Analysis of xx-top500-288-base.sdk
Contents
Original Sudoku
level: medium
position: 2..7.5....6......1...4.....7.....84..3..6...........5...1.3.6..5........4........ initial
Autosolve
position: 2..7.536..6.....713.74.6...7.....84613..6....6.....153..1.3.6..5........4........ autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 8,9 => CTR => B1: 1,4 * DIS # B3: 8,9 => CTR => B3: 1,5 * DIS # C5: 8 => CTR => C5: 4,5 * PRF # C4: 5,9 => SOL * PRF # E4: 2 => SOL * DIS # B3: 5,9 => CTR => B3: 1,8 * DIS # C5: 5,8 => CTR => C5: 4 * DIS # D9: 5,8 => CTR => D9: 1,2,6,9 * DIS # F6: 4,8 => CTR => F6: 2,7,9 * DIS # C5: 5 => CTR => C5: 4,8 * DIS # F8: 4,8 => CTR => F8: 1,2,7,9 * DIS # B7: 8,9 => CTR => B7: 2,7 * DIS # D7: 8,9 => CTR => D7: 2,5 * DIS # F7: 8,9 => CTR => F7: 2,4,7 * DIS # I7: 8,9 => CTR => I7: 2,4,5,7 * CNT 15 HDP CHAINS / 44 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B1: 8,9 => CTR => B1: 1,4 * DIS B1: 1,4 # B3: 8,9 => CTR => B3: 1,5 * DIS B1: 1,4 + B3: 1,5 # C5: 8 => CTR => C5: 4,5 * PRF B1: 1,4 + B3: 1,5 + C5: 4,5 # E4: 2 => SOL * STA B1: 1,4 + B3: 1,5 + C5: 4,5 + E4: 2 * CNT 4 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 2..7.5....6......1...4.....7.....84..3..6...........5...1.3.6..5........4........ | initial |
| 2..7.536..6.....713.74.6...7.....84613..6....6.....153..1.3.6..5........4........ | autosolve |
| 248715369965382471317496582759123846134568927682947153871234695596871234423659718 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) A2: 8,9 C2: 4,5 G2: 4,5 B4: 5,9 D4: 1,3 F4: 1,3 D5: 5,8 F5: 4,8 H5: 2,9 A7: 8,9 C8: 3,6 C9: 3,6 H8: 1,3 H9: 1,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,B3: 1.. / B1 = 1 => 0 pairs (X) / B3 = 1 => 17 pairs (_) E1,E3: 1.. / E1 = 1 => 17 pairs (_) / E3 = 1 => 0 pairs (X) D4,F4: 1.. / D4 = 1 => 12 pairs (_) / F4 = 1 => 14 pairs (_) H8,H9: 1.. / H8 = 1 => 10 pairs (_) / H9 = 1 => 10 pairs (_) B1,E1: 1.. / B1 = 1 => 0 pairs (X) / E1 = 1 => 17 pairs (_) B3,E3: 1.. / B3 = 1 => 17 pairs (_) / E3 = 1 => 0 pairs (X) C4,C6: 2.. / C4 = 2 => 15 pairs (_) / C6 = 2 => 0 pairs (*) C4,E4: 2.. / C4 = 2 => 15 pairs (_) / E4 = 2 => 0 pairs (*) D2,F2: 3.. / D2 = 3 => 12 pairs (_) / F2 = 3 => 14 pairs (_) D4,F4: 3.. / D4 = 3 => 14 pairs (_) / F4 = 3 => 12 pairs (_) C8,C9: 3.. / C8 = 3 => 10 pairs (_) / C9 = 3 => 10 pairs (_) H8,H9: 3.. / H8 = 3 => 10 pairs (_) / H9 = 3 => 10 pairs (_) C8,H8: 3.. / C8 = 3 => 10 pairs (_) / H8 = 3 => 10 pairs (_) C9,H9: 3.. / C9 = 3 => 10 pairs (_) / H9 = 3 => 10 pairs (_) D2,D4: 3.. / D2 = 3 => 12 pairs (_) / D4 = 3 => 14 pairs (_) F2,F4: 3.. / F2 = 3 => 14 pairs (_) / F4 = 3 => 12 pairs (_) I1,G2: 4.. / I1 = 4 => 0 pairs (X) / G2 = 4 => 17 pairs (_) C2,G2: 4.. / C2 = 4 => 0 pairs (X) / G2 = 4 => 17 pairs (_) C5,F5: 4.. / C5 = 4 => 17 pairs (_) / F5 = 4 => 0 pairs (X) F7,I7: 4.. / F7 = 4 => 17 pairs (_) / I7 = 4 => 0 pairs (X) B1,B6: 4.. / B1 = 4 => 17 pairs (_) / B6 = 4 => 0 pairs (X) E6,E8: 4.. / E6 = 4 => 17 pairs (_) / E8 = 4 => 0 pairs (X) G2,G8: 4.. / G2 = 4 => 17 pairs (_) / G8 = 4 => 0 pairs (X) C2,B3: 5.. / C2 = 5 => 17 pairs (_) / B3 = 5 => 0 pairs (X) E4,D5: 5.. / E4 = 5 => 0 pairs (X) / D5 = 5 => 17 pairs (_) C2,G2: 5.. / C2 = 5 => 17 pairs (_) / G2 = 5 => 0 pairs (X) C5,D5: 5.. / C5 = 5 => 0 pairs (X) / D5 = 5 => 17 pairs (_) D7,I7: 5.. / D7 = 5 => 0 pairs (X) / I7 = 5 => 17 pairs (_) B3,B4: 5.. / B3 = 5 => 0 pairs (X) / B4 = 5 => 17 pairs (_) E4,E9: 5.. / E4 = 5 => 0 pairs (X) / E9 = 5 => 17 pairs (_) C8,C9: 6.. / C8 = 6 => 10 pairs (_) / C9 = 6 => 10 pairs (_) D8,D9: 6.. / D8 = 6 => 10 pairs (_) / D9 = 6 => 10 pairs (_) C8,D8: 6.. / C8 = 6 => 10 pairs (_) / D8 = 6 => 10 pairs (_) C9,D9: 6.. / C9 = 6 => 10 pairs (_) / D9 = 6 => 10 pairs (_) E6,F6: 7.. / E6 = 7 => 0 pairs (X) / F6 = 7 => 14 pairs (_) G5,I5: 7.. / G5 = 7 => 15 pairs (_) / I5 = 7 => 15 pairs (_) A2,A7: 8.. / A2 = 8 => 18 pairs (_) / A7 = 8 => 0 pairs (*) H3,H7: 8.. / H3 = 8 => 17 pairs (_) / H7 = 8 => 20 pairs (_) A2,A7: 9.. / A2 = 9 => 0 pairs (*) / A7 = 9 => 0 pairs (X) * DURATION: 0:01:21.608422 START: 12:46:59.191326 END: 12:48:20.799748 2017-05-04 * CP COUNT: (39) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,B4,C2,C8,C9,D4,D5,F4,F5,G2,H5,H8,H9) * 2..7.536..6.....713.74.6...7.....84613..6....6.....153..1.3.6..5........4........ * PAIR A2: 8,9 BLK 1 B1: 8,9,1,4 # reduction candidate for 8,9 B1: 8,9 => CTR * 2..71536..6.....713174.6...75....84613.56....64....153..1.3.6.55...4....4...5.... B1: 1,4 # 15 pairs C1: 8,9,4 # reduction candidate for 8,9 C1: 8,9 # 17 pairs B3: 8,9,1,5 # reduction candidate for 8,9 B3: 8,9 => CTR * 21.7.536..65...4713.7416...75....84613.56....64....153..1.3.6.55...4....4...5.... B3: 1,5 # 15 pairs * PAIR A2: 8,9 ROW 2 D2: 8,9,2,3 # reduction candidate for 8,9 D2: 8,9 # 16 pairs E2: 8,9,2 # reduction candidate for 8,9 E2: 8,9 # 19 pairs F2: 8,9,2,3 # reduction candidate for 8,9 F2: 8,9 # 14 pairs * PAIR C2: 4,5 COL C C5: 4,5,8 # reduction candidate for 4,5 C5: 8 => CTR * 2..7.536..6.....713.74.6...7.....846138564...6.....153..1.3.6..5........4........ C5: 4,5 # 20 pairs * PAIR B4: 5,9 BLK 4 C4: 5,9,2 # reduction candidate for 5,9 C4: 5,9 => SOLVED * 248715369965382471317496582759123846134568927682947153871234695596871234423659718 C4: 2 # 15 pairs * PAIR B4: 5,9 ROW 4 E4: 5,9,2 # reduction candidate for 5,9 E4: 2 => SOLVED * 248715369965382471317496582759123846134568927682947153871234695596871234423659718 E4: 5,9 # 15 pairs * PAIR B4: 5,9 COL B B3: 5,9,1,8 # reduction candidate for 5,9 B3: 5,9 => CTR * 2147.536.865...471397416...75....846138564...64....1539.1.3.6.45...4....4...5.... B3: 1,8 # 17 pairs * PAIR D5: 5,8 ROW 5 C5: 5,8,4 # reduction candidate for 5,8 C5: 5,8 => CTR * 2..7.536..65...4713.74.6...75....846138.64...6.....153..153.6.45...4....4........ C5: 4 # 17 pairs * PAIR D5: 5,8 COL D D7: 5,8,2,9 # reduction candidate for 5,8 D7: 5,8 # 16 pairs D9: 5,8,1,2,6,9 # reduction candidate for 5,8 D9: 5,8 => CTR * 24.71536.8653..4713174865..75.1.3846134568...698247153.71.3468558367..14426851.3. D9: 1,2,6,9 # 14 pairs * PAIR F5: 4,8 BLK 5 E6: 4,8,2,7,9 # reduction candidate for 4,8 E6: 4,8 # 17 pairs F6: 4,8,2,7,9 # reduction candidate for 4,8 F6: 4,8 => CTR * 2..7.536..65...4713.74.6...75....84613.56....6...7.153..1.3.6.45...4....4...5.... F6: 2,7,9 # 14 pairs * PAIR F5: 4,8 ROW 5 C5: 4,8,5 # reduction candidate for 4,8 C5: 5 => CTR * 2..7.536..6.....713.74.6...7.....846135864...6.....153..1.3.6.45...4....4........ C5: 4,8 # 17 pairs * PAIR F5: 4,8 COL F F7: 4,8,2,7,9 # reduction candidate for 4,8 F7: 4,8 # 15 pairs F8: 4,8,1,2,7,9 # reduction candidate for 4,8 F8: 4,8 => CTR * 2..7.536..65...4713.74.6...75....84613.864...6.....153..153.6.45........4........ F8: 1,2,7,9 # 14 pairs * PAIR H5: 2,9 BLK 6 G5: 2,9,7 # reduction candidate for 2,9 G5: 2,9 # 15 pairs I5: 2,9,7 # reduction candidate for 2,9 I5: 2,9 # 15 pairs * PAIR H5: 2,9 COL H H3: 2,9,8 # reduction candidate for 2,9 H3: 2,9 # 20 pairs H7: 2,9,8 # reduction candidate for 2,9 H7: 2,9 # 17 pairs * PAIR A7: 8,9 BLK 7 B7: 8,9,2,7 # reduction candidate for 8,9 B7: 8,9 => CTR * 2..7.536..6.....713.74.6.8.7...5.846135864.9.6.....153..15376245...4....4........ B7: 2,7 # 15 pairs B8: 8,9,2,7 # reduction candidate for 8,9 B8: 8,9 # 17 pairs B9: 8,9,2,7 # reduction candidate for 8,9 B9: 8,9 # 17 pairs * PAIR A7: 8,9 ROW 7 D7: 8,9,2,5 # reduction candidate for 8,9 D7: 8,9 => CTR * 248715369965.8.471317496582759.2.846134568297682947153871.346255...7.9.44...5.7.8 D7: 2,5 # 15 pairs F7: 8,9,2,4,7 # reduction candidate for 8,9 F7: 8,9 => CTR * 2..7.536..65...4713.74.6.8.75....84613.864...6.....153.7153.6245........4........ F7: 2,4,7 # 14 pairs H7: 8,9,2 # reduction candidate for 8,9 H7: 8,9 # 17 pairs I7: 8,9,2,4,5,7 # reduction candidate for 8,9 I7: 8,9 => CTR * 2..7.536..6.....713.74.6...7.....84613..6....6.....153..15346..5........4........ I7: 2,4,5,7 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-288-base-pr-000.dot * REASONING * DIS # B1: 8,9 => CTR => B1: 1,4 * DIS # B3: 8,9 => CTR => B3: 1,5 * DIS # C5: 8 => CTR => C5: 4,5 * PRF # C4: 5,9 => SOL * PRF # E4: 2 => SOL * DIS # B3: 5,9 => CTR => B3: 1,8 * DIS # C5: 5,8 => CTR => C5: 4 * DIS # D9: 5,8 => CTR => D9: 1,2,6,9 * DIS # F6: 4,8 => CTR => F6: 2,7,9 * DIS # C5: 5 => CTR => C5: 4,8 * DIS # F8: 4,8 => CTR => F8: 1,2,7,9 * DIS # B7: 8,9 => CTR => B7: 2,7 * DIS # D7: 8,9 => CTR => D7: 2,5 * DIS # F7: 8,9 => CTR => F7: 2,4,7 * DIS # I7: 8,9 => CTR => I7: 2,4,5,7 * CNT 15 HDP CHAINS / 44 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,B4,C2,C8,C9,D4,D5,F4,F5,G2,H5,H8,H9) * 2..7.536..6.....713.74.6...7.....84613..6....6.....153..1.3.6..5........4........ * PAIR A2: 8,9 BLK 1 B1: 8,9,1,4 # reduction candidate for 8,9 B1: 8,9 => CTR * 2..71536..6.....713174.6...75....84613.56....64....153..1.3.6.55...4....4...5.... C1: 8,9,4 # reduction candidate for 8,9 C1: 8,9 # 17 pairs B3: 8,9,1,5 # reduction candidate for 8,9 B3: 8,9 => CTR * 21.7.536..65...4713.7416...75....84613.56....64....153..1.3.6.55...4....4...5.... * RESTART * PAIR A2: 8,9 ROW 2 D2: 8,9,2,3 # reduction candidate for 8,9 D2: 8,9 # 19 pairs E2: 8,9,2 # reduction candidate for 8,9 E2: 8,9 # 22 pairs F2: 8,9,2,3 # reduction candidate for 8,9 F2: 8,9 # 17 pairs * PAIR C2: 4,5 COL C C5: 4,5,8 # reduction candidate for 4,5 C5: 8 => CTR * 2..7.536..6.....713.74.6...7.....846138564...6.....153..1.3.6..5........4........ * PAIR RESTART * PAIR B4: 5,9 ROW 4 E4: 5,9,2 # reduction candidate for 5,9 E4: 2 => SOLVED * 248715369965382471317496582759123846134568927682947153871234695596871234423659718 * DURATION: 0:00:12.644930 START: 12:49:09.161045 END: 12:49:21.805975 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-288-base-pr-001.dot * REASONING * DIS # B1: 8,9 => CTR => B1: 1,4 * DIS B1: 1,4 # B3: 8,9 => CTR => B3: 1,5 * DIS B1: 1,4 + B3: 1,5 # C5: 8 => CTR => C5: 4,5 * PRF B1: 1,4 + B3: 1,5 + C5: 4,5 # E4: 2 => SOL * STA B1: 1,4 + B3: 1,5 + C5: 4,5 + E4: 2 * CNT 4 HDP CHAINS / 10 HYP OPENED
Header Info
Top 500 Minimum 17 288 solution: 248715369965382471317496582759123846134568927682947153871234695596871234423659718 info: 2351 FNBTHWX S8.f 27906 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 248715369965382471317496582759123846134568927682947153871234695596871234423659718 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 # B1: 8,9 => CTR => B1: 1,4 * INC # B1: 1,4 => UNS * INC # C1: 8,9 => UNS * DIS # B3: 8,9 => CTR => B3: 1,5 * INC # B3: 1,5 => UNS * INC # D2: 8,9 => UNS * INC # E2: 8,9 => UNS * INC # F2: 8,9 => UNS * INC # C5: 4,5 => UNS * DIS # C5: 8 => CTR => C5: 4,5 * PRF # C4: 5,9 => SOL * INC # C4: 2 => UNS * INC # E4: 5,9 => UNS * PRF # E4: 2 => SOL * DIS # B3: 5,9 => CTR => B3: 1,8 * INC # B3: 1,8 => UNS * DIS # C5: 5,8 => CTR => C5: 4 * INC # C5: 4 => UNS * INC # D7: 5,8 => UNS * DIS # D9: 5,8 => CTR => D9: 1,2,6,9 * INC # D9: 1,2,6,9 => UNS * INC # E6: 4,8 => UNS * DIS # F6: 4,8 => CTR => F6: 2,7,9 * INC # F6: 2,7,9 => UNS * INC # C5: 4,8 => UNS * DIS # C5: 5 => CTR => C5: 4,8 * INC # F7: 4,8 => UNS * DIS # F8: 4,8 => CTR => F8: 1,2,7,9 * INC # F8: 1,2,7,9 => UNS * INC # G5: 2,9 => UNS * INC # I5: 2,9 => UNS * INC # H3: 2,9 => UNS * INC # H7: 2,9 => UNS * DIS # B7: 8,9 => CTR => B7: 2,7 * INC # B7: 2,7 => UNS * INC # B8: 8,9 => UNS * INC # B9: 8,9 => UNS * DIS # D7: 8,9 => CTR => D7: 2,5 * INC # D7: 2,5 => UNS * DIS # F7: 8,9 => CTR => F7: 2,4,7 * INC # F7: 2,4,7 => UNS * INC # H7: 8,9 => UNS * DIS # I7: 8,9 => CTR => I7: 2,4,5,7 * INC # I7: 2,4,5,7 => UNS * CNT 44 HDP CHAINS / 44 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B1: 8,9 => CTR => B1: 1,4 * INC B1: 1,4 # C1: 8,9 => UNS * DIS B1: 1,4 # B3: 8,9 => CTR => B3: 1,5 * INC B1: 1,4 + B3: 1,5 # D2: 8,9 => UNS * INC B1: 1,4 + B3: 1,5 # E2: 8,9 => UNS * INC B1: 1,4 + B3: 1,5 # F2: 8,9 => UNS * INC B1: 1,4 + B3: 1,5 # C5: 4,5 => UNS * DIS B1: 1,4 + B3: 1,5 # C5: 8 => CTR => C5: 4,5 * INC B1: 1,4 + B3: 1,5 + C5: 4,5 # E4: 5,9 => UNS * PRF B1: 1,4 + B3: 1,5 + C5: 4,5 # E4: 2 => SOL * STA B1: 1,4 + B3: 1,5 + C5: 4,5 + E4: 2 * CNT 10 HDP CHAINS / 10 HYP OPENED