Analysis of xx-top500-484-base.sdk
Contents
Original Sudoku
level: medium
position: ...4...3..51........8.............139..5...........68..7...82..4.....5......1.... initial
Autosolve
position: ...4...3..51.......48....5.......9139.65...........685.7...82..4.....5......1.3.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F3: 1,7 => CTR => F3: 2,3,6,9 * PRF # D4: 2,8 => SOL * DIS # D4: 6,7 => CTR => D4: 2,8 * DIS # E4: 2,8 => CTR => E4: 4,6,7 * DIS # F6: 1,7 => CTR => F6: 2,3,4,9 * PRF # C4: 4,7 => SOL * DIS # E6: 4,7 => CTR => E6: 2,3,9 * DIS # F6: 4,7 => CTR => F6: 1,2,3,9 * PRF # B5: 3,8 => SOL * DIS # B5: 1 => CTR => B5: 3,8 * DIS # E2: 3,8 => CTR => E2: 2,6,7,9 * DIS # D6: 1,3 => CTR => D6: 2,7,9 * PRF # D6: 2,7,9 => SOL * DIS # F6: 1,3 => CTR => F6: 2,4,7,9 * DIS # B5: 1,3 => CTR => B5: 8 * PRF # B5: 8 => SOL * DIS # F3: 1,3 => CTR => F3: 2,6,7,9 * DIS # G2: 4,7 => CTR => G2: 8 * PRF # G2: 8 => SOL * DIS # B5: 3 => CTR => B5: 1,8 * PRF # I9: 6,9 => SOL * CNT 21 HDP CHAINS / 38 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F3: 1,7 => CTR => F3: 2,3,6,9 * DIS F3: 2,3,6,9 # D3: 2,3,6,9 => CTR => D3: 1,7 * PRF F3: 2,3,6,9 + D3: 1,7 # D4: 2,8 => SOL * STA F3: 2,3,6,9 + D3: 1,7 + D4: 2,8 * CNT 3 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...4...3..51........8.............139..5...........68..7...82..4.....5......1.... | initial |
| ...4...3..51.......48....5.......9139.65...........685.7...82..4.....5......1.3.. | autosolve |
| 769485132251397864348162759527846913986531427134729685673958241412673598895214376 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) B1: 6,9 E1: 5,8 F1: 1,5 G1: 1,8 G3: 1,7 B4: 2,8 A6: 1,7 C6: 4,7 E5: 3,8 F5: 1,3 G5: 4,7 B8: 1,8 B9: 6,9 E7: 4,5 F9: 4,5 I8: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G1,G3: 1.. / G1 = 1 => 0 pairs (*) / G3 = 1 => 0 pairs (X) A7,B8: 1.. / A7 = 1 => 0 pairs (X) / B8 = 1 => 0 pairs (_) I7,I8: 1.. / I7 = 1 => 0 pairs (*) / I8 = 1 => 0 pairs (X) F1,G1: 1.. / F1 = 1 => 0 pairs (X) / G1 = 1 => 0 pairs (_) B5,F5: 1.. / B5 = 1 => 0 pairs (X) / F5 = 1 => 0 pairs (_) A7,I7: 1.. / A7 = 1 => 0 pairs (X) / I7 = 1 => 0 pairs (_) B8,I8: 1.. / B8 = 1 => 0 pairs (*) / I8 = 1 => 0 pairs (X) A6,A7: 1.. / A6 = 1 => 0 pairs (*) / A7 = 1 => 0 pairs (X) D3,D6: 1.. / D3 = 1 => 0 pairs (*) / D6 = 1 => 0 pairs (X) B4,B6: 2.. / B4 = 2 => 16 pairs (_) / B6 = 2 => 0 pairs (X) H5,I5: 2.. / H5 = 2 => 17 pairs (_) / I5 = 2 => 19 pairs (_) H2,H5: 2.. / H2 = 2 => 19 pairs (_) / H5 = 2 => 17 pairs (_) A2,A3: 3.. / A2 = 3 => 16 pairs (_) / A3 = 3 => 16 pairs (_) B5,B6: 3.. / B5 = 3 => 0 pairs (X) / B6 = 3 => 16 pairs (_) C7,C8: 3.. / C7 = 3 => 18 pairs (_) / C8 = 3 => 17 pairs (_) C7,D7: 3.. / C7 = 3 => 18 pairs (_) / D7 = 3 => 17 pairs (_) C4,C6: 4.. / C4 = 4 => 0 pairs (X) / C6 = 4 => 16 pairs (_) E7,F9: 4.. / E7 = 4 => 0 pairs (X) / F9 = 4 => 0 pairs (_) G2,G5: 4.. / G2 = 4 => 0 pairs (X) / G5 = 4 => 19 pairs (_) E1,F1: 5.. / E1 = 5 => 0 pairs (X) / F1 = 5 => 0 pairs (_) A4,C4: 5.. / A4 = 5 => 0 pairs (*) / C4 = 5 => 0 pairs (X) E7,F9: 5.. / E7 = 5 => 0 pairs (*) / F9 = 5 => 0 pairs (X) E1,E7: 5.. / E1 = 5 => 0 pairs (X) / E7 = 5 => 0 pairs (_) F1,F9: 5.. / F1 = 5 => 0 pairs (*) / F9 = 5 => 0 pairs (X) B1,B9: 6.. / B1 = 6 => 0 pairs (*) / B9 = 6 => 0 pairs (X) G1,G2: 8.. / G1 = 8 => 0 pairs (X) / G2 = 8 => 0 pairs (_) B8,A9: 8.. / B8 = 8 => 0 pairs (X) / A9 = 8 => 0 pairs (_) I8,I9: 8.. / I8 = 8 => 0 pairs (*) / I9 = 8 => 0 pairs (X) E1,G1: 8.. / E1 = 8 => 0 pairs (*) / G1 = 8 => 0 pairs (X) B5,E5: 8.. / B5 = 8 => 0 pairs (*) / E5 = 8 => 0 pairs (X) B8,I8: 8.. / B8 = 8 => 0 pairs (X) / I8 = 8 => 0 pairs (_) A9,I9: 8.. / A9 = 8 => 0 pairs (*) / I9 = 8 => 0 pairs (X) A4,A9: 8.. / A4 = 8 => 0 pairs (X) / A9 = 8 => 0 pairs (_) D2,D4: 8.. / D2 = 8 => 0 pairs (X) / D4 = 8 => 0 pairs (_) B1,C1: 9.. / B1 = 9 => 16 pairs (_) / C1 = 9 => 0 pairs (*) B1,B9: 9.. / B1 = 9 => 16 pairs (_) / B9 = 9 => 0 pairs (*) * DURATION: 0:01:12.981062 START: 19:10:17.681038 END: 19:11:30.662100 2017-05-04 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B1,B4,B8,B9,C6,E1,E5,E7,F1,F5,F9,G1,G3,G5,I8) * ...4...3..51.......48....5.......9139.65...........685.7...82..4.....5......1.3.. * PAIR G3: 1,7 ROW 3 D3: 1,7,2,3,6,9 # reduction candidate for 1,7 D3: 1,7 # 17 pairs F3: 1,7,2,3,6,9 # reduction candidate for 1,7 F3: 1,7 => CTR * ...4...3..51.......48....5.825...913916583...7341..68517..582..48....5.1....1.3.8 F3: 2,3,6,9 # 16 pairs * PAIR B4: 2,8 ROW 4 D4: 2,8,6,7 # reduction candidate for 2,8 D4: 2,8 => SOLVED * 769485132251397864348162759527846913986531427134729685673958241412673598895214376 D4: 6,7 => CTR * ...45183..518......48...15.......913916583...7341..685175..82..4.....5......1.3.. E4: 2,8,4,6,7 # reduction candidate for 2,8 E4: 2,8 => CTR * ...45183..518......48...15.......9139165...........685.7...82..4.....5..8...1.3.. E4: 4,6,7 # 16 pairs * PAIR A6: 1,7 ROW 6 D6: 1,7,2,3,9 # reduction candidate for 1,7 D6: 1,7 # 18 pairs F6: 1,7,2,3,4,9 # reduction candidate for 1,7 F6: 1,7 => CTR * ...48513..51...8.4.481..75.5278469139865314..13492768567.35824141....5.88.52143.. F6: 2,3,4,9 # 16 pairs * PAIR C6: 4,7 BLK 4 C4: 4,7,5 # reduction candidate for 4,7 C4: 4,7 => SOLVED * 769485132251397864348162759527846913986531427134729685673958241412673598895214376 C4: 5 # 20 pairs * PAIR C6: 4,7 ROW 6 E6: 4,7,2,3,9 # reduction candidate for 4,7 E6: 4,7 => CTR * ...48513..51...8.4.481..75.52.8..9139865314..13.9.2685679.5824141....5.88.52143.. E6: 2,3,9 # 16 pairs F6: 4,7,1,2,3,9 # reduction candidate for 4,7 F6: 4,7 => CTR * ...48513..51...8.4.481..75.52.8469139865314..134927685679.5824141....5.88.52143.. F6: 1,2,3,9 # 16 pairs * PAIR E5: 3,8 ROW 5 B5: 3,8,1 # reduction candidate for 3,8 B5: 3,8 => SOLVED * 769485132251397864348162759527846913986531427134729685673958241412673598895214376 B5: 1 => CTR * ..745183..518......48...15.825...913916583...7341..68517..482..48....5.15...1.3.8 * PAIR E5: 3,8 COL E E2: 3,8,2,6,7,9 # reduction candidate for 3,8 E2: 3,8 => CTR * ...45183..51.......48...15.......913916583...7341..685175..82..4.....5......1.3.. E2: 2,6,7,9 # 16 pairs * PAIR F5: 1,3 BLK 5 D6: 1,3,2,7,9 # reduction candidate for 1,3 D6: 1,3 => CTR * ...45183..518......48...15.......913916583...7341..685175..82..4.....5......1.3.. D6: 2,7,9 => SOLVED * 769485132251397864348162759527846913986531427134729685673958241412673598895214376 F6: 1,3,2,4,7,9 # reduction candidate for 1,3 F6: 1,3 => CTR * ...4.513..51...8...481..75....8..9139.65...........685.7...82..4.....5......1.3.. F6: 2,4,7,9 # 16 pairs * PAIR F5: 1,3 ROW 5 B5: 1,3,8 # reduction candidate for 1,3 B5: 1,3 => CTR * ...45183..518......48...15.......913916583...7341..685175..82..4.....5......1.3.. B5: 8 => SOLVED * 769485132251397864348162759527846913986531427134729685673958241412673598895214376 * PAIR F5: 1,3 COL F F3: 1,3,2,6,7,9 # reduction candidate for 1,3 F3: 1,3 => CTR * .694851323516..8.42481.375.52.8..9139865314..13....68567..582.14123..5.88952143.. F3: 2,6,7,9 # 16 pairs * PAIR G5: 4,7 BLK 6 H5: 4,7,2 # reduction candidate for 4,7 H5: 4,7 # 19 pairs I5: 4,7,2 # reduction candidate for 4,7 I5: 4,7 # 17 pairs * PAIR G5: 4,7 COL G G2: 4,7,8 # reduction candidate for 4,7 G2: 4,7 => CTR * ...45183..51.......48...15.825...913916583...7341..68517..482..48....5.15...1.3.8 G2: 8 => SOLVED * 769485132251397864348162759527846913986531427134729685673958241412673598895214376 * PAIR B8: 1,8 COL B B5: 1,8,3 # reduction candidate for 1,8 B5: 3 => CTR * ...4...3..51.......48....5.......913936581.........685.7...82..4.....5......1.3.. B5: 1,8 # 16 pairs * PAIR B9: 6,9 ROW 9 D9: 6,9,2,7 # reduction candidate for 6,9 D9: 6,9 # 21 pairs H9: 6,9,4,7 # reduction candidate for 6,9 H9: 6,9 # 19 pairs I9: 6,9,4,7,8 # reduction candidate for 6,9 I9: 6,9 => SOLVED * 769485132251397864348162759527846913986531427134729685673958241412673598895214376 I9: 4,7,8 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-484-base-pr-000.dot * REASONING * DIS # F3: 1,7 => CTR => F3: 2,3,6,9 * PRF # D4: 2,8 => SOL * DIS # D4: 6,7 => CTR => D4: 2,8 * DIS # E4: 2,8 => CTR => E4: 4,6,7 * DIS # F6: 1,7 => CTR => F6: 2,3,4,9 * PRF # C4: 4,7 => SOL * DIS # E6: 4,7 => CTR => E6: 2,3,9 * DIS # F6: 4,7 => CTR => F6: 1,2,3,9 * PRF # B5: 3,8 => SOL * DIS # B5: 1 => CTR => B5: 3,8 * DIS # E2: 3,8 => CTR => E2: 2,6,7,9 * DIS # D6: 1,3 => CTR => D6: 2,7,9 * PRF # D6: 2,7,9 => SOL * DIS # F6: 1,3 => CTR => F6: 2,4,7,9 * DIS # B5: 1,3 => CTR => B5: 8 * PRF # B5: 8 => SOL * DIS # F3: 1,3 => CTR => F3: 2,6,7,9 * DIS # G2: 4,7 => CTR => G2: 8 * PRF # G2: 8 => SOL * DIS # B5: 3 => CTR => B5: 1,8 * PRF # I9: 6,9 => SOL * CNT 21 HDP CHAINS / 38 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B1,B4,B8,B9,C6,E1,E5,E7,F1,F5,F9,G1,G3,G5,I8) * ...4...3..51.......48....5.......9139.65...........685.7...82..4.....5......1.3.. * PAIR G3: 1,7 ROW 3 D3: 1,7,2,3,6,9 # reduction candidate for 1,7 D3: 1,7 # 17 pairs F3: 1,7,2,3,6,9 # reduction candidate for 1,7 F3: 1,7 => CTR * ...4...3..51.......48....5.825...913916583...7341..68517..582..48....5.1....1.3.8 * RESTART * PAIR G3: 1,7 ROW 3 D3: 1,7,2,3,6,9 # reduction candidate for 1,7 D3: 2,3,6,9 => CTR * ...4.183..51.......48...15.......913916583...7341..68517...82..48....5.1....153.8 * PAIR RESTART * PAIR B4: 2,8 ROW 4 D4: 2,8,6,7 # reduction candidate for 2,8 D4: 2,8 => SOLVED * 769485132251397864348162759527846913986531427134729685673958241412673598895214376 * DURATION: 0:00:07.098909 START: 19:12:12.810727 END: 19:12:19.909636 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-484-base-pr-001.dot * REASONING * DIS # F3: 1,7 => CTR => F3: 2,3,6,9 * DIS F3: 2,3,6,9 # D3: 2,3,6,9 => CTR => D3: 1,7 * PRF F3: 2,3,6,9 + D3: 1,7 # D4: 2,8 => SOL * STA F3: 2,3,6,9 + D3: 1,7 + D4: 2,8 * CNT 3 HDP CHAINS / 5 HYP OPENED
Header Info
Top 500 Minimum 17 484 solution: 769485132251397864348162759527846913986531427134729685673958241412673598895214376 info: 95821 FNBHYK S8.f 40239 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 769485132251397864348162759527846913986531427134729685673958241412673598895214376 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:
* INC # D3: 1,7 => UNS * DIS # F3: 1,7 => CTR => F3: 2,3,6,9 * INC # F3: 2,3,6,9 => UNS * PRF # D4: 2,8 => SOL * DIS # D4: 6,7 => CTR => D4: 2,8 * DIS # E4: 2,8 => CTR => E4: 4,6,7 * INC # E4: 4,6,7 => UNS * INC # D6: 1,7 => UNS * DIS # F6: 1,7 => CTR => F6: 2,3,4,9 * INC # F6: 2,3,4,9 => UNS * PRF # C4: 4,7 => SOL * INC # C4: 5 => UNS * DIS # E6: 4,7 => CTR => E6: 2,3,9 * INC # E6: 2,3,9 => UNS * DIS # F6: 4,7 => CTR => F6: 1,2,3,9 * INC # F6: 1,2,3,9 => UNS * PRF # B5: 3,8 => SOL * DIS # B5: 1 => CTR => B5: 3,8 * DIS # E2: 3,8 => CTR => E2: 2,6,7,9 * INC # E2: 2,6,7,9 => UNS * DIS # D6: 1,3 => CTR => D6: 2,7,9 * PRF # D6: 2,7,9 => SOL * DIS # F6: 1,3 => CTR => F6: 2,4,7,9 * INC # F6: 2,4,7,9 => UNS * DIS # B5: 1,3 => CTR => B5: 8 * PRF # B5: 8 => SOL * DIS # F3: 1,3 => CTR => F3: 2,6,7,9 * INC # F3: 2,6,7,9 => UNS * INC # H5: 4,7 => UNS * INC # I5: 4,7 => UNS * DIS # G2: 4,7 => CTR => G2: 8 * PRF # G2: 8 => SOL * INC # B5: 1,8 => UNS * DIS # B5: 3 => CTR => B5: 1,8 * INC # D9: 6,9 => UNS * INC # H9: 6,9 => UNS * PRF # I9: 6,9 => SOL * INC # I9: 4,7,8 => UNS * CNT 38 HDP CHAINS / 38 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D3: 1,7 => UNS * DIS # F3: 1,7 => CTR => F3: 2,3,6,9 * INC F3: 2,3,6,9 # D3: 1,7 => UNS * DIS F3: 2,3,6,9 # D3: 2,3,6,9 => CTR => D3: 1,7 * PRF F3: 2,3,6,9 + D3: 1,7 # D4: 2,8 => SOL * STA F3: 2,3,6,9 + D3: 1,7 + D4: 2,8 * CNT 5 HDP CHAINS / 5 HYP OPENED