UNS * DIS # A5: 7 => CTR => A5: 3,8,9 * STA A5: 3,8,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
Full list of HDP chains traversed for B4,I4: 4..:
* INC # B4: 4 => UNS * DIS # I4: 4 => CTR => I4: 6,8,9 * STA I4: 6,8,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
Full list of HDP chains traversed for C7,C9: 4..:
* INC # C9: 4 => UNS * DIS # C7: 4 => CTR => C7: 2,3,6,9 * STA C7: 2,3,6,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
Full list of HDP chains traversed for B4,B6: 4..:
* INC # B4: 4 => UNS * DIS # B6: 4 => CTR => B6: 3,8,9 * STA B6: 3,8,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
Full list of HDP chains traversed for B6,D6: 3..:
* INC # D6: 3 => UNS * DIS # B6: 3 => CTR => B6: 4,8,9 * STA B6: 4,8,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
Full list of HDP chains traversed for D5,D6: 3..:
* INC # D6: 3 => UNS * DIS # D5: 3 => CTR => D5: 6,8,9 * STA D5: 6,8,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
Full list of HDP chains traversed for A1,A5: 8..:
* PRF # A1: 8 => SOL * STA A1: 8 * CNT 1 HDP CHAINS / 1 HYP OPENED