Analysis of xx-top500-374-base.sdk
Contents
Original Sudoku
level: medium
position: 6.....17....3....21............176...2.....3...........3.2....5...46..........8.. initial
Autosolve
position: 6.3.2.17..7.3.1.621.27.63..3...1762..2.6...3..6..32...4362..715.1.4652932..173846 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # G6: 5,9 => SOL * PRF # A5: 5,9 => SOL * DIS # C5: 5,9 => CTR => C5: 1,7,8 * DIS # E5: 5,9 => CTR => E5: 4,8 * PRF # G2: 4 => SOL * DIS # C6: 5,8 => CTR => C6: 1,4,7,9 * PRF # C6: 4,5,8,9 => SOL * PRF # A6: 7,8 => SOL * DIS # B3: 5,9 => CTR => B3: 4,8 * DIS # B4: 5,9 => CTR => B4: 4,8 * DIS # C5: 5,9 => CTR => C5: 1,7,8 * DIS # C6: 5,9 => CTR => C6: 1,4,7,8 * PRF # E3: 8,9 => SOL * DIS # E5: 8,9 => CTR => E5: 4,5 * CNT 14 HDP CHAINS / 43 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # G6: 5,9 => SOL * STA G6: 5,9 * CNT 1 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6.....17....3....21............176...2.....3...........3.2....5...46..........8.. | initial |
| 6.3.2.17..7.3.1.621.27.63..3...1762..2.6...3..6..32...4362..715.1.4652932..173846 | autosolve |
| 653824179978351462142796358389517624521648937764932581436289715817465293295173846 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) H3: 5,8 G5: 5,9 I5: 1,7 H6: 5,8 I6: 1,7 A8: 7,8 C8: 7,8 B9: 5,9 C9: 5,9 E7: 8,9 F7: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C5,C6: 1.. / C5 = 1 => 9 pairs (_) / C6 = 1 => 11 pairs (_) I5,I6: 1.. / I5 = 1 => 11 pairs (_) / I6 = 1 => 9 pairs (_) C5,I5: 1.. / C5 = 1 => 9 pairs (_) / I5 = 1 => 11 pairs (_) C6,I6: 1.. / C6 = 1 => 11 pairs (_) / I6 = 1 => 9 pairs (_) E5,F5: 4.. / E5 = 4 => 19 pairs (_) / F5 = 4 => 12 pairs (_) I4,G6: 4.. / I4 = 4 => 0 pairs (*) / G6 = 4 => 0 pairs (X) C6,G6: 4.. / C6 = 4 => 0 pairs (*) / G6 = 4 => 0 pairs (X) F1,F5: 4.. / F1 = 4 => 19 pairs (_) / F5 = 4 => 12 pairs (_) G2,G6: 4.. / G2 = 4 => 0 pairs (*) / G6 = 4 => 0 pairs (X) G2,H3: 5.. / G2 = 5 => 0 pairs (X) / H3 = 5 => 12 pairs (_) B9,C9: 5.. / B9 = 5 => 0 pairs (X) / C9 = 5 => 11 pairs (_) B1,D1: 5.. / B1 = 5 => 16 pairs (_) / D1 = 5 => 0 pairs (X) H3,H6: 5.. / H3 = 5 => 12 pairs (_) / H6 = 5 => 0 pairs (X) I5,I6: 7.. / I5 = 7 => 9 pairs (_) / I6 = 7 => 11 pairs (_) A8,C8: 7.. / A8 = 7 => 13 pairs (_) / C8 = 7 => 10 pairs (_) I4,H6: 8.. / I4 = 8 => 0 pairs (X) / H6 = 8 => 12 pairs (_) A8,C8: 8.. / A8 = 8 => 10 pairs (_) / C8 = 8 => 13 pairs (_) E7,F7: 8.. / E7 = 8 => 0 pairs (*) / F7 = 8 => 0 pairs (X) H3,H6: 8.. / H3 = 8 => 0 pairs (X) / H6 = 8 => 12 pairs (_) B9,C9: 9.. / B9 = 9 => 11 pairs (_) / C9 = 9 => 0 pairs (X) E7,F7: 9.. / E7 = 9 => 12 pairs (_) / F7 = 9 => 0 pairs (*) * DURATION: 0:00:34.591113 START: 15:40:34.802480 END: 15:41:09.393593 2017-05-04 * CP COUNT: (21) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B9,C8,C9,E7,F7,G5,H3,H6,I5,I6) * 6.3.2.17..7.3.1.621.27.63..3...1762..2.6...3..6..32...4362..715.1.4652932..173846 * PAIR H3: 5,8 ROW 3 B3: 5,8,4,9 # reduction candidate for 5,8 B3: 5,8 # 14 pairs E3: 5,8,4,9 # reduction candidate for 5,8 E3: 5,8 # 14 pairs * PAIR G5: 5,9 BLK 6 G6: 5,9,4 # reduction candidate for 5,9 G6: 5,9 => SOLVED * 653824179978351462142796358389517624521648937764932581436289715817465293295173846 G6: 4 # 13 pairs * PAIR G5: 5,9 ROW 5 A5: 5,9,7,8 # reduction candidate for 5,9 A5: 5,9 => SOLVED * 653824179978351462142796358389517624521648937764932581436289715817465293295173846 A5: 7,8 # 19 pairs C5: 5,9,1,7,8 # reduction candidate for 5,9 C5: 5,9 => CTR * 6.382.174.783419621427.63..3...1762972.6..531.61.324874362..7158174652932..173846 C5: 1,7,8 # 11 pairs E5: 5,9,4,8 # reduction candidate for 5,9 E5: 5,9 => CTR * 6.352917.5793814621827463593...17624.2.65493.964832...436298715.1.4652932..173846 E5: 4,8 # 17 pairs * PAIR G5: 5,9 COL G G2: 5,9,4 # reduction candidate for 5,9 G2: 4 => SOLVED * 653824179978351462142796358389517624521648937764932581436289715817465293295173846 G2: 5,9 # 13 pairs * PAIR I5: 1,7 ROW 5 C5: 1,7,5,8,9 # reduction candidate for 1,7 C5: 5,8,9 # 13 pairs C5: 1,7 # 12 pairs * PAIR H6: 5,8 ROW 6 A6: 5,8,7,9 # reduction candidate for 5,8 A6: 5,8 # 18 pairs C6: 5,8,1,4,7,9 # reduction candidate for 5,8 C6: 5,8 => CTR * 6.382.17..78341.621.275638.3...1762..216...3776.9324.14362..7158174652932..173846 C6: 1,4,7,9 # 11 pairs D6: 5,8,9 # reduction candidate for 5,8 D6: 5,8 # 14 pairs * PAIR I6: 1,7 ROW 6 C6: 1,7,4,5,8,9 # reduction candidate for 1,7 C6: 4,5,8,9 => SOLVED * 653824179978351462142796358389517624521648937764932581436289715817465293295173846 C6: 1,7 # 14 pairs * PAIR A8: 7,8 COL A A5: 7,8,5,9 # reduction candidate for 7,8 A5: 7,8 # 19 pairs A6: 7,8,5,9 # reduction candidate for 7,8 A6: 7,8 => SOLVED * 653824179978351462142796358389517624521648937764932581436289715817465293295173846 A6: 5,9 # 15 pairs * PAIR C8: 7,8 COL C C5: 7,8,1,5,9 # reduction candidate for 7,8 C5: 7,8 # 12 pairs C6: 7,8,1,4,5,9 # reduction candidate for 7,8 C6: 7,8 # 12 pairs * PAIR B9: 5,9 COL B B1: 5,9,4,8 # reduction candidate for 5,9 B1: 5,9 # 14 pairs B3: 5,9,4,8 # reduction candidate for 5,9 B3: 5,9 => CTR * 6.352.17.57.3914621927463583.5917624.2.65493.964832...4362..715.1.465293259173846 B3: 4,8 # 12 pairs B4: 5,9,4,8 # reduction candidate for 5,9 B4: 5,9 => CTR * 6435291785793814621827463593..817624.2165493..64.32581436298715.1.4652932..173846 B4: 4,8 # 12 pairs * PAIR C9: 5,9 COL C C2: 5,9,4,8 # reduction candidate for 5,9 C2: 5,9 # 13 pairs C4: 5,9,4,8 # reduction candidate for 5,9 C4: 5,9 # 13 pairs C5: 5,9,1,7,8 # reduction candidate for 5,9 C5: 5,9 => CTR * 6.382.174.783419621427.63..3...1762972.6..531.61.324874362..7158174652932..173846 C5: 1,7,8 # 11 pairs C6: 5,9,1,4,7,8 # reduction candidate for 5,9 C6: 5,9 => CTR * 6.382.1745783419621427.63..3...17629.216..53776..324814362..7158174652932..173846 C6: 1,4,7,8 # 11 pairs * PAIR E7: 8,9 COL E E2: 8,9,4,5 # reduction candidate for 8,9 E2: 8,9 # 14 pairs E3: 8,9,4,5 # reduction candidate for 8,9 E3: 8,9 => SOLVED * 653824179978351462142796358389517624521648937764932581436289715817465293295173846 E3: 4,5 # 12 pairs E5: 8,9,4,5 # reduction candidate for 8,9 E5: 8,9 => CTR * 653.2.174.7.3.156214275638938.51762..2.6.4.3..6..324..4362..715.1.465293295173846 E5: 4,5 # 12 pairs * PAIR F7: 8,9 COL F F1: 8,9,4 # reduction candidate for 8,9 F1: 8,9 # 12 pairs F5: 8,9,4 # reduction candidate for 8,9 F5: 8,9 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-374-base-pr-000.dot * REASONING * PRF # G6: 5,9 => SOL * PRF # A5: 5,9 => SOL * DIS # C5: 5,9 => CTR => C5: 1,7,8 * DIS # E5: 5,9 => CTR => E5: 4,8 * PRF # G2: 4 => SOL * DIS # C6: 5,8 => CTR => C6: 1,4,7,9 * PRF # C6: 4,5,8,9 => SOL * PRF # A6: 7,8 => SOL * DIS # B3: 5,9 => CTR => B3: 4,8 * DIS # B4: 5,9 => CTR => B4: 4,8 * DIS # C5: 5,9 => CTR => C5: 1,7,8 * DIS # C6: 5,9 => CTR => C6: 1,4,7,8 * PRF # E3: 8,9 => SOL * DIS # E5: 8,9 => CTR => E5: 4,5 * CNT 14 HDP CHAINS / 43 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B9,C8,C9,E7,F7,G5,H3,H6,I5,I6) * 6.3.2.17..7.3.1.621.27.63..3...1762..2.6...3..6..32...4362..715.1.4652932..173846 * PAIR H3: 5,8 ROW 3 B3: 5,8,4,9 # reduction candidate for 5,8 B3: 5,8 # 14 pairs E3: 5,8,4,9 # reduction candidate for 5,8 E3: 5,8 # 14 pairs * PAIR G5: 5,9 BLK 6 G6: 5,9,4 # reduction candidate for 5,9 G6: 5,9 => SOLVED * 653824179978351462142796358389517624521648937764932581436289715817465293295173846 * DURATION: 0:00:03.942483 START: 15:41:52.143227 END: 15:41:56.085710 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-374-base-pr-001.dot * REASONING * PRF # G6: 5,9 => SOL * STA G6: 5,9 * CNT 1 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 374 solution: 653824179978351462142796358389517624521648937764932581436289715817465293295173846 info: 6483 FNBHWY S8.f 42464 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 653824179978351462142796358389517624521648937764932581436289715817465293295173846 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 # B3: 5,8 => UNS * INC # E3: 5,8 => UNS * PRF # G6: 5,9 => SOL * INC # G6: 4 => UNS * PRF # A5: 5,9 => SOL * INC # A5: 7,8 => UNS * DIS # C5: 5,9 => CTR => C5: 1,7,8 * INC # C5: 1,7,8 => UNS * DIS # E5: 5,9 => CTR => E5: 4,8 * INC # E5: 4,8 => UNS * INC # G2: 5,9 => UNS * PRF # G2: 4 => SOL * INC # C5: 1,7 => UNS * INC # C5: 5,8,9 => UNS * INC # A6: 5,8 => UNS * DIS # C6: 5,8 => CTR => C6: 1,4,7,9 * INC # C6: 1,4,7,9 => UNS * INC # D6: 5,8 => UNS * INC # C6: 1,7 => UNS * PRF # C6: 4,5,8,9 => SOL * INC # A5: 7,8 => UNS * PRF # A6: 7,8 => SOL * INC # A6: 5,9 => UNS * INC # C5: 7,8 => UNS * INC # C6: 7,8 => UNS * INC # B1: 5,9 => UNS * DIS # B3: 5,9 => CTR => B3: 4,8 * INC # B3: 4,8 => UNS * DIS # B4: 5,9 => CTR => B4: 4,8 * INC # B4: 4,8 => UNS * INC # C2: 5,9 => UNS * INC # C4: 5,9 => UNS * DIS # C5: 5,9 => CTR => C5: 1,7,8 * INC # C5: 1,7,8 => UNS * DIS # C6: 5,9 => CTR => C6: 1,4,7,8 * INC # C6: 1,4,7,8 => UNS * INC # E2: 8,9 => UNS * PRF # E3: 8,9 => SOL * INC # E3: 4,5 => UNS * DIS # E5: 8,9 => CTR => E5: 4,5 * INC # E5: 4,5 => UNS * INC # F1: 8,9 => UNS * INC # F5: 8,9 => UNS * CNT 43 HDP CHAINS / 43 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B3: 5,8 => UNS * INC # E3: 5,8 => UNS * PRF # G6: 5,9 => SOL * STA G6: 5,9 * CNT 3 HDP CHAINS / 3 HYP OPENED