Analysis of xx-top500-140-base.sdk
Contents
Original Sudoku
level: medium
position: 6.5....2.....71.............1....7.23..6.........4.....7....3..4..8........5...6. initial
Autosolve
position: 6.54..127..4.71.567.1.5643..16..5742347612..525.74.6135721643..46.82.5711..5.7264 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # E1: 3,9 => SOL * DIS # E1: 8 => CTR => E1: 3,9 * DIS # F1: 3,9 => CTR => F1: 8 * PRF # F1: 8 => SOL * DIS # B3: 8,9 => CTR => B3: 2 * PRF # B3: 2 => SOL * PRF # B3: 2,9 => SOL * DIS # B3: 8 => CTR => B3: 2,9 * DIS # B3: 8,9 => CTR => B3: 2 * PRF # B3: 2 => SOL * PRF # E4: 8,9 => SOL * DIS # E4: 3 => CTR => E4: 8,9 * DIS # C9: 8,9 => CTR => C9: 3 * PRF # C9: 3 => SOL * DIS # E4: 3,9 => CTR => E4: 8 * PRF # E4: 8 => SOL * PRF # E4: 8,9 => SOL * DIS # E4: 3 => CTR => E4: 8,9 * PRF # F1: 8,9 => SOL * DIS # F1: 3 => CTR => F1: 8,9 * PRF # C9: 3,9 => SOL * DIS # C9: 8 => CTR => C9: 3,9 * DIS # C9: 8,9 => CTR => C9: 3 * PRF # C9: 3 => SOL * DIS # B3: 8,9 => CTR => B3: 2 * PRF # B3: 2 => SOL * DIS # F1: 3,9 => CTR => F1: 8 * PRF # F1: 8 => SOL * PRF # C9: 3,9 => SOL * DIS # C9: 8 => CTR => C9: 3,9 * PRF # E1: 3,9 => SOL * DIS # E1: 8 => CTR => E1: 3,9 * DIS # E4: 3,9 => CTR => E4: 8 * PRF # E4: 8 => SOL * CNT 34 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # E1: 3,9 => SOL * STA E1: 3,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6.5....2.....71.............1....7.23..6.........4.....7....3..4..8........5...6. | initial |
| 6.54..127..4.71.567.1.5643..16..5742347612..525.74.6135721643..46.82.5711..5.7264 | autosolve |
| 695438127834271956721956438916385742347612895258749613572164389469823571183597264 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) B1: 3,9 A2: 8,9 B2: 2,3 D2: 2,3 D3: 2,9 G2: 8,9 I3: 8,9 A4: 8,9 C6: 8,9 D4: 3,9 F6: 8,9 G5: 8,9 H5: 8,9 C8: 3,9 B9: 8,9 F8: 3,9 E9: 3,9 H7: 8,9 I7: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,B3: 2.. / B2 = 2 => 0 pairs (X) / B3 = 2 => 0 pairs (_) D2,D3: 2.. / D2 = 2 => 0 pairs (*) / D3 = 2 => 0 pairs (X) B2,D2: 2.. / B2 = 2 => 0 pairs (X) / D2 = 2 => 0 pairs (_) B3,D3: 2.. / B3 = 2 => 0 pairs (*) / D3 = 2 => 0 pairs (X) B1,B2: 3.. / B1 = 3 => 0 pairs (X) / B2 = 3 => 0 pairs (_) D4,E4: 3.. / D4 = 3 => 0 pairs (*) / E4 = 3 => 0 pairs (X) C8,C9: 3.. / C8 = 3 => 0 pairs (X) / C9 = 3 => 0 pairs (_) F8,E9: 3.. / F8 = 3 => 0 pairs (*) / E9 = 3 => 0 pairs (X) B2,D2: 3.. / B2 = 3 => 0 pairs (*) / D2 = 3 => 0 pairs (X) C8,F8: 3.. / C8 = 3 => 0 pairs (X) / F8 = 3 => 0 pairs (_) C9,E9: 3.. / C9 = 3 => 0 pairs (*) / E9 = 3 => 0 pairs (X) D2,D4: 3.. / D2 = 3 => 0 pairs (X) / D4 = 3 => 0 pairs (_) F1,F8: 3.. / F1 = 3 => 0 pairs (X) / F8 = 3 => 0 pairs (_) A2,B3: 8.. / A2 = 8 => 0 pairs (*) / B3 = 8 => 0 pairs (X) E1,F1: 8.. / E1 = 8 => 0 pairs (X) / F1 = 8 => 0 pairs (_) G2,I3: 8.. / G2 = 8 => 0 pairs (X) / I3 = 8 => 0 pairs (_) A4,C6: 8.. / A4 = 8 => 0 pairs (X) / C6 = 8 => 0 pairs (_) E4,F6: 8.. / E4 = 8 => 0 pairs (*) / F6 = 8 => 0 pairs (X) G5,H5: 8.. / G5 = 8 => 0 pairs (*) / H5 = 8 => 0 pairs (X) B9,C9: 8.. / B9 = 8 => 0 pairs (*) / C9 = 8 => 0 pairs (X) H7,I7: 8.. / H7 = 8 => 0 pairs (*) / I7 = 8 => 0 pairs (X) A2,G2: 8.. / A2 = 8 => 0 pairs (*) / G2 = 8 => 0 pairs (X) B3,I3: 8.. / B3 = 8 => 0 pairs (X) / I3 = 8 => 0 pairs (_) A4,E4: 8.. / A4 = 8 => 0 pairs (X) / E4 = 8 => 0 pairs (_) C6,F6: 8.. / C6 = 8 => 0 pairs (*) / F6 = 8 => 0 pairs (X) A2,A4: 8.. / A2 = 8 => 0 pairs (*) / A4 = 8 => 0 pairs (X) B3,B9: 8.. / B3 = 8 => 0 pairs (X) / B9 = 8 => 0 pairs (_) C6,C9: 8.. / C6 = 8 => 0 pairs (*) / C9 = 8 => 0 pairs (X) E1,E4: 8.. / E1 = 8 => 0 pairs (X) / E4 = 8 => 0 pairs (_) F1,F6: 8.. / F1 = 8 => 0 pairs (*) / F6 = 8 => 0 pairs (X) G2,G5: 8.. / G2 = 8 => 0 pairs (X) / G5 = 8 => 0 pairs (_) H5,H7: 8.. / H5 = 8 => 0 pairs (X) / H7 = 8 => 0 pairs (_) I3,I7: 8.. / I3 = 8 => 0 pairs (*) / I7 = 8 => 0 pairs (X) G2,I3: 9.. / G2 = 9 => 0 pairs (*) / I3 = 9 => 0 pairs (X) A4,C6: 9.. / A4 = 9 => 0 pairs (*) / C6 = 9 => 0 pairs (X) G5,H5: 9.. / G5 = 9 => 0 pairs (X) / H5 = 9 => 0 pairs (_) F8,E9: 9.. / F8 = 9 => 0 pairs (X) / E9 = 9 => 0 pairs (_) H7,I7: 9.. / H7 = 9 => 0 pairs (X) / I7 = 9 => 0 pairs (_) A2,G2: 9.. / A2 = 9 => 0 pairs (X) / G2 = 9 => 0 pairs (_) C6,F6: 9.. / C6 = 9 => 0 pairs (X) / F6 = 9 => 0 pairs (_) C8,F8: 9.. / C8 = 9 => 0 pairs (*) / F8 = 9 => 0 pairs (X) A2,A4: 9.. / A2 = 9 => 0 pairs (X) / A4 = 9 => 0 pairs (_) D3,D4: 9.. / D3 = 9 => 0 pairs (*) / D4 = 9 => 0 pairs (X) G2,G5: 9.. / G2 = 9 => 0 pairs (*) / G5 = 9 => 0 pairs (X) H5,H7: 9.. / H5 = 9 => 0 pairs (*) / H7 = 9 => 0 pairs (X) I3,I7: 9.. / I3 = 9 => 0 pairs (X) / I7 = 9 => 0 pairs (_) * DURATION: 0:01:18.243282 START: 07:31:35.092812 END: 07:32:53.336094 2017-05-04 * CP COUNT: (46) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,B1,B2,B9,C6,C8,D2,D3,D4,E9,F6,F8,G2,G5,H5,H7,I3,I7) * 6.54..127..4.71.567.1.5643..16..5742347612..525.74.6135721643..46.82.5711..5.7264 * PAIR B1: 3,9 ROW 1 E1: 3,9,8 # reduction candidate for 3,9 E1: 3,9 => SOLVED * 695438127834271956721956438916385742347612895258749613572164389469823571183597264 E1: 8 => CTR * 6.548.127..4.71.567.1.5643.816..5742347612..52597486135721643..463829571198537264 F1: 3,9,8 # reduction candidate for 3,9 F1: 3,9 => CTR * 6.548.127..4.71.567.1.5643.816..5742347612..52597486135721643..463829571198537264 F1: 8 => SOLVED * 695438127834271956721956438916385742347612895258749613572164389469823571183597264 * PAIR A2: 8,9 BLK 1 B3: 8,9,2 # reduction candidate for 8,9 B3: 8,9 => CTR * 6.54..127.24371.567.125643..16935742347612..52597486135721643..46.82.5711..5.7264 B3: 2 => SOLVED * 695438127834271956721956438916385742347612895258749613572164389469823571183597264 * PAIR D3: 2,9 ROW 3 B3: 2,9,8 # reduction candidate for 2,9 B3: 2,9 => SOLVED * 695438127834271956721956438916385742347612895258749613572164389469823571183597264 B3: 8 => CTR * 6.54..127.24371.5678125643981693574234761298525974.6135721643..46.82.5711..5.7264 * PAIR I3: 8,9 ROW 3 B3: 8,9,2 # reduction candidate for 8,9 B3: 8,9 => CTR * 6.54..127.24371.567.125643..16935742347612..52597486135721643..46.82.5711..5.7264 B3: 2 => SOLVED * 695438127834271956721956438916385742347612895258749613572164389469823571183597264 * PAIR A4: 8,9 ROW 4 E4: 8,9,3 # reduction candidate for 8,9 E4: 8,9 => SOLVED * 695438127834271956721956438916385742347612895258749613572164389469823571183597264 E4: 3 => CTR * 6.548.127..4.71.567.1.5643.816935742347612..525974.6135721643..46.82.5711..5.7264 * PAIR C6: 8,9 COL C C9: 8,9,3 # reduction candidate for 8,9 C9: 8,9 => CTR * 6.54.3127.34271.56721956438.163957423476128952597486135721643894638295711..537264 C9: 3 => SOLVED * 695438127834271956721956438916385742347612895258749613572164389469823571183597264 * PAIR D4: 3,9 BLK 5 E4: 3,9,8 # reduction candidate for 3,9 E4: 3,9 => CTR * 6.548.127..4.71.567.1.5643.816..5742347612..52597486135721643..463829571198537264 E4: 8 => SOLVED * 695438127834271956721956438916385742347612895258749613572164389469823571183597264 * PAIR F6: 8,9 BLK 5 E4: 8,9,3 # reduction candidate for 8,9 E4: 8,9 => SOLVED * 695438127834271956721956438916385742347612895258749613572164389469823571183597264 E4: 3 => CTR * 6.548.127..4.71.567.1.5643.816935742347612..525974.6135721643..46.82.5711..5.7264 * PAIR F6: 8,9 COL F F1: 8,9,3 # reduction candidate for 8,9 F1: 8,9 => SOLVED * 695438127834271956721956438916385742347612895258749613572164389469823571183597264 F1: 3 => CTR * 6.5483127.34271.5672195643881639574234761289525974861357216438946382.5711..5.7264 * PAIR C8: 3,9 BLK 7 C9: 3,9,8 # reduction candidate for 3,9 C9: 3,9 => SOLVED * 695438127834271956721956438916385742347612895258749613572164389469823571183597264 C9: 8 => CTR * 635498127..4.71.567.1.5643..16..5742347612..525.74.6135721643..463829571198537264 * PAIR B9: 8,9 BLK 7 C9: 8,9,3 # reduction candidate for 8,9 C9: 8,9 => CTR * 6.54.3127.34271.56721956438.163957423476128952597486135721643894638295711..537264 C9: 3 => SOLVED * 695438127834271956721956438916385742347612895258749613572164389469823571183597264 * PAIR B9: 8,9 COL B B3: 8,9,2 # reduction candidate for 8,9 B3: 8,9 => CTR * 6.54..127.24371.567.125643..16935742347612..52597486135721643..46.82.5711..5.7264 B3: 2 => SOLVED * 695438127834271956721956438916385742347612895258749613572164389469823571183597264 * PAIR F8: 3,9 COL F F1: 3,9,8 # reduction candidate for 3,9 F1: 3,9 => CTR * 6.548.127..4.71.567.1.5643.816..5742347612..52597486135721643..463829571198537264 F1: 8 => SOLVED * 695438127834271956721956438916385742347612895258749613572164389469823571183597264 * PAIR E9: 3,9 ROW 9 C9: 3,9,8 # reduction candidate for 3,9 C9: 3,9 => SOLVED * 695438127834271956721956438916385742347612895258749613572164389469823571183597264 C9: 8 => CTR * 635498127..4.71.567.1.5643..16..5742347612..525.74.6135721643..463829571198537264 * PAIR E9: 3,9 COL E E1: 3,9,8 # reduction candidate for 3,9 E1: 3,9 => SOLVED * 695438127834271956721956438916385742347612895258749613572164389469823571183597264 E1: 8 => CTR * 6.548.127..4.71.567.1.5643.816..5742347612..52597486135721643..463829571198537264 E4: 3,9,8 # reduction candidate for 3,9 E4: 3,9 => CTR * 6.548.127..4.71.567.1.5643.816..5742347612..52597486135721643..463829571198537264 E4: 8 => SOLVED * 695438127834271956721956438916385742347612895258749613572164389469823571183597264 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-140-base-pr-000.dot * REASONING * PRF # E1: 3,9 => SOL * DIS # E1: 8 => CTR => E1: 3,9 * DIS # F1: 3,9 => CTR => F1: 8 * PRF # F1: 8 => SOL * DIS # B3: 8,9 => CTR => B3: 2 * PRF # B3: 2 => SOL * PRF # B3: 2,9 => SOL * DIS # B3: 8 => CTR => B3: 2,9 * DIS # B3: 8,9 => CTR => B3: 2 * PRF # B3: 2 => SOL * PRF # E4: 8,9 => SOL * DIS # E4: 3 => CTR => E4: 8,9 * DIS # C9: 8,9 => CTR => C9: 3 * PRF # C9: 3 => SOL * DIS # E4: 3,9 => CTR => E4: 8 * PRF # E4: 8 => SOL * PRF # E4: 8,9 => SOL * DIS # E4: 3 => CTR => E4: 8,9 * PRF # F1: 8,9 => SOL * DIS # F1: 3 => CTR => F1: 8,9 * PRF # C9: 3,9 => SOL * DIS # C9: 8 => CTR => C9: 3,9 * DIS # C9: 8,9 => CTR => C9: 3 * PRF # C9: 3 => SOL * DIS # B3: 8,9 => CTR => B3: 2 * PRF # B3: 2 => SOL * DIS # F1: 3,9 => CTR => F1: 8 * PRF # F1: 8 => SOL * PRF # C9: 3,9 => SOL * DIS # C9: 8 => CTR => C9: 3,9 * PRF # E1: 3,9 => SOL * DIS # E1: 8 => CTR => E1: 3,9 * DIS # E4: 3,9 => CTR => E4: 8 * PRF # E4: 8 => SOL * CNT 34 HDP CHAINS / 34 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,B1,B2,B9,C6,C8,D2,D3,D4,E9,F6,F8,G2,G5,H5,H7,I3,I7) * 6.54..127..4.71.567.1.5643..16..5742347612..525.74.6135721643..46.82.5711..5.7264 * PAIR B1: 3,9 ROW 1 E1: 3,9,8 # reduction candidate for 3,9 E1: 3,9 => SOLVED * 695438127834271956721956438916385742347612895258749613572164389469823571183597264 * DURATION: 0:00:01.873097 START: 07:33:32.391315 END: 07:33:34.264412 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-140-base-pr-001.dot * REASONING * PRF # E1: 3,9 => SOL * STA E1: 3,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 140 solution: 695438127834271956721956438916385742347612895258749613572164389469823571183597264 info: 1813 FNBTWY S8.f 35525 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 695438127834271956721956438916385742347612895258749613572164389469823571183597264 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:
* PRF # E1: 3,9 => SOL * DIS # E1: 8 => CTR => E1: 3,9 * DIS # F1: 3,9 => CTR => F1: 8 * PRF # F1: 8 => SOL * DIS # B3: 8,9 => CTR => B3: 2 * PRF # B3: 2 => SOL * PRF # B3: 2,9 => SOL * DIS # B3: 8 => CTR => B3: 2,9 * DIS # B3: 8,9 => CTR => B3: 2 * PRF # B3: 2 => SOL * PRF # E4: 8,9 => SOL * DIS # E4: 3 => CTR => E4: 8,9 * DIS # C9: 8,9 => CTR => C9: 3 * PRF # C9: 3 => SOL * DIS # E4: 3,9 => CTR => E4: 8 * PRF # E4: 8 => SOL * PRF # E4: 8,9 => SOL * DIS # E4: 3 => CTR => E4: 8,9 * PRF # F1: 8,9 => SOL * DIS # F1: 3 => CTR => F1: 8,9 * PRF # C9: 3,9 => SOL * DIS # C9: 8 => CTR => C9: 3,9 * DIS # C9: 8,9 => CTR => C9: 3 * PRF # C9: 3 => SOL * DIS # B3: 8,9 => CTR => B3: 2 * PRF # B3: 2 => SOL * DIS # F1: 3,9 => CTR => F1: 8 * PRF # F1: 8 => SOL * PRF # C9: 3,9 => SOL * DIS # C9: 8 => CTR => C9: 3,9 * PRF # E1: 3,9 => SOL * DIS # E1: 8 => CTR => E1: 3,9 * DIS # E4: 3,9 => CTR => E4: 8 * PRF # E4: 8 => SOL * CNT 34 HDP CHAINS / 34 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # E1: 3,9 => SOL * STA E1: 3,9 * CNT 1 HDP CHAINS / 1 HYP OPENED