Analysis of xx-top500-042-base.sdk
Contents
Original Sudoku
level: medium
position: ..26...3.4...7.................1.7.5.34............1.....3.2.6.75..........8..... initial
Autosolve
position: .726.153.4.357..1.61523..7.26..137.51347.5...5.7...1.3.41352.6775.1..3..32.8.7.51 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C8: 6 => CTR => C8: 8,9 * PRF # E6: 6 => SOL * DIS # H5: 2,8 => CTR => H5: 9 * PRF # E6: 6,8 => SOL * PRF # H6: 2 => SOL * DIS # C8: 6 => CTR => C8: 8,9 * PRF # C8: 6,9 => SOL * DIS # E9: 4 => CTR => E9: 6,9 * DIS # G3: 4 => CTR => G3: 8,9 * DIS # E9: 6 => CTR => E9: 4,9 * PRF # G3: 8 => SOL * CNT 11 HDP CHAINS / 35 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C8: 6 => CTR => C8: 8,9 * PRF C8: 8,9 # E6: 6 => SOL * STA C8: 8,9 + E6: 6 * CNT 2 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..26...3.4...7.................1.7.5.34............1.....3.2.6.75..........8..... | initial |
| .726.153.4.357..1.61523..7.26..137.51347.5...5.7...1.3.41352.6775.1..3..32.8.7.51 | autosolve |
| 972681534483579216615234879268913745134725698597468123841352967759146382326897451 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) A1: 8,9 B2: 8,9 F2: 8,9 G2: 2,6 I2: 2,6 C4: 8,9 B6: 8,9 D4: 4,9 E5: 2,8 D6: 4,9 F6: 6,8 H4: 4,8 G5: 2,6 A7: 8,9 C9: 6,9 G7: 8,9 G9: 4,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G2,I2: 2.. / G2 = 2 => 14 pairs (_) / I2 = 2 => 15 pairs (_) E5,E6: 2.. / E5 = 2 => 0 pairs (*) / E6 = 2 => 0 pairs (X) H8,I8: 2.. / H8 = 2 => 19 pairs (_) / I8 = 2 => 17 pairs (_) E6,H6: 2.. / E6 = 2 => 20 pairs (_) / H6 = 2 => 0 pairs (*) G2,G5: 2.. / G2 = 2 => 14 pairs (_) / G5 = 2 => 15 pairs (_) E1,F3: 4.. / E1 = 4 => 21 pairs (_) / F3 = 4 => 21 pairs (_) D4,D6: 4.. / D4 = 4 => 12 pairs (_) / D6 = 4 => 0 pairs (*) H4,H6: 4.. / H4 = 4 => 0 pairs (*) / H6 = 4 => 0 pairs (X) I8,G9: 4.. / I8 = 4 => 0 pairs (X) / G9 = 4 => 18 pairs (_) E1,I1: 4.. / E1 = 4 => 21 pairs (_) / I1 = 4 => 21 pairs (_) D4,H4: 4.. / D4 = 4 => 12 pairs (_) / H4 = 4 => 0 pairs (*) D6,H6: 4.. / D6 = 4 => 0 pairs (*) / H6 = 4 => 0 pairs (X) E9,G9: 4.. / E9 = 4 => 0 pairs (X) / G9 = 4 => 18 pairs (_) F3,F8: 4.. / F3 = 4 => 21 pairs (_) / F8 = 4 => 21 pairs (_) G3,G9: 4.. / G3 = 4 => 0 pairs (X) / G9 = 4 => 18 pairs (_) G2,I2: 6.. / G2 = 6 => 15 pairs (_) / I2 = 6 => 14 pairs (_) E6,F6: 6.. / E6 = 6 => 0 pairs (*) / F6 = 6 => 0 pairs (X) G5,I5: 6.. / G5 = 6 => 14 pairs (_) / I5 = 6 => 15 pairs (_) C8,C9: 6.. / C8 = 6 => 0 pairs (X) / C9 = 6 => 18 pairs (_) C9,E9: 6.. / C9 = 6 => 18 pairs (_) / E9 = 6 => 0 pairs (X) F6,F8: 6.. / F6 = 6 => 19 pairs (_) / F8 = 6 => 0 pairs (*) G2,G5: 6.. / G2 = 6 => 15 pairs (_) / G5 = 6 => 14 pairs (_) I2,I5: 6.. / I2 = 6 => 14 pairs (_) / I5 = 6 => 15 pairs (_) A1,B2: 8.. / A1 = 8 => 12 pairs (_) / B2 = 8 => 0 pairs (*) C4,B6: 8.. / C4 = 8 => 0 pairs (*) / B6 = 8 => 0 pairs (X) A7,C8: 8.. / A7 = 8 => 0 pairs (*) / C8 = 8 => 0 pairs (X) B2,F2: 8.. / B2 = 8 => 0 pairs (*) / F2 = 8 => 0 pairs (X) C4,H4: 8.. / C4 = 8 => 0 pairs (*) / H4 = 8 => 0 pairs (X) A7,G7: 8.. / A7 = 8 => 0 pairs (*) / G7 = 8 => 0 pairs (X) A1,A7: 8.. / A1 = 8 => 12 pairs (_) / A7 = 8 => 0 pairs (*) B2,B6: 8.. / B2 = 8 => 0 pairs (*) / B6 = 8 => 0 pairs (X) C4,C8: 8.. / C4 = 8 => 0 pairs (*) / C8 = 8 => 0 pairs (X) G3,G7: 8.. / G3 = 8 => 0 pairs (*) / G7 = 8 => 0 pairs (X) A1,B2: 9.. / A1 = 9 => 0 pairs (*) / B2 = 9 => 0 pairs (X) C4,B6: 9.. / C4 = 9 => 12 pairs (_) / B6 = 9 => 0 pairs (*) D4,D6: 9.. / D4 = 9 => 0 pairs (*) / D6 = 9 => 0 pairs (X) H5,I5: 9.. / H5 = 9 => 18 pairs (_) / I5 = 9 => 0 pairs (X) B2,F2: 9.. / B2 = 9 => 12 pairs (_) / F2 = 9 => 0 pairs (*) C4,D4: 9.. / C4 = 9 => 12 pairs (_) / D4 = 9 => 0 pairs (*) B6,D6: 9.. / B6 = 9 => 0 pairs (*) / D6 = 9 => 0 pairs (X) A7,G7: 9.. / A7 = 9 => 12 pairs (_) / G7 = 9 => 0 pairs (*) A1,A7: 9.. / A1 = 9 => 0 pairs (*) / A7 = 9 => 0 pairs (X) B2,B6: 9.. / B2 = 9 => 12 pairs (_) / B6 = 9 => 0 pairs (*) H5,H8: 9.. / H5 = 9 => 18 pairs (_) / H8 = 9 => 0 pairs (X) * DURATION: 0:01:21.087541 START: 04:06:15.628698 END: 04:07:36.716239 2017-05-04 * CP COUNT: (44) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A7,B2,B6,C4,C9,D4,D6,E5,F2,F6,G2,G5,G7,G9,H4,I2) * .726.153.4.357..1.61523..7.26..137.51347.5...5.7...1.3.41352.6775.1..3..32.8.7.51 * PAIR A1: 8,9 ROW 1 E1: 8,9,4 # reduction candidate for 8,9 E1: 8,9 # 21 pairs I1: 8,9,4 # reduction candidate for 8,9 I1: 8,9 # 21 pairs * PAIR F2: 8,9 BLK 2 E1: 8,9,4 # reduction candidate for 8,9 E1: 8,9 # 21 pairs F3: 8,9,4 # reduction candidate for 8,9 F3: 8,9 # 21 pairs * PAIR I2: 2,6 COL I I5: 2,6,8,9 # reduction candidate for 2,6 I5: 2,6 # 19 pairs I5: 8,9 # 17 pairs * PAIR C4: 8,9 COL C C8: 8,9,6 # reduction candidate for 8,9 C8: 6 => CTR * 9726.153.483579.1.61523.8792689137451347.5.9.5974..1.38413529677561..3..329867451 C8: 8,9 # 18 pairs * PAIR E5: 2,8 BLK 5 E6: 2,8,6 # reduction candidate for 2,8 E6: 6 => SOLVED * 972681534483579216615234879268913745134725698597468123841352967759146382326897451 E6: 2,8 # 19 pairs * PAIR E5: 2,8 ROW 5 H5: 2,8,9 # reduction candidate for 2,8 H5: 2,8 => CTR * 9726.153.48357921661523.97.26..137.51347.5..95.7...1.3.41352.6775.1..39232.897451 H5: 9 # 18 pairs I5: 2,8,6,9 # reduction candidate for 2,8 I5: 2,8 # 16 pairs * PAIR F6: 6,8 BLK 5 E6: 6,8,2 # reduction candidate for 6,8 E6: 6,8 => SOLVED * 972681534483579216615234879268913745134725698597468123841352967759146382326897451 E6: 2 # 20 pairs * PAIR H4: 4,8 BLK 6 H6: 4,8,2 # reduction candidate for 4,8 H6: 2 => SOLVED * 972681534483579216615234879268913745134725698597468123841352967759146382326897451 H6: 4,8 # 20 pairs * PAIR G5: 2,6 BLK 6 I5: 2,6,8,9 # reduction candidate for 2,6 I5: 2,6 # 19 pairs I5: 8,9 # 17 pairs * PAIR A7: 8,9 BLK 7 C8: 8,9,6 # reduction candidate for 8,9 C8: 6 => CTR * 9726.153.483579.1.61523.8792689137451347.5.9.5974..1.38413529677561..3..329867451 C8: 8,9 # 18 pairs * PAIR C9: 6,9 BLK 7 C8: 6,9,8 # reduction candidate for 6,9 C8: 6,9 => SOLVED * 972681534483579216615234879268913745134725698597468123841352967759146382326897451 C8: 8 # 12 pairs * PAIR C9: 6,9 ROW 9 E9: 6,9,4 # reduction candidate for 6,9 E9: 4 => CTR * .726.15344.357..1.61523487.26..137.51347.5...5.7...1.3.41352.6775.1..3..326847951 E9: 6,9 # 18 pairs * PAIR G7: 8,9 BLK 9 H8: 8,9,2 # reduction candidate for 8,9 H8: 8,9 # 17 pairs I8: 8,9,2,4 # reduction candidate for 8,9 I8: 8,9 # 21 pairs * PAIR G7: 8,9 COL G G3: 8,9,4 # reduction candidate for 8,9 G3: 4 => CTR * .726.153.4.357..1.61523.47.26..137.51347.5...5.7...1.3.413528677581.43..326897.51 G3: 8,9 # 18 pairs * PAIR G9: 4,9 BLK 9 I8: 4,9,2,8 # reduction candidate for 4,9 I8: 2,8 # 19 pairs I8: 4,9 # 12 pairs * PAIR G9: 4,9 ROW 9 E9: 4,9,6 # reduction candidate for 4,9 E9: 6 => CTR * 9726.153.483579.1.61523897.26..137.51347.5...5.7..61.3.41352.677561..3..329867451 E9: 4,9 # 18 pairs * PAIR G9: 4,9 COL G G3: 4,9,8 # reduction candidate for 4,9 G3: 8 => SOLVED * 972681534483579216615234879268913745134725698597468123841352967759146382326897451 G3: 4,9 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-042-base-pr-000.dot * REASONING * DIS # C8: 6 => CTR => C8: 8,9 * PRF # E6: 6 => SOL * DIS # H5: 2,8 => CTR => H5: 9 * PRF # E6: 6,8 => SOL * PRF # H6: 2 => SOL * DIS # C8: 6 => CTR => C8: 8,9 * PRF # C8: 6,9 => SOL * DIS # E9: 4 => CTR => E9: 6,9 * DIS # G3: 4 => CTR => G3: 8,9 * DIS # E9: 6 => CTR => E9: 4,9 * PRF # G3: 8 => SOL * CNT 11 HDP CHAINS / 35 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A7,B2,B6,C4,C9,D4,D6,E5,F2,F6,G2,G5,G7,G9,H4,I2) * .726.153.4.357..1.61523..7.26..137.51347.5...5.7...1.3.41352.6775.1..3..32.8.7.51 * PAIR A1: 8,9 ROW 1 E1: 8,9,4 # reduction candidate for 8,9 E1: 8,9 # 21 pairs I1: 8,9,4 # reduction candidate for 8,9 I1: 8,9 # 21 pairs * PAIR F2: 8,9 BLK 2 E1: 8,9,4 # reduction candidate for 8,9 E1: 8,9 # 21 pairs F3: 8,9,4 # reduction candidate for 8,9 F3: 8,9 # 21 pairs * PAIR I2: 2,6 COL I I5: 2,6,8,9 # reduction candidate for 2,6 I5: 2,6 # 19 pairs I5: 8,9 # 17 pairs * PAIR C4: 8,9 COL C C8: 8,9,6 # reduction candidate for 8,9 C8: 6 => CTR * 9726.153.483579.1.61523.8792689137451347.5.9.5974..1.38413529677561..3..329867451 * PAIR RESTART * PAIR E5: 2,8 BLK 5 E6: 2,8,6 # reduction candidate for 2,8 E6: 6 => SOLVED * 972681534483579216615234879268913745134725698597468123841352967759146382326897451 * DURATION: 0:00:11.299279 START: 04:08:14.702671 END: 04:08:26.001950 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-042-base-pr-001.dot * REASONING * DIS # C8: 6 => CTR => C8: 8,9 * PRF C8: 8,9 # E6: 6 => SOL * STA C8: 8,9 + E6: 6 * CNT 2 HDP CHAINS / 10 HYP OPENED
Header Info
Top 500 Minimum 17 042 solution: 972681534483579216615234879268913745134725698597468123841352967759146382326897451 info: 1374 FNBTHWX S8.f 13330 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 972681534483579216615234879268913745134725698597468123841352967759146382326897451 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 # E1: 8,9 => UNS * INC # I1: 8,9 => UNS * INC # E1: 8,9 => UNS * INC # F3: 8,9 => UNS * INC # I5: 2,6 => UNS * INC # I5: 8,9 => UNS * INC # C8: 8,9 => UNS * DIS # C8: 6 => CTR => C8: 8,9 * INC # E6: 2,8 => UNS * PRF # E6: 6 => SOL * DIS # H5: 2,8 => CTR => H5: 9 * INC # H5: 9 => UNS * INC # I5: 2,8 => UNS * PRF # E6: 6,8 => SOL * INC # E6: 2 => UNS * INC # H6: 4,8 => UNS * PRF # H6: 2 => SOL * INC # I5: 2,6 => UNS * INC # I5: 8,9 => UNS * INC # C8: 8,9 => UNS * DIS # C8: 6 => CTR => C8: 8,9 * PRF # C8: 6,9 => SOL * INC # C8: 8 => UNS * INC # E9: 6,9 => UNS * DIS # E9: 4 => CTR => E9: 6,9 * INC # H8: 8,9 => UNS * INC # I8: 8,9 => UNS * INC # G3: 8,9 => UNS * DIS # G3: 4 => CTR => G3: 8,9 * INC # I8: 4,9 => UNS * INC # I8: 2,8 => UNS * INC # E9: 4,9 => UNS * DIS # E9: 6 => CTR => E9: 4,9 * INC # G3: 4,9 => UNS * PRF # G3: 8 => SOL * CNT 35 HDP CHAINS / 35 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E1: 8,9 => UNS * INC # I1: 8,9 => UNS * INC # E1: 8,9 => UNS * INC # F3: 8,9 => UNS * INC # I5: 2,6 => UNS * INC # I5: 8,9 => UNS * INC # C8: 8,9 => UNS * DIS # C8: 6 => CTR => C8: 8,9 * INC C8: 8,9 # E6: 2,8 => UNS * PRF C8: 8,9 # E6: 6 => SOL * STA C8: 8,9 + E6: 6 * CNT 10 HDP CHAINS / 10 HYP OPENED