Analysis of xx-top500-003-base.sdk
Contents
Original Sudoku
level: medium
position: 7..1........7..3.......84..2......5.....3.6..1.........6.....1..3..4.......5...7. initial
Autosolve
position: 7.4163..565.7.43.131..58467243679158.75.3164.1.64.573..673.2.14.31.47..64..516.73 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C2: 2,9 => SOL * PRF # C9: 8 => SOL * PRF # C2: 2,9 => SOL * DIS # B9: 8,9 => CTR => B9: 2 * DIS # B9: 8,9 => CTR => B9: 2 * CNT 5 HDP CHAINS / 26 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C2: 2,9 => SOL * STA C2: 2,9 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 7..1........7..3.......84..2......5.....3.6..1.........6.....1..3..4.......5...7. | initial |
| 7.4163..565.7.43.131..58467243679158.75.3164.1.64.573..673.2.14.31.47..64..516.73 | autosolve |
| 784163295659724381312958467243679158875231649196485732567392814931847526428516973 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) C3: 2,9 E2: 2,9 D3: 2,9 A5: 8,9 B6: 8,9 D5: 2,8 E6: 2,8 I5: 2,9 I6: 2,9 E7: 8,9 D8: 8,9 G9: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,D3: 2.. / E2 = 2 => 0 pairs (*) / D3 = 2 => 0 pairs (X) D5,E6: 2.. / D5 = 2 => 0 pairs (*) / E6 = 2 => 0 pairs (X) I5,I6: 2.. / I5 = 2 => 0 pairs (X) / I6 = 2 => 0 pairs (_) B9,C9: 2.. / B9 = 2 => 15 pairs (_) / C9 = 2 => 0 pairs (X) G8,H8: 2.. / G8 = 2 => 15 pairs (_) / H8 = 2 => 16 pairs (_) C3,D3: 2.. / C3 = 2 => 0 pairs (*) / D3 = 2 => 0 pairs (X) D5,I5: 2.. / D5 = 2 => 0 pairs (*) / I5 = 2 => 0 pairs (X) E6,I6: 2.. / E6 = 2 => 0 pairs (X) / I6 = 2 => 0 pairs (_) B1,B9: 2.. / B1 = 2 => 0 pairs (X) / B9 = 2 => 15 pairs (_) D3,D5: 2.. / D3 = 2 => 0 pairs (X) / D5 = 2 => 0 pairs (_) E2,E6: 2.. / E2 = 2 => 0 pairs (*) / E6 = 2 => 0 pairs (X) G1,G8: 2.. / G1 = 2 => 16 pairs (_) / G8 = 2 => 15 pairs (_) A7,A8: 5.. / A7 = 5 => 18 pairs (_) / A8 = 5 => 13 pairs (_) G7,G8: 5.. / G7 = 5 => 13 pairs (_) / G8 = 5 => 18 pairs (_) A7,G7: 5.. / A7 = 5 => 18 pairs (_) / G7 = 5 => 13 pairs (_) A8,G8: 5.. / A8 = 5 => 13 pairs (_) / G8 = 5 => 18 pairs (_) B1,C2: 8.. / B1 = 8 => 0 pairs (*) / C2 = 8 => 0 pairs (X) A5,B6: 8.. / A5 = 8 => 0 pairs (*) / B6 = 8 => 0 pairs (X) D5,E6: 8.. / D5 = 8 => 0 pairs (X) / E6 = 8 => 0 pairs (_) E7,D8: 8.. / E7 = 8 => 0 pairs (X) / D8 = 8 => 0 pairs (_) C2,H2: 8.. / C2 = 8 => 15 pairs (_) / H2 = 8 => 0 pairs (*) A5,D5: 8.. / A5 = 8 => 0 pairs (*) / D5 = 8 => 0 pairs (X) B6,E6: 8.. / B6 = 8 => 0 pairs (X) / E6 = 8 => 0 pairs (_) C2,C9: 8.. / C2 = 8 => 15 pairs (_) / C9 = 8 => 0 pairs (*) D5,D8: 8.. / D5 = 8 => 0 pairs (X) / D8 = 8 => 0 pairs (_) E6,E7: 8.. / E6 = 8 => 0 pairs (*) / E7 = 8 => 0 pairs (X) E2,D3: 9.. / E2 = 9 => 0 pairs (X) / D3 = 9 => 0 pairs (_) A5,B6: 9.. / A5 = 9 => 0 pairs (X) / B6 = 9 => 0 pairs (_) I5,I6: 9.. / I5 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) E7,D8: 9.. / E7 = 9 => 0 pairs (*) / D8 = 9 => 0 pairs (X) C3,D3: 9.. / C3 = 9 => 0 pairs (X) / D3 = 9 => 0 pairs (_) A5,I5: 9.. / A5 = 9 => 0 pairs (X) / I5 = 9 => 0 pairs (_) B6,I6: 9.. / B6 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) D3,D8: 9.. / D3 = 9 => 0 pairs (*) / D8 = 9 => 0 pairs (X) E2,E7: 9.. / E2 = 9 => 0 pairs (X) / E7 = 9 => 0 pairs (_) * DURATION: 0:01:02.935034 START: 02:41:04.936990 END: 02:42:07.872024 2017-05-04 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B6,C3,D3,D5,D8,E2,E6,E7,G9,I5,I6) * 7.4163..565.7.43.131..58467243679158.75.3164.1.64.573..673.2.14.31.47..64..516.73 * PAIR C3: 2,9 BLK 1 B1: 2,9,8 # reduction candidate for 2,9 B1: 2,9 # 15 pairs C2: 2,9,8 # reduction candidate for 2,9 C2: 2,9 => SOLVED * 784163295659724381312958467243679158875231649196485732567392814931847526428516973 C2: 8 # 15 pairs * PAIR C3: 2,9 COL C C9: 2,9,8 # reduction candidate for 2,9 C9: 8 => SOLVED * 784163295659724381312958467243679158875231649196485732567392814931847526428516973 C9: 2,9 # 15 pairs * PAIR E2: 2,9 ROW 2 C2: 2,9,8 # reduction candidate for 2,9 C2: 2,9 => SOLVED * 784163295659724381312958467243679158875231649196485732567392814931847526428516973 C2: 8 # 15 pairs H2: 2,9,8 # reduction candidate for 2,9 H2: 2,9 # 15 pairs * PAIR A5: 8,9 COL A A7: 8,9,5 # reduction candidate for 8,9 A7: 8,9 # 13 pairs A8: 8,9,5 # reduction candidate for 8,9 A8: 8,9 # 18 pairs * PAIR B6: 8,9 COL B B1: 8,9,2 # reduction candidate for 8,9 B1: 8,9 # 15 pairs B9: 8,9,2 # reduction candidate for 8,9 B9: 8,9 => CTR * 724163..56587.4321319258467243679158.75831642186425739.67382.14831947..64..516.73 B9: 2 # 15 pairs * PAIR E7: 8,9 ROW 7 A7: 8,9,5 # reduction candidate for 8,9 A7: 8,9 # 13 pairs G7: 8,9,5 # reduction candidate for 8,9 G7: 8,9 # 18 pairs * PAIR D8: 8,9 ROW 8 A8: 8,9,5 # reduction candidate for 8,9 A8: 8,9 # 18 pairs G8: 8,9,2,5 # reduction candidate for 8,9 G8: 8,9 # 18 pairs H8: 8,9,2 # reduction candidate for 8,9 H8: 8,9 # 15 pairs * PAIR G9: 8,9 BLK 9 G7: 8,9,5 # reduction candidate for 8,9 G7: 8,9 # 18 pairs G8: 8,9,2,5 # reduction candidate for 8,9 G8: 8,9 # 18 pairs H8: 8,9,2 # reduction candidate for 8,9 H8: 8,9 # 15 pairs * PAIR G9: 8,9 ROW 9 B9: 8,9,2 # reduction candidate for 8,9 B9: 8,9 => CTR * 724163..56587.4321319258467243679158.75831642186425739.67382.14831947..64..516.73 B9: 2 # 15 pairs C9: 8,9,2 # reduction candidate for 8,9 C9: 8,9 # 15 pairs * PAIR G9: 8,9 COL G G1: 8,9,2 # reduction candidate for 8,9 G1: 2 # 16 pairs G1: 8,9 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-003-base-pr-000.dot * REASONING * PRF # C2: 2,9 => SOL * PRF # C9: 8 => SOL * PRF # C2: 2,9 => SOL * DIS # B9: 8,9 => CTR => B9: 2 * DIS # B9: 8,9 => CTR => B9: 2 * CNT 5 HDP CHAINS / 26 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B6,C3,D3,D5,D8,E2,E6,E7,G9,I5,I6) * 7.4163..565.7.43.131..58467243679158.75.3164.1.64.573..673.2.14.31.47..64..516.73 * PAIR C3: 2,9 BLK 1 B1: 2,9,8 # reduction candidate for 2,9 B1: 2,9 # 15 pairs C2: 2,9,8 # reduction candidate for 2,9 C2: 2,9 => SOLVED * 784163295659724381312958467243679158875231649196485732567392814931847526428516973 * DURATION: 0:00:02.843571 START: 02:42:35.112579 END: 02:42:37.956150 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-003-base-pr-001.dot * REASONING * PRF # C2: 2,9 => SOL * STA C2: 2,9 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 003 solution: 784163295659724381312958467243679158875231649196485732567392814931847526428516973 info: 1305 FNBWXY S8.f 36787 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 784163295659724381312958467243679158875231649196485732567392814931847526428516973 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 # B1: 2,9 => UNS * PRF # C2: 2,9 => SOL * INC # C2: 8 => UNS * INC # C9: 2,9 => UNS * PRF # C9: 8 => SOL * PRF # C2: 2,9 => SOL * INC # C2: 8 => UNS * INC # H2: 2,9 => UNS * INC # A7: 8,9 => UNS * INC # A8: 8,9 => UNS * INC # B1: 8,9 => UNS * DIS # B9: 8,9 => CTR => B9: 2 * INC # B9: 2 => UNS * INC # A7: 8,9 => UNS * INC # G7: 8,9 => UNS * INC # A8: 8,9 => UNS * INC # G8: 8,9 => UNS * INC # H8: 8,9 => UNS * INC # G7: 8,9 => UNS * INC # G8: 8,9 => UNS * INC # H8: 8,9 => UNS * DIS # B9: 8,9 => CTR => B9: 2 * INC # B9: 2 => UNS * INC # C9: 8,9 => UNS * INC # G1: 8,9 => UNS * INC # G1: 2 => UNS * CNT 26 HDP CHAINS / 26 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 2,9 => UNS * PRF # C2: 2,9 => SOL * STA C2: 2,9 * CNT 2 HDP CHAINS / 2 HYP OPENED