Analysis of xx-top500-229-base.sdk
Contents
Original Sudoku
level: medium
position: ...6....12......4.....5......67..5...1.....2....3.....8...24...4.....6........3.. initial
Autosolve
position: .3864.2512518...466.4251.3..467.251..1.4...2..8231.46.8639241754.51..6.212.5..3.4 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A5: 7,9 => CTR => A5: 3,5 * DIS # A5: 3,9 => CTR => A5: 5,7 * DIS # A5: 7,9 => CTR => A5: 3,5 * DIS # I5: 7,9 => CTR => I5: 3,8 * DIS # I4: 3 => CTR => I4: 8,9 * DIS # F5: 5,9 => CTR => F5: 6,8 * DIS # A6: 7 => CTR => A6: 5,9 * DIS # I5: 7,9 => CTR => I5: 3,8 * DIS # A6: 5 => CTR => A6: 7,9 * CNT 9 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 # A5: 7,9 => CTR => A5: 3,5 * DIS A5: 3,5 # A6: 5 => CTR => A6: 7,9 * PRF A5: 3,5 + A6: 7,9 # G3: 7,9 => SOL * STA A5: 3,5 + A6: 7,9 + G3: 7,9 * CNT 3 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...6....12......4.....5......67..5...1.....2....3.....8...24...4.....6........3.. | initial |
| .3864.2512518...466.4251.3..467.251..1.4...2..8231.46.8639241754.51..6.212.5..3.4 | autosolve |
| 738649251251873946694251738346782519517496823982315467863924175475138692129567384 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) A1: 7,9 B3: 7,9 F1: 7,9 G2: 7,9 A4: 3,9 C5: 7,9 E4: 8,9 F6: 5,9 I6: 7,9 B8: 7,9 C9: 7,9 H8: 8,9 H9: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,F2: 3.. / E2 = 3 => 17 pairs (_) / F2 = 3 => 15 pairs (_) A4,A5: 3.. / A4 = 3 => 13 pairs (_) / A5 = 3 => 0 pairs (X) I4,I5: 3.. / I4 = 3 => 0 pairs (X) / I5 = 3 => 13 pairs (_) E8,F8: 3.. / E8 = 3 => 15 pairs (_) / F8 = 3 => 17 pairs (_) A4,I4: 3.. / A4 = 3 => 13 pairs (_) / I4 = 3 => 0 pairs (X) A5,I5: 3.. / A5 = 3 => 0 pairs (X) / I5 = 3 => 13 pairs (_) E2,E8: 3.. / E2 = 3 => 17 pairs (_) / E8 = 3 => 15 pairs (_) F2,F8: 3.. / F2 = 3 => 15 pairs (_) / F8 = 3 => 17 pairs (_) A5,A6: 5.. / A5 = 5 => 13 pairs (_) / A6 = 5 => 0 pairs (X) F5,F6: 5.. / F5 = 5 => 0 pairs (X) / F6 = 5 => 13 pairs (_) A5,F5: 5.. / A5 = 5 => 13 pairs (_) / F5 = 5 => 0 pairs (X) A6,F6: 5.. / A6 = 5 => 0 pairs (X) / F6 = 5 => 13 pairs (_) E5,F5: 6.. / E5 = 6 => 14 pairs (_) / F5 = 6 => 17 pairs (_) E9,F9: 6.. / E9 = 6 => 17 pairs (_) / F9 = 6 => 14 pairs (_) E5,E9: 6.. / E5 = 6 => 14 pairs (_) / E9 = 6 => 17 pairs (_) F5,F9: 6.. / F5 = 6 => 17 pairs (_) / F9 = 6 => 14 pairs (_) A1,B3: 7.. / A1 = 7 => 0 pairs (*) / B3 = 7 => 0 pairs (X) B8,C9: 7.. / B8 = 7 => 0 pairs (*) / C9 = 7 => 0 pairs (X) A1,F1: 7.. / A1 = 7 => 0 pairs (*) / F1 = 7 => 0 pairs (X) A6,I6: 7.. / A6 = 7 => 0 pairs (X) / I6 = 7 => 15 pairs (_) B3,B8: 7.. / B3 = 7 => 0 pairs (X) / B8 = 7 => 0 pairs (_) C5,C9: 7.. / C5 = 7 => 0 pairs (*) / C9 = 7 => 0 pairs (X) G3,I3: 8.. / G3 = 8 => 19 pairs (_) / I3 = 8 => 17 pairs (_) H8,H9: 8.. / H8 = 8 => 0 pairs (X) / H9 = 8 => 0 pairs (_) E4,I4: 8.. / E4 = 8 => 16 pairs (_) / I4 = 8 => 16 pairs (_) G3,G5: 8.. / G3 = 8 => 19 pairs (_) / G5 = 8 => 17 pairs (_) A1,B3: 9.. / A1 = 9 => 0 pairs (X) / B3 = 9 => 0 pairs (_) B8,C9: 9.. / B8 = 9 => 0 pairs (X) / C9 = 9 => 0 pairs (_) H8,H9: 9.. / H8 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) A1,F1: 9.. / A1 = 9 => 0 pairs (X) / F1 = 9 => 0 pairs (_) B8,H8: 9.. / B8 = 9 => 0 pairs (X) / H8 = 9 => 0 pairs (_) C9,H9: 9.. / C9 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) B3,B8: 9.. / B3 = 9 => 0 pairs (*) / B8 = 9 => 0 pairs (X) C5,C9: 9.. / C5 = 9 => 0 pairs (X) / C9 = 9 => 0 pairs (_) * DURATION: 0:00:55.674381 START: 10:40:15.139462 END: 10:41:10.813843 2017-05-04 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,B3,B8,C5,C9,E4,F1,F6,G2,H8,H9,I6) * .3864.2512518...466.4251.3..467.251..1.4...2..8231.46.8639241754.51..6.212.5..3.4 * PAIR A1: 7,9 COL A A5: 7,9,3,5 # reduction candidate for 7,9 A5: 7,9 => CTR * 938647251251893746674251.3.34678251..1.4.5.235823194678639241754.51..6.212.5.63.4 A5: 3,5 # 14 pairs A6: 7,9,5 # reduction candidate for 7,9 A6: 7,9 # 13 pairs * PAIR B3: 7,9 ROW 3 G3: 7,9,8 # reduction candidate for 7,9 G3: 7,9 # 17 pairs I3: 7,9,8 # reduction candidate for 7,9 I3: 7,9 # 19 pairs * PAIR F1: 7,9 BLK 2 E2: 7,9,3 # reduction candidate for 7,9 E2: 7,9 # 15 pairs F2: 7,9,3 # reduction candidate for 7,9 F2: 7,9 # 17 pairs * PAIR G2: 7,9 BLK 3 G3: 7,9,8 # reduction candidate for 7,9 G3: 7,9 # 17 pairs I3: 7,9,8 # reduction candidate for 7,9 I3: 7,9 # 19 pairs * PAIR G2: 7,9 ROW 2 E2: 7,9,3 # reduction candidate for 7,9 E2: 7,9 # 15 pairs F2: 7,9,3 # reduction candidate for 7,9 F2: 7,9 # 17 pairs * PAIR G2: 7,9 COL G G5: 7,9,8 # reduction candidate for 7,9 G5: 7,9 # 19 pairs G5: 8 # 17 pairs * PAIR A4: 3,9 BLK 4 A5: 3,9,5,7 # reduction candidate for 3,9 A5: 3,9 => CTR * .3864.2512518...466.4251.3..467.251..1.4.5.2.5823194678639241754.51..6.212.5.63.4 A5: 5,7 # 14 pairs * PAIR A4: 3,9 ROW 4 I4: 3,9,8 # reduction candidate for 3,9 I4: 8 # 16 pairs I4: 3,9 # 16 pairs * PAIR C5: 7,9 BLK 4 A5: 7,9,3,5 # reduction candidate for 7,9 A5: 7,9 => CTR * 938647251251893746674251.3.34678251..1.4.5.235823194678639241754.51..6.212.5.63.4 A5: 3,5 # 14 pairs A6: 7,9,5 # reduction candidate for 7,9 A6: 7,9 # 13 pairs * PAIR C5: 7,9 ROW 5 G5: 7,9,8 # reduction candidate for 7,9 G5: 7,9 # 19 pairs I5: 7,9,3,8 # reduction candidate for 7,9 I5: 7,9 => CTR * .3864.2512518...466.4251.3..467.251331.4.582.5823194678639241754.51..6.212.5.63.4 I5: 3,8 # 14 pairs * PAIR E4: 8,9 BLK 5 E5: 8,9,6 # reduction candidate for 8,9 E5: 8,9 # 17 pairs F5: 8,9,5,6 # reduction candidate for 8,9 F5: 8,9 # 15 pairs * PAIR E4: 8,9 ROW 4 I4: 8,9,3 # reduction candidate for 8,9 I4: 3 => CTR * .3864.2512518...466.4251.3..4678251331.4.5.2.5823194678639241754.51..6.212.5.6384 I4: 8,9 # 13 pairs * PAIR F6: 5,9 BLK 5 F5: 5,9,6,8 # reduction candidate for 5,9 F5: 5,9 => CTR * .3864.2512518937466.4251.3..4678251..1.46..2..8231.46.8639241754.51.8692129576384 F5: 6,8 # 15 pairs * PAIR F6: 5,9 ROW 6 A6: 5,9,7 # reduction candidate for 5,9 A6: 7 => CTR * 9386472512518..746674251938.467.251.51.4...237823154698639241754.51..6.21275..394 A6: 5,9 # 15 pairs * PAIR I6: 7,9 BLK 6 G5: 7,9,8 # reduction candidate for 7,9 G5: 7,9 # 19 pairs I5: 7,9,3,8 # reduction candidate for 7,9 I5: 7,9 => CTR * .3864.2512518...466.4251.3..467.251331.4.582.5823194678639241754.51..6.212.5.63.4 I5: 3,8 # 14 pairs * PAIR I6: 7,9 ROW 6 A6: 7,9,5 # reduction candidate for 7,9 A6: 5 => CTR * 938647251251893746674251.3.34678251..1.4...2.5823194678639241754.51..6.212.5..3.4 A6: 7,9 # 13 pairs * PAIR I6: 7,9 COL I I3: 7,9,8 # reduction candidate for 7,9 I3: 7,9 # 19 pairs I3: 8 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-229-base-pr-000.dot * REASONING * DIS # A5: 7,9 => CTR => A5: 3,5 * DIS # A5: 3,9 => CTR => A5: 5,7 * DIS # A5: 7,9 => CTR => A5: 3,5 * DIS # I5: 7,9 => CTR => I5: 3,8 * DIS # I4: 3 => CTR => I4: 8,9 * DIS # F5: 5,9 => CTR => F5: 6,8 * DIS # A6: 7 => CTR => A6: 5,9 * DIS # I5: 7,9 => CTR => I5: 3,8 * DIS # A6: 5 => CTR => A6: 7,9 * CNT 9 HDP CHAINS / 38 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,B3,B8,C5,C9,E4,F1,F6,G2,H8,H9,I6) * .3864.2512518...466.4251.3..467.251..1.4...2..8231.46.8639241754.51..6.212.5..3.4 * PAIR A1: 7,9 COL A A5: 7,9,3,5 # reduction candidate for 7,9 A5: 7,9 => CTR * 938647251251893746674251.3.34678251..1.4.5.235823194678639241754.51..6.212.5.63.4 A6: 7,9,5 # reduction candidate for 7,9 A6: 7,9 # 13 pairs * RESTART * PAIR A1: 7,9 COL A A6: 7,9,5 # reduction candidate for 7,9 A6: 5 => CTR * 7386492512518..946694251.3.946782513.1.4...2..8231.46.8639241754.51..6.212.5..3.4 * PAIR RESTART * PAIR B3: 7,9 ROW 3 G3: 7,9,8 # reduction candidate for 7,9 G3: 7,9 => SOLVED * 738649251251873946694251738346782519517496823982315467863924175475138692129567384 * DURATION: 0:00:05.659849 START: 10:41:43.184912 END: 10:41:48.844761 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-229-base-pr-001.dot * REASONING * DIS # A5: 7,9 => CTR => A5: 3,5 * DIS A5: 3,5 # A6: 5 => CTR => A6: 7,9 * PRF A5: 3,5 + A6: 7,9 # G3: 7,9 => SOL * STA A5: 3,5 + A6: 7,9 + G3: 7,9 * CNT 3 HDP CHAINS / 5 HYP OPENED
Header Info
Top 500 Minimum 17 229 solution: 738649251251873946694251738346782519517496823982315467863924175475138692129567384 info: 2065 FNWXY S8.f 10313 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 738649251251873946694251738346782519517496823982315467863924175475138692129567384 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 # A5: 7,9 => CTR => A5: 3,5 * INC # A5: 3,5 => UNS * INC # A6: 7,9 => UNS * INC # G3: 7,9 => UNS * INC # I3: 7,9 => UNS * INC # E2: 7,9 => UNS * INC # F2: 7,9 => UNS * INC # G3: 7,9 => UNS * INC # I3: 7,9 => UNS * INC # E2: 7,9 => UNS * INC # F2: 7,9 => UNS * INC # G5: 7,9 => UNS * INC # G5: 8 => UNS * DIS # A5: 3,9 => CTR => A5: 5,7 * INC # A5: 5,7 => UNS * INC # I4: 3,9 => UNS * INC # I4: 8 => UNS * DIS # A5: 7,9 => CTR => A5: 3,5 * INC # A5: 3,5 => UNS * INC # A6: 7,9 => UNS * INC # G5: 7,9 => UNS * DIS # I5: 7,9 => CTR => I5: 3,8 * INC # I5: 3,8 => UNS * INC # E5: 8,9 => UNS * INC # F5: 8,9 => UNS * INC # I4: 8,9 => UNS * DIS # I4: 3 => CTR => I4: 8,9 * DIS # F5: 5,9 => CTR => F5: 6,8 * INC # F5: 6,8 => UNS * INC # A6: 5,9 => UNS * DIS # A6: 7 => CTR => A6: 5,9 * INC # G5: 7,9 => UNS * DIS # I5: 7,9 => CTR => I5: 3,8 * INC # I5: 3,8 => UNS * INC # A6: 7,9 => UNS * DIS # A6: 5 => CTR => A6: 7,9 * INC # I3: 7,9 => UNS * INC # I3: 8 => UNS * CNT 38 HDP CHAINS / 38 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A5: 7,9 => CTR => A5: 3,5 * INC A5: 3,5 # A6: 7,9 => UNS * INC A5: 3,5 # A6: 7,9 => UNS * DIS A5: 3,5 # A6: 5 => CTR => A6: 7,9 * PRF A5: 3,5 + A6: 7,9 # G3: 7,9 => SOL * STA A5: 3,5 + A6: 7,9 + G3: 7,9 * CNT 5 HDP CHAINS / 5 HYP OPENED