Analysis of xx-top500-031-base.sdk
Contents
Original Sudoku
level: medium
position: 3.......4.7.6........1.......8....1......23......3.....5....16.2...74.........8.. initial
Autosolve
position: 3812.76.4.7264...164.1..72.4387..219.6.4.23...2.93.4.6854329167216874...7935..842 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A5: 5,9 => CTR => A5: 1 * PRF # A5: 1 => SOL * PRF # E3: 5,9 => SOL * DIS # E3: 8 => CTR => E3: 5,9 * DIS # C5: 7 => CTR => C5: 5,9 * PRF # E3: 5,9 => SOL * DIS # E3: 8 => CTR => E3: 5,9 * PRF # F3: 3,8 => SOL * DIS # F3: 5 => CTR => F3: 3,8 * PRF # H8: 5,9 => SOL * DIS # H8: 3 => CTR => H8: 5,9 * PRF # F3: 3,8 => SOL * DIS # F3: 5 => CTR => F3: 3,8 * PRF # A5: 1,5 => SOL * DIS # A5: 9 => CTR => A5: 1,5 * DIS # C5: 5,7 => CTR => C5: 9 * PRF # C5: 9 => SOL * DIS # H6: 5,7 => CTR => H6: 8 * PRF # H6: 8 => SOL * DIS # H5: 5,8 => CTR => H5: 7 * PRF # H8: 5,9 => SOL * DIS # H8: 3 => CTR => H8: 5,9 * PRF # H8: 3,5 => SOL * DIS # H8: 9 => CTR => H8: 3,5 * CNT 24 HDP CHAINS / 27 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A5: 5,9 => CTR => A5: 1 * PRF A5: 1 => SOL * STA A5: 1 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 3.......4.7.6........1.......8....1......23......3.....5....16.2...74.........8.. | initial |
| 3812.76.4.7264...164.1..72.4387..219.6.4.23...2.93.4.6854329167216874...7935..842 | autosolve |
| 381257694972648531645193728438765219169482375527931486854329167216874953793516842 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) A2: 5,9 C3: 5,9 E1: 5,9 F2: 3,8 H1: 5,9 G2: 5,9 H2: 3,8 I3: 3,8 A6: 1,5 C6: 5,7 E4: 5,6 F4: 5,6 E5: 1,8 F6: 1,8 I5: 5,8 E9: 1,6 F9: 1,6 G8: 5,9 I8: 3,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A5,A6: 1.. / A5 = 1 => 0 pairs (*) / A6 = 1 => 0 pairs (X) E5,F6: 1.. / E5 = 1 => 0 pairs (X) / F6 = 1 => 0 pairs (_) E9,F9: 1.. / E9 = 1 => 0 pairs (*) / F9 = 1 => 0 pairs (X) A5,E5: 1.. / A5 = 1 => 0 pairs (*) / E5 = 1 => 0 pairs (X) A6,F6: 1.. / A6 = 1 => 0 pairs (X) / F6 = 1 => 0 pairs (_) E5,E9: 1.. / E5 = 1 => 0 pairs (X) / E9 = 1 => 0 pairs (_) F6,F9: 1.. / F6 = 1 => 0 pairs (*) / F9 = 1 => 0 pairs (X) F2,F3: 3.. / F2 = 3 => 0 pairs (X) / F3 = 3 => 0 pairs (_) H2,I3: 3.. / H2 = 3 => 0 pairs (*) / I3 = 3 => 0 pairs (X) H8,I8: 3.. / H8 = 3 => 0 pairs (X) / I8 = 3 => 0 pairs (_) F2,H2: 3.. / F2 = 3 => 0 pairs (X) / H2 = 3 => 0 pairs (_) F3,I3: 3.. / F3 = 3 => 0 pairs (*) / I3 = 3 => 0 pairs (X) H2,H8: 3.. / H2 = 3 => 0 pairs (*) / H8 = 3 => 0 pairs (X) I3,I8: 3.. / I3 = 3 => 0 pairs (X) / I8 = 3 => 0 pairs (_) A2,C3: 5.. / A2 = 5 => 0 pairs (X) / C3 = 5 => 0 pairs (_) H1,G2: 5.. / H1 = 5 => 0 pairs (X) / G2 = 5 => 0 pairs (_) E4,F4: 5.. / E4 = 5 => 0 pairs (X) / F4 = 5 => 0 pairs (_) E1,H1: 5.. / E1 = 5 => 0 pairs (*) / H1 = 5 => 0 pairs (X) A2,G2: 5.. / A2 = 5 => 0 pairs (X) / G2 = 5 => 0 pairs (_) F3,F4: 5.. / F3 = 5 => 0 pairs (X) / F4 = 5 => 0 pairs (_) G2,G8: 5.. / G2 = 5 => 0 pairs (*) / G8 = 5 => 0 pairs (X) I5,I8: 5.. / I5 = 5 => 0 pairs (*) / I8 = 5 => 0 pairs (X) E4,F4: 6.. / E4 = 6 => 0 pairs (*) / F4 = 6 => 0 pairs (X) E9,F9: 6.. / E9 = 6 => 0 pairs (X) / F9 = 6 => 0 pairs (_) E4,E9: 6.. / E4 = 6 => 0 pairs (*) / E9 = 6 => 0 pairs (X) F4,F9: 6.. / F4 = 6 => 0 pairs (X) / F9 = 6 => 0 pairs (_) C5,C6: 7.. / C5 = 7 => 0 pairs (X) / C6 = 7 => 20 pairs (_) H5,H6: 7.. / H5 = 7 => 20 pairs (_) / H6 = 7 => 0 pairs (X) C5,H5: 7.. / C5 = 7 => 0 pairs (X) / H5 = 7 => 20 pairs (_) C6,H6: 7.. / C6 = 7 => 20 pairs (_) / H6 = 7 => 0 pairs (X) H2,I3: 8.. / H2 = 8 => 0 pairs (X) / I3 = 8 => 0 pairs (_) E5,F6: 8.. / E5 = 8 => 0 pairs (*) / F6 = 8 => 0 pairs (X) F2,H2: 8.. / F2 = 8 => 0 pairs (*) / H2 = 8 => 0 pairs (X) F6,H6: 8.. / F6 = 8 => 0 pairs (X) / H6 = 8 => 0 pairs (_) E3,E5: 8.. / E3 = 8 => 0 pairs (X) / E5 = 8 => 0 pairs (_) I3,I5: 8.. / I3 = 8 => 0 pairs (*) / I5 = 8 => 0 pairs (X) A2,C3: 9.. / A2 = 9 => 0 pairs (*) / C3 = 9 => 0 pairs (X) E1,E3: 9.. / E1 = 9 => 0 pairs (X) / E3 = 9 => 0 pairs (_) H1,G2: 9.. / H1 = 9 => 0 pairs (*) / G2 = 9 => 0 pairs (X) A5,C5: 9.. / A5 = 9 => 0 pairs (X) / C5 = 9 => 0 pairs (_) G8,H8: 9.. / G8 = 9 => 0 pairs (*) / H8 = 9 => 0 pairs (X) E1,H1: 9.. / E1 = 9 => 0 pairs (X) / H1 = 9 => 0 pairs (_) A2,G2: 9.. / A2 = 9 => 0 pairs (*) / G2 = 9 => 0 pairs (X) C3,E3: 9.. / C3 = 9 => 0 pairs (X) / E3 = 9 => 0 pairs (_) A2,A5: 9.. / A2 = 9 => 0 pairs (*) / A5 = 9 => 0 pairs (X) C3,C5: 9.. / C3 = 9 => 0 pairs (X) / C5 = 9 => 0 pairs (_) G2,G8: 9.. / G2 = 9 => 0 pairs (X) / G8 = 9 => 0 pairs (_) H1,H8: 9.. / H1 = 9 => 0 pairs (*) / H8 = 9 => 0 pairs (X) * DURATION: 0:02:00.293388 START: 03:41:42.092530 END: 03:43:42.385918 2017-05-04 * CP COUNT: (48) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,C3,C6,E1,E4,E5,E9,F2,F4,F6,F9,G2,G8,H1,H2,I3,I5,I8) * 3812.76.4.7264...164.1..72.4387..219.6.4.23...2.93.4.6854329167216874...7935..842 * PAIR A2: 5,9 COL A A5: 5,9,1 # reduction candidate for 5,9 A5: 5,9 => CTR * 3812.76.4.72643.8164.185723438756219.6.4123.812.9384.6854329167216874.35793561842 A5: 1 => SOLVED * 381257694972648531645193728438765219169482375527931486854329167216874953793516842 * PAIR C3: 5,9 ROW 3 E3: 5,9,8 # reduction candidate for 5,9 E3: 5,9 => SOLVED * 381257694972648531645193728438765219169482375527931486854329167216874953793516842 E3: 8 => CTR * 38129765457264.9.16491857234387..219.6.4.23...2.93.4.6854329167216874...7935..842 * PAIR C3: 5,9 COL C C5: 5,9,7 # reduction candidate for 5,9 C5: 7 => CTR * 3812976545726439816491..72.4387..2199674123..125938476854329167216874...793561842 C5: 5,9 # 20 pairs * PAIR E1: 5,9 BLK 2 E3: 5,9,8 # reduction candidate for 5,9 E3: 5,9 => SOLVED * 381257694972648531645193728438765219169482375527931486854329167216874953793516842 E3: 8 => CTR * 38129765457264.9.16491857234387..219.6.4.23...2.93.4.6854329167216874...7935..842 * PAIR F2: 3,8 BLK 2 F3: 3,8,5 # reduction candidate for 3,8 F3: 3,8 => SOLVED * 381257694972648531645193728438765219169482375527931486854329167216874953793516842 F3: 5 => CTR * 3812.76.4.72643.8164.185723438756219.6.4123.812.9384.6854329167216874.35793561842 * PAIR H1: 5,9 COL H H8: 5,9,3 # reduction candidate for 5,9 H8: 5,9 => SOLVED * 381257694972648531645193728438765219169482375527931486854329167216874953793516842 H8: 3 => CTR * 3812.769497264.5.164519.72.4387.5219.69482375.2.93.4.6854329167216874...7935..842 * PAIR I3: 3,8 ROW 3 F3: 3,8,5 # reduction candidate for 3,8 F3: 3,8 => SOLVED * 381257694972648531645193728438765219169482375527931486854329167216874953793516842 F3: 5 => CTR * 3812.76.4.72643.8164.185723438756219.6.4123.812.9384.6854329167216874.35793561842 * PAIR A6: 1,5 BLK 4 A5: 1,5,9 # reduction candidate for 1,5 A5: 1,5 => SOLVED * 381257694972648531645193728438765219169482375527931486854329167216874953793516842 A5: 9 => CTR * 3812.76.457264398164.1..72.4387..21996.4123..12.9384.6854329167216874...793561842 * PAIR C6: 5,7 BLK 4 C5: 5,7,9 # reduction candidate for 5,7 C5: 5,7 => CTR * 3812976545726439816491..72.4387..21996.4123..12.9384.6854329167216874...793561842 C5: 9 => SOLVED * 381257694972648531645193728438765219169482375527931486854329167216874953793516842 * PAIR C6: 5,7 ROW 6 H6: 5,7,8 # reduction candidate for 5,7 H6: 5,7 => CTR * 3812.76.4.72643.8164.185723438756219.6.4123.812.9384.6854329167216874.35793561842 H6: 8 => SOLVED * 381257694972648531645193728438765219169482375527931486854329167216874953793516842 * PAIR I5: 5,8 BLK 6 H5: 5,8,7 # reduction candidate for 5,8 H5: 5,8 => CTR * 3812.76.457264.9.16491..72.4387..2199674123..125938476854329167216874593793561842 H5: 7 # 20 pairs H6: 5,8,7 # reduction candidate for 5,8 H6: 5,8 # 20 pairs * PAIR G8: 5,9 BLK 9 H8: 5,9,3 # reduction candidate for 5,9 H8: 5,9 => SOLVED * 381257694972648531645193728438765219169482375527931486854329167216874953793516842 H8: 3 => CTR * 3812.769497264.5.164519.72.4387.5219.69482375.2.93.4.6854329167216874...7935..842 * PAIR I8: 3,5 BLK 9 H8: 3,5,9 # reduction candidate for 3,5 H8: 3,5 => SOLVED * 381257694972648531645193728438765219169482375527931486854329167216874953793516842 H8: 9 => CTR * 38129765457264..3164.1.37284387.5219.6.4823.5.2.931486854329167216874593793516842 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-031-base-pr-000.dot * REASONING * DIS # A5: 5,9 => CTR => A5: 1 * PRF # A5: 1 => SOL * PRF # E3: 5,9 => SOL * DIS # E3: 8 => CTR => E3: 5,9 * DIS # C5: 7 => CTR => C5: 5,9 * PRF # E3: 5,9 => SOL * DIS # E3: 8 => CTR => E3: 5,9 * PRF # F3: 3,8 => SOL * DIS # F3: 5 => CTR => F3: 3,8 * PRF # H8: 5,9 => SOL * DIS # H8: 3 => CTR => H8: 5,9 * PRF # F3: 3,8 => SOL * DIS # F3: 5 => CTR => F3: 3,8 * PRF # A5: 1,5 => SOL * DIS # A5: 9 => CTR => A5: 1,5 * DIS # C5: 5,7 => CTR => C5: 9 * PRF # C5: 9 => SOL * DIS # H6: 5,7 => CTR => H6: 8 * PRF # H6: 8 => SOL * DIS # H5: 5,8 => CTR => H5: 7 * PRF # H8: 5,9 => SOL * DIS # H8: 3 => CTR => H8: 5,9 * PRF # H8: 3,5 => SOL * DIS # H8: 9 => CTR => H8: 3,5 * CNT 24 HDP CHAINS / 27 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,C3,C6,E1,E4,E5,E9,F2,F4,F6,F9,G2,G8,H1,H2,I3,I5,I8) * 3812.76.4.7264...164.1..72.4387..219.6.4.23...2.93.4.6854329167216874...7935..842 * PAIR A2: 5,9 COL A A5: 5,9,1 # reduction candidate for 5,9 A5: 5,9 => CTR * 3812.76.4.72643.8164.185723438756219.6.4123.812.9384.6854329167216874.35793561842 A5: 1 => SOLVED * 381257694972648531645193728438765219169482375527931486854329167216874953793516842 * DURATION: 0:00:04.003070 START: 03:44:26.787005 END: 03:44:30.790075 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-031-base-pr-001.dot * REASONING * DIS # A5: 5,9 => CTR => A5: 1 * PRF A5: 1 => SOL * STA A5: 1 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 031 solution: 381257694972648531645193728438765219169482375527931486854329167216874953793516842 info: 1331 FNBTWXY S8.f 28638 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 381257694972648531645193728438765219169482375527931486854329167216874953793516842 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 # A5: 5,9 => CTR => A5: 1 * PRF # A5: 1 => SOL * PRF # E3: 5,9 => SOL * DIS # E3: 8 => CTR => E3: 5,9 * INC # C5: 5,9 => UNS * DIS # C5: 7 => CTR => C5: 5,9 * PRF # E3: 5,9 => SOL * DIS # E3: 8 => CTR => E3: 5,9 * PRF # F3: 3,8 => SOL * DIS # F3: 5 => CTR => F3: 3,8 * PRF # H8: 5,9 => SOL * DIS # H8: 3 => CTR => H8: 5,9 * PRF # F3: 3,8 => SOL * DIS # F3: 5 => CTR => F3: 3,8 * PRF # A5: 1,5 => SOL * DIS # A5: 9 => CTR => A5: 1,5 * DIS # C5: 5,7 => CTR => C5: 9 * PRF # C5: 9 => SOL * DIS # H6: 5,7 => CTR => H6: 8 * PRF # H6: 8 => SOL * DIS # H5: 5,8 => CTR => H5: 7 * INC # H5: 7 => UNS * INC # H6: 5,8 => UNS * PRF # H8: 5,9 => SOL * DIS # H8: 3 => CTR => H8: 5,9 * PRF # H8: 3,5 => SOL * DIS # H8: 9 => CTR => H8: 3,5 * CNT 27 HDP CHAINS / 27 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A5: 5,9 => CTR => A5: 1 * PRF A5: 1 => SOL * STA A5: 1 * CNT 2 HDP CHAINS / 1 HYP OPENED