Analysis of xx-top500-213-base.sdk
Contents
Original Sudoku
level: medium
position: .45....8...92........3.....2..7..4..6...8..5..........3.....2...7..5.........1... initial
Autosolve
position: .45...382.392......263.....25.7..4..6...82.5....5...2.3.....2.5.72.53...5...21... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E1: 1,7 => CTR => E1: 6,9 * DIS # B6: 1,9 => CTR => B6: 8 * PRF # D5: 1,9 => SOL * DIS # D5: 4 => CTR => D5: 1,9 * DIS # G5: 1,9 => CTR => G5: 7 * DIS # I5: 1,9 => CTR => I5: 3,7 * DIS # F6: 6 => CTR => F6: 4,9 * DIS # E4: 6,9 => CTR => E4: 1,3 * DIS # E6: 6,9 => CTR => E6: 1,3 * DIS # F6: 6,9 => CTR => F6: 4 * PRF # F6: 4 => SOL * DIS # I4: 6,9 => CTR => I4: 1,3,8 * PRF # F1: 6,9 => SOL * DIS # F1: 7 => CTR => F1: 6,9 * DIS # F7: 6,9 => CTR => F7: 4,7 * DIS # C7: 4,8 => CTR => C7: 1 * DIS # I9: 4,8 => CTR => I9: 3,6,7,9 * DIS # C6: 4,8 => CTR => C6: 1,3,7 * CNT 18 HDP CHAINS / 39 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E1: 1,7 => CTR => E1: 6,9 * DIS E1: 6,9 # B6: 1,9 => CTR => B6: 8 * PRF E1: 6,9 + B6: 8 # D5: 1,9 => SOL * STA E1: 6,9 + B6: 8 + D5: 1,9 * CNT 3 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .45....8...92........3.....2..7..4..6...8..5..........3.....2...7..5.........1... | initial |
| .45...382.392......263.....25.7..4..6...82.5....5...2.3.....2.5.72.53...5...21... | autosolve |
| 745169382139278564826345971253716498614982753987534126361897245472653819598421637 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) A1: 1,7 F2: 5,8 F3: 5,8 B5: 1,9 A6: 4,9 F4: 6,9 A8: 4,9 C9: 4,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B7,C7: 1.. / B7 = 1 => 0 pairs (X) / C7 = 1 => 9 pairs (_) D1,D5: 1.. / D1 = 1 => 0 pairs (*) / D5 = 1 => 0 pairs (X) E4,E6: 3.. / E4 = 3 => 0 pairs (X) / E6 = 3 => 8 pairs (_) H9,I9: 3.. / H9 = 3 => 8 pairs (_) / I9 = 3 => 0 pairs (X) C5,I5: 3.. / C5 = 3 => 0 pairs (X) / I5 = 3 => 8 pairs (_) H4,H9: 3.. / H4 = 3 => 0 pairs (X) / H9 = 3 => 8 pairs (_) E2,E3: 4.. / E2 = 4 => 9 pairs (_) / E3 = 4 => 9 pairs (_) D5,F6: 4.. / D5 = 4 => 0 pairs (X) / F6 = 4 => 0 pairs (_) C5,D5: 4.. / C5 = 4 => 0 pairs (*) / D5 = 4 => 0 pairs (X) A6,A8: 4.. / A6 = 4 => 0 pairs (X) / A8 = 4 => 0 pairs (_) F6,F7: 4.. / F6 = 4 => 0 pairs (*) / F7 = 4 => 0 pairs (X) F2,F3: 5.. / F2 = 5 => 7 pairs (_) / F3 = 5 => 7 pairs (_) G2,G3: 5.. / G2 = 5 => 7 pairs (_) / G3 = 5 => 7 pairs (_) F2,G2: 5.. / F2 = 5 => 7 pairs (_) / G2 = 5 => 7 pairs (_) F3,G3: 5.. / F3 = 5 => 7 pairs (_) / G3 = 5 => 7 pairs (_) B7,B9: 6.. / B7 = 6 => 13 pairs (_) / B9 = 6 => 8 pairs (_) C5,C6: 7.. / C5 = 7 => 0 pairs (X) / C6 = 7 => 8 pairs (_) E7,F7: 7.. / E7 = 7 => 0 pairs (X) / F7 = 7 => 0 pairs (_) F1,F7: 7.. / F1 = 7 => 0 pairs (X) / F7 = 7 => 0 pairs (_) A2,A3: 8.. / A2 = 8 => 7 pairs (_) / A3 = 8 => 7 pairs (_) F2,F3: 8.. / F2 = 8 => 7 pairs (_) / F3 = 8 => 7 pairs (_) A2,F2: 8.. / A2 = 8 => 7 pairs (_) / F2 = 8 => 7 pairs (_) A3,F3: 8.. / A3 = 8 => 7 pairs (_) / F3 = 8 => 7 pairs (_) C4,I4: 8.. / C4 = 8 => 0 pairs (X) / I4 = 8 => 9 pairs (_) A6,A8: 9.. / A6 = 9 => 0 pairs (*) / A8 = 9 => 0 pairs (X) * DURATION: 0:00:36.544990 START: 10:05:52.649540 END: 10:06:29.194530 2017-05-04 * CP COUNT: (25) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,A8,B5,C9,F2,F3,F4) * .45...382.392......263.....25.7..4..6...82.5....5...2.3.....2.5.72.53...5...21... * PAIR A1: 1,7 BLK 1 A2: 1,7,8 # reduction candidate for 1,7 A2: 1,7 # 7 pairs A3: 1,7,8 # reduction candidate for 1,7 A3: 1,7 # 7 pairs * PAIR A1: 1,7 ROW 1 E1: 1,7,6,9 # reduction candidate for 1,7 E1: 1,7 => CTR * .45...382.392......263.....25.7..4..6..182.5....5.4.2.3....72.5472.53...5.8.21... E1: 6,9 # 9 pairs * PAIR B5: 1,9 BLK 4 B6: 1,9,8 # reduction candidate for 1,9 B6: 1,9 => CTR * .451.7382.392......263.....25.7..4..6..482.5.4..5...2.3.1..42.5972.53...5.4.21... B6: 8 # 10 pairs * PAIR B5: 1,9 ROW 5 D5: 1,9,4 # reduction candidate for 1,9 D5: 1,9 => SOLVED * 745169382139278564826345971253716498614982753987534126361897245472653819598421637 D5: 4 => CTR * 7451..382.392......263.....25.7..4..6..482.5....5...2.3...742.5.72.53...5...21... G5: 1,9,7 # reduction candidate for 1,9 G5: 1,9 => CTR * 7451..382.392......263.....25.7..4..6..482.5....5...2.3...742.5.72.53...5...21... G5: 7 # 10 pairs I5: 1,9,3,7 # reduction candidate for 1,9 I5: 1,9 => CTR * .451.7382.392......263.....25.7..4..6.348275...75...2.3....42.5.72.53...5.4.21... I5: 3,7 # 9 pairs * PAIR B5: 1,9 COL B B7: 1,9,6,8 # reduction candidate for 1,9 B7: 6,8 # 10 pairs B7: 1,9 # 10 pairs * PAIR A6: 4,9 ROW 6 F6: 4,9,6 # reduction candidate for 4,9 F6: 6 => CTR * .4516.382.392......263.....25.7..4..6..482.5....5.6.2.3....42.5.72.53...5...21... F6: 4,9 # 10 pairs * PAIR F4: 6,9 BLK 5 E4: 6,9,1,3 # reduction candidate for 6,9 E4: 6,9 => CTR * .45...382.392......263.....25.7..4..6..182.5....534.2.3.....2.5472.53...5.8.21... E4: 1,3 # 9 pairs E6: 6,9,1,3 # reduction candidate for 6,9 E6: 6,9 => CTR * .45...382.392......263.....25.73.4..6..182.5....5.4.2.3.....2.5472.53...5.8.21.3. E6: 1,3 # 9 pairs F6: 6,9,4 # reduction candidate for 6,9 F6: 6,9 => CTR * .451.7382.392......263.....25.7..4..6..482.5....5...2.3....42.5.72.53...5...21... F6: 4 => SOLVED * 745169382139278564826345971253716498614982753987534126361897245472653819598421637 * PAIR F4: 6,9 ROW 4 H4: 6,9,1,3 # reduction candidate for 6,9 H4: 6,9 # 10 pairs I4: 6,9,1,3,8 # reduction candidate for 6,9 I4: 6,9 => CTR * .451.7382.392......263.....2587..4..6..482.5.4..5...2.3.1..42.5972.53...5.4.21... I4: 1,3,8 # 8 pairs * PAIR F4: 6,9 COL F F1: 6,9,7 # reduction candidate for 6,9 F1: 6,9 => SOLVED * 745169382139278564826345971253716498614982753987534126361897245472653819598421637 F1: 7 => CTR * 145..7382.392......263.....25.7..4..6..182.5....5.4.2.3...7.2.5472.53...5.8.21... F7: 6,9,4,7 # reduction candidate for 6,9 F7: 6,9 => CTR * 145..7382.392......263.....25.7..4.86.4182.539..5.4.2.3...7.2.5472.53...5.8.21... F7: 4,7 # 9 pairs * PAIR A8: 4,9 ROW 8 D8: 4,9,6,8 # reduction candidate for 4,9 D8: 4,9 # 12 pairs H8: 4,9,1,6 # reduction candidate for 4,9 H8: 4,9 # 10 pairs I8: 4,9,1,6,8 # reduction candidate for 4,9 I8: 4,9 # 11 pairs * PAIR C9: 4,8 BLK 7 C7: 4,8,1 # reduction candidate for 4,8 C7: 4,8 => CTR * 145..7382.392......263.....25.7..4.869.482.5.48.5...2.318.742.5972.53...564.21... C7: 1 # 9 pairs * PAIR C9: 4,8 ROW 9 D9: 4,8,6,9 # reduction candidate for 4,8 D9: 4,8 # 10 pairs I9: 4,8,3,6,7,9 # reduction candidate for 4,8 I9: 4,8 => CTR * 7451..382.392......263.....25.7..4..6..482.5....5...2.3...742.5.72.53...5...2173. I9: 3,6,7,9 # 8 pairs * PAIR C9: 4,8 COL C C6: 4,8,1,3,7 # reduction candidate for 4,8 C6: 4,8 => CTR * .451.7382.392......263.....25.7..4..6.7482.53...53..2.3....42.5.72.53...5...21.3. C6: 1,3,7 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-213-base-pr-000.dot * REASONING * DIS # E1: 1,7 => CTR => E1: 6,9 * DIS # B6: 1,9 => CTR => B6: 8 * PRF # D5: 1,9 => SOL * DIS # D5: 4 => CTR => D5: 1,9 * DIS # G5: 1,9 => CTR => G5: 7 * DIS # I5: 1,9 => CTR => I5: 3,7 * DIS # F6: 6 => CTR => F6: 4,9 * DIS # E4: 6,9 => CTR => E4: 1,3 * DIS # E6: 6,9 => CTR => E6: 1,3 * DIS # F6: 6,9 => CTR => F6: 4 * PRF # F6: 4 => SOL * DIS # I4: 6,9 => CTR => I4: 1,3,8 * PRF # F1: 6,9 => SOL * DIS # F1: 7 => CTR => F1: 6,9 * DIS # F7: 6,9 => CTR => F7: 4,7 * DIS # C7: 4,8 => CTR => C7: 1 * DIS # I9: 4,8 => CTR => I9: 3,6,7,9 * DIS # C6: 4,8 => CTR => C6: 1,3,7 * CNT 18 HDP CHAINS / 39 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,A8,B5,C9,F2,F3,F4) * .45...382.392......263.....25.7..4..6...82.5....5...2.3.....2.5.72.53...5...21... * PAIR A1: 1,7 BLK 1 A2: 1,7,8 # reduction candidate for 1,7 A2: 1,7 # 7 pairs A3: 1,7,8 # reduction candidate for 1,7 A3: 1,7 # 7 pairs * PAIR A1: 1,7 ROW 1 E1: 1,7,6,9 # reduction candidate for 1,7 E1: 1,7 => CTR * .45...382.392......263.....25.7..4..6..182.5....5.4.2.3....72.5472.53...5.8.21... * PAIR RESTART * PAIR A1: 1,7 BLK 1 A2: 1,7,8 # reduction candidate for 1,7 A2: 1,7 # 8 pairs A3: 1,7,8 # reduction candidate for 1,7 A3: 1,7 # 8 pairs * PAIR B5: 1,9 BLK 4 B6: 1,9,8 # reduction candidate for 1,9 B6: 1,9 => CTR * .451.7382.392......263.....25.7..4..6..482.5.4..5...2.3.1..42.5972.53...5.4.21... * PAIR B5: 1,9 ROW 5 D5: 1,9,4 # reduction candidate for 1,9 D5: 1,9 => SOLVED * 745169382139278564826345971253716498614982753987534126361897245472653819598421637 * DURATION: 0:00:08.429650 START: 10:06:59.584442 END: 10:07:08.014092 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-213-base-pr-001.dot * REASONING * DIS # E1: 1,7 => CTR => E1: 6,9 * DIS E1: 6,9 # B6: 1,9 => CTR => B6: 8 * PRF E1: 6,9 + B6: 8 # D5: 1,9 => SOL * STA E1: 6,9 + B6: 8 + D5: 1,9 * CNT 3 HDP CHAINS / 7 HYP OPENED
Header Info
Top 500 Minimum 17 213 solution: 745169382139278564826345971253716498614982753987534126361897245472653819598421637 info: 1945 FNBHWXY S8.f 19452 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 745169382139278564826345971253716498614982753987534126361897245472653819598421637 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 # A2: 1,7 => UNS * INC # A3: 1,7 => UNS * DIS # E1: 1,7 => CTR => E1: 6,9 * INC # E1: 6,9 => UNS * DIS # B6: 1,9 => CTR => B6: 8 * INC # B6: 8 => UNS * PRF # D5: 1,9 => SOL * DIS # D5: 4 => CTR => D5: 1,9 * DIS # G5: 1,9 => CTR => G5: 7 * INC # G5: 7 => UNS * DIS # I5: 1,9 => CTR => I5: 3,7 * INC # I5: 3,7 => UNS * INC # B7: 1,9 => UNS * INC # B7: 6,8 => UNS * INC # F6: 4,9 => UNS * DIS # F6: 6 => CTR => F6: 4,9 * DIS # E4: 6,9 => CTR => E4: 1,3 * INC # E4: 1,3 => UNS * DIS # E6: 6,9 => CTR => E6: 1,3 * INC # E6: 1,3 => UNS * DIS # F6: 6,9 => CTR => F6: 4 * PRF # F6: 4 => SOL * INC # H4: 6,9 => UNS * DIS # I4: 6,9 => CTR => I4: 1,3,8 * INC # I4: 1,3,8 => UNS * PRF # F1: 6,9 => SOL * DIS # F1: 7 => CTR => F1: 6,9 * DIS # F7: 6,9 => CTR => F7: 4,7 * INC # F7: 4,7 => UNS * INC # D8: 4,9 => UNS * INC # H8: 4,9 => UNS * INC # I8: 4,9 => UNS * DIS # C7: 4,8 => CTR => C7: 1 * INC # C7: 1 => UNS * INC # D9: 4,8 => UNS * DIS # I9: 4,8 => CTR => I9: 3,6,7,9 * INC # I9: 3,6,7,9 => UNS * DIS # C6: 4,8 => CTR => C6: 1,3,7 * INC # C6: 1,3,7 => UNS * CNT 39 HDP CHAINS / 39 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A2: 1,7 => UNS * INC # A3: 1,7 => UNS * DIS # E1: 1,7 => CTR => E1: 6,9 * INC E1: 6,9 # A2: 1,7 => UNS * INC E1: 6,9 # A3: 1,7 => UNS * DIS E1: 6,9 # B6: 1,9 => CTR => B6: 8 * PRF E1: 6,9 + B6: 8 # D5: 1,9 => SOL * STA E1: 6,9 + B6: 8 + D5: 1,9 * CNT 7 HDP CHAINS / 7 HYP OPENED