Analysis of xx-top500-236-base.sdk
Contents
Original Sudoku
level: medium
position: 5.2..........5..8.....13...6..74..........3.18...........6...5....2..4...1....... initial
Autosolve
position: 5.2.679131.3.5268..6..132.5631749528...5283618251367..3..6.4152.5628143.2143.58.6 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D3: 9 => CTR => D3: 4,8 * PRF # B2: 4,9 => SOL * DIS # B2: 7 => CTR => B2: 4,9 * DIS # B2: 9 => CTR => B2: 4,7 * PRF # A3: 9 => SOL * DIS # A5: 7,9 => CTR => A5: 4 * DIS # A5: 7,9 => CTR => A5: 4 * CNT 7 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D3: 9 => CTR => D3: 4,8 * PRF D3: 4,8 # A3: 9 => SOL * STA D3: 4,8 + A3: 9 * CNT 2 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 5.2..........5..8.....13...6..74..........3.18...........6...5....2..4...1....... | initial |
| 5.2.679131.3.5268..6..132.5631749528...5283618251367..3..6.4152.5628143.2143.58.6 | autosolve |
| 582467913143952687967813245631749528479528361825136794398674152756281439214395876 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) B1: 4,8 D1: 4,8 D2: 4,9 I2: 4,7 H3: 4,7 C5: 7,9 H6: 4,9 I6: 4,9 A8: 7,9 E7: 7,9 E9: 7,9 I8: 7,9 H9: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I2,H3: 4.. / I2 = 4 => 0 pairs (X) / H3 = 4 => 0 pairs (_) A5,B5: 4.. / A5 = 4 => 15 pairs (_) / B5 = 4 => 0 pairs (X) H6,I6: 4.. / H6 = 4 => 0 pairs (X) / I6 = 4 => 0 pairs (_) B1,D1: 4.. / B1 = 4 => 16 pairs (_) / D1 = 4 => 13 pairs (_) A3,A5: 4.. / A3 = 4 => 0 pairs (X) / A5 = 4 => 15 pairs (_) H3,H6: 4.. / H3 = 4 => 0 pairs (*) / H6 = 4 => 0 pairs (X) I2,I6: 4.. / I2 = 4 => 0 pairs (X) / I6 = 4 => 0 pairs (_) I2,H3: 7.. / I2 = 7 => 0 pairs (*) / H3 = 7 => 0 pairs (X) E7,E9: 7.. / E7 = 7 => 0 pairs (*) / E9 = 7 => 0 pairs (X) I8,H9: 7.. / I8 = 7 => 0 pairs (X) / H9 = 7 => 0 pairs (_) B2,I2: 7.. / B2 = 7 => 0 pairs (X) / I2 = 7 => 0 pairs (_) A8,I8: 7.. / A8 = 7 => 0 pairs (*) / I8 = 7 => 0 pairs (X) E9,H9: 7.. / E9 = 7 => 0 pairs (X) / H9 = 7 => 0 pairs (_) H3,H9: 7.. / H3 = 7 => 0 pairs (X) / H9 = 7 => 0 pairs (_) I2,I8: 7.. / I2 = 7 => 0 pairs (*) / I8 = 7 => 0 pairs (X) B1,C3: 8.. / B1 = 8 => 13 pairs (_) / C3 = 8 => 16 pairs (_) D1,D3: 8.. / D1 = 8 => 16 pairs (_) / D3 = 8 => 13 pairs (_) B7,C7: 8.. / B7 = 8 => 16 pairs (_) / C7 = 8 => 13 pairs (_) B1,D1: 8.. / B1 = 8 => 13 pairs (_) / D1 = 8 => 16 pairs (_) C3,D3: 8.. / C3 = 8 => 16 pairs (_) / D3 = 8 => 13 pairs (_) B1,B7: 8.. / B1 = 8 => 13 pairs (_) / B7 = 8 => 16 pairs (_) C3,C7: 8.. / C3 = 8 => 16 pairs (_) / C7 = 8 => 13 pairs (_) D2,D3: 9.. / D2 = 9 => 14 pairs (_) / D3 = 9 => 0 pairs (X) H6,I6: 9.. / H6 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) E7,E9: 9.. / E7 = 9 => 0 pairs (X) / E9 = 9 => 0 pairs (_) I8,H9: 9.. / I8 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) B2,D2: 9.. / B2 = 9 => 0 pairs (X) / D2 = 9 => 14 pairs (_) A8,I8: 9.. / A8 = 9 => 0 pairs (X) / I8 = 9 => 0 pairs (_) E9,H9: 9.. / E9 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) H6,H9: 9.. / H6 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) I6,I8: 9.. / I6 = 9 => 0 pairs (X) / I8 = 9 => 0 pairs (_) * DURATION: 0:00:55.533261 START: 10:53:38.351019 END: 10:54:33.884280 2017-05-04 * CP COUNT: (31) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B1,C5,D1,D2,E7,E9,H3,H6,H9,I2,I6,I8) * 5.2.679131.3.5268..6..132.5631749528...5283618251367..3..6.4152.5628143.2143.58.6 * PAIR D1: 4,8 BLK 2 D3: 4,8,9 # reduction candidate for 4,8 D3: 9 => CTR * 5.28679131.3452687.689132456317495284..52836182513679438.6.4152.5628143.2143.58.6 D3: 4,8 # 14 pairs * PAIR D2: 4,9 BLK 2 D3: 4,9,8 # reduction candidate for 4,9 D3: 4,9 # 16 pairs D3: 8 # 13 pairs * PAIR D2: 4,9 ROW 2 B2: 4,9,7 # reduction candidate for 4,9 B2: 4,9 => SOLVED * 582467913143952687967813245631749528479528361825136794398674152756281439214395876 B2: 7 => CTR * 5.2.679131739526844698132756317495287..5283618251367493..6.4152956281437214375896 * PAIR I2: 4,7 ROW 2 B2: 4,7,9 # reduction candidate for 4,7 B2: 9 => CTR * 5.2.67913193452687.6.91324563174952847952836182513679438.6.4152.5628143.2143.58.6 B2: 4,7 # 14 pairs * PAIR H3: 4,7 ROW 3 A3: 4,7,9 # reduction candidate for 4,7 A3: 9 => SOLVED * 582467913143952687967813245631749528479528361825136794398674152756281439214395876 A3: 4,7 # 16 pairs * PAIR C5: 7,9 BLK 4 A5: 7,9,4 # reduction candidate for 7,9 A5: 7,9 => CTR * 5.2.679131.3.5268.46..13275631749528.4.5283618251367493..6.4152956281437214375896 A5: 4 # 15 pairs B5: 7,9,4 # reduction candidate for 7,9 B5: 7,9 # 15 pairs * PAIR C5: 7,9 COL C C3: 7,9,8 # reduction candidate for 7,9 C3: 7,9 # 13 pairs C7: 7,9,8 # reduction candidate for 7,9 C7: 7,9 # 16 pairs * PAIR A8: 7,9 BLK 7 B7: 7,9,8 # reduction candidate for 7,9 B7: 7,9 # 13 pairs C7: 7,9,8 # reduction candidate for 7,9 C7: 7,9 # 16 pairs * PAIR A8: 7,9 COL A A3: 7,9,4 # reduction candidate for 7,9 A3: 7,9 # 15 pairs A5: 7,9,4 # reduction candidate for 7,9 A5: 7,9 => CTR * 5.2.679131.3.5268.46..13275631749528.4.5283618251367493..6.4152956281437214375896 A5: 4 # 15 pairs * PAIR E7: 7,9 ROW 7 B7: 7,9,8 # reduction candidate for 7,9 B7: 7,9 # 13 pairs C7: 7,9,8 # reduction candidate for 7,9 C7: 7,9 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-236-base-pr-000.dot * REASONING * DIS # D3: 9 => CTR => D3: 4,8 * PRF # B2: 4,9 => SOL * DIS # B2: 7 => CTR => B2: 4,9 * DIS # B2: 9 => CTR => B2: 4,7 * PRF # A3: 9 => SOL * DIS # A5: 7,9 => CTR => A5: 4 * DIS # A5: 7,9 => CTR => A5: 4 * CNT 7 HDP CHAINS / 22 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B1,C5,D1,D2,E7,E9,H3,H6,H9,I2,I6,I8) * 5.2.679131.3.5268..6..132.5631749528...5283618251367..3..6.4152.5628143.2143.58.6 * PAIR D1: 4,8 BLK 2 D3: 4,8,9 # reduction candidate for 4,8 D3: 9 => CTR * 5.28679131.3452687.689132456317495284..52836182513679438.6.4152.5628143.2143.58.6 * PAIR H3: 4,7 ROW 3 A3: 4,7,9 # reduction candidate for 4,7 A3: 9 => SOLVED * 582467913143952687967813245631749528479528361825136794398674152756281439214395876 * DURATION: 0:00:04.999962 START: 10:54:56.819543 END: 10:55:01.819505 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-236-base-pr-001.dot * REASONING * DIS # D3: 9 => CTR => D3: 4,8 * PRF D3: 4,8 # A3: 9 => SOL * STA D3: 4,8 + A3: 9 * CNT 2 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 236 solution: 582467913143952687967813245631749528479528361825136794398674152756281439214395876 info: 2068 FNWXY S8.f 46765 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 582467913143952687967813245631749528479528361825136794398674152756281439214395876 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 # D3: 4,8 => UNS * DIS # D3: 9 => CTR => D3: 4,8 * INC # D3: 4,9 => UNS * INC # D3: 8 => UNS * PRF # B2: 4,9 => SOL * DIS # B2: 7 => CTR => B2: 4,9 * INC # B2: 4,7 => UNS * DIS # B2: 9 => CTR => B2: 4,7 * INC # A3: 4,7 => UNS * PRF # A3: 9 => SOL * DIS # A5: 7,9 => CTR => A5: 4 * INC # A5: 4 => UNS * INC # B5: 7,9 => UNS * INC # C3: 7,9 => UNS * INC # C7: 7,9 => UNS * INC # B7: 7,9 => UNS * INC # C7: 7,9 => UNS * INC # A3: 7,9 => UNS * DIS # A5: 7,9 => CTR => A5: 4 * INC # A5: 4 => UNS * INC # B7: 7,9 => UNS * INC # C7: 7,9 => UNS * CNT 22 HDP CHAINS / 22 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D3: 4,8 => UNS * DIS # D3: 9 => CTR => D3: 4,8 * INC D3: 4,8 # A3: 4,7 => UNS * PRF D3: 4,8 # A3: 9 => SOL * STA D3: 4,8 + A3: 9 * CNT 4 HDP CHAINS / 4 HYP OPENED