Analysis of xx-top500-039-base.sdk
Contents
Original Sudoku
level: medium
position: 6....27....8.5.....4.......7.....2.....48.......3.....2....3..........491......3. initial
Autosolve
position: 6..94278332875.49.947.38.2.783.192.459248.3..4..32.9.82.4.93...83.27..49179.64.32 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I3: 1,6 => CTR => I3: 5 * DIS # I3: 1,6 => CTR => I3: 5 * DIS # I7: 1,6 => CTR => I7: 5,7 * DIS # H5: 6,7 => CTR => H5: 1 * DIS # G7: 5,6 => CTR => G7: 1,8 * DIS # I7: 5,6 => CTR => I7: 1,7 * PRF # G8: 5,6 => SOL * DIS # G8: 1 => CTR => G8: 5,6 * PRF # D7: 8 => SOL * DIS # G8: 6 => CTR => G8: 1,5 * PRF # D7: 5,8 => SOL * DIS # D7: 1 => CTR => D7: 5,8 * PRF # G7: 1,6 => SOL * CNT 13 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:
* DIS # I3: 1,6 => CTR => I3: 5 * DIS I3: 5 # I7: 1,6 => CTR => I7: 7 * DIS I3: 5 + I7: 7 # H5: 6,7 => CTR => H5: 1 * PRF I3: 5 + I7: 7 + H5: 1 => SOL * STA I3: 5 + I7: 7 + H5: 1 * CNT 4 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6....27....8.5.....4.......7.....2.....48.......3.....2....3..........491......3. | initial |
| 6..94278332875.49.947.38.2.783.192.459248.3..4..32.9.82.4.93...83.27..49179.64.32 | autosolve |
| 615942783328756491947138625783619254592487316461325978254893167836271549179564832 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) B1: 1,5 C1: 1,5 F2: 1,6 D3: 1,6 I2: 1,6 B6: 1,6 C6: 1,6 D4: 5,6 F5: 6,7 F6: 5,7 H4: 5,6 H6: 5,7 B7: 5,6 C8: 5,6 F8: 1,5 D9: 5,8 G9: 5,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,C1: 1.. / B1 = 1 => 14 pairs (_) / C1 = 1 => 0 pairs (X) F2,D3: 1.. / F2 = 1 => 0 pairs (X) / D3 = 1 => 0 pairs (_) B6,C6: 1.. / B6 = 1 => 0 pairs (X) / C6 = 1 => 14 pairs (_) H5,I5: 1.. / H5 = 1 => 19 pairs (_) / I5 = 1 => 0 pairs (X) D7,F8: 1.. / D7 = 1 => 0 pairs (X) / F8 = 1 => 0 pairs (_) F2,I2: 1.. / F2 = 1 => 0 pairs (X) / I2 = 1 => 0 pairs (_) F8,G8: 1.. / F8 = 1 => 0 pairs (*) / G8 = 1 => 0 pairs (X) B1,B6: 1.. / B1 = 1 => 14 pairs (_) / B6 = 1 => 0 pairs (X) C1,C6: 1.. / C1 = 1 => 0 pairs (X) / C6 = 1 => 14 pairs (_) D3,D7: 1.. / D3 = 1 => 0 pairs (*) / D7 = 1 => 0 pairs (X) F2,F8: 1.. / F2 = 1 => 0 pairs (X) / F8 = 1 => 0 pairs (_) H5,H7: 1.. / H5 = 1 => 19 pairs (_) / H7 = 1 => 0 pairs (X) B1,C1: 5.. / B1 = 5 => 0 pairs (X) / C1 = 5 => 14 pairs (_) G3,I3: 5.. / G3 = 5 => 0 pairs (X) / I3 = 5 => 18 pairs (_) D4,F6: 5.. / D4 = 5 => 0 pairs (X) / F6 = 5 => 0 pairs (_) H4,H6: 5.. / H4 = 5 => 0 pairs (*) / H6 = 5 => 0 pairs (X) B7,C8: 5.. / B7 = 5 => 14 pairs (_) / C8 = 5 => 0 pairs (X) D4,H4: 5.. / D4 = 5 => 0 pairs (X) / H4 = 5 => 0 pairs (_) F6,H6: 5.. / F6 = 5 => 0 pairs (*) / H6 = 5 => 0 pairs (X) D9,G9: 5.. / D9 = 5 => 0 pairs (*) / G9 = 5 => 0 pairs (X) B1,B7: 5.. / B1 = 5 => 0 pairs (X) / B7 = 5 => 14 pairs (_) C1,C8: 5.. / C1 = 5 => 14 pairs (_) / C8 = 5 => 0 pairs (X) F6,F8: 5.. / F6 = 5 => 0 pairs (*) / F8 = 5 => 0 pairs (X) I3,I7: 5.. / I3 = 5 => 18 pairs (_) / I7 = 5 => 0 pairs (X) F2,D3: 6.. / F2 = 6 => 0 pairs (*) / D3 = 6 => 0 pairs (X) B6,C6: 6.. / B6 = 6 => 14 pairs (_) / C6 = 6 => 0 pairs (X) D4,F5: 6.. / D4 = 6 => 0 pairs (*) / F5 = 6 => 0 pairs (X) B7,C8: 6.. / B7 = 6 => 0 pairs (X) / C8 = 6 => 14 pairs (_) F2,I2: 6.. / F2 = 6 => 0 pairs (*) / I2 = 6 => 0 pairs (X) D4,H4: 6.. / D4 = 6 => 0 pairs (*) / H4 = 6 => 0 pairs (X) C8,G8: 6.. / C8 = 6 => 14 pairs (_) / G8 = 6 => 0 pairs (X) B6,B7: 6.. / B6 = 6 => 14 pairs (_) / B7 = 6 => 0 pairs (X) C6,C8: 6.. / C6 = 6 => 0 pairs (X) / C8 = 6 => 14 pairs (_) D3,D4: 6.. / D3 = 6 => 0 pairs (X) / D4 = 6 => 0 pairs (_) F2,F5: 6.. / F2 = 6 => 0 pairs (*) / F5 = 6 => 0 pairs (X) F5,F6: 7.. / F5 = 7 => 0 pairs (*) / F6 = 7 => 0 pairs (X) H7,I7: 7.. / H7 = 7 => 0 pairs (X) / I7 = 7 => 20 pairs (_) F6,H6: 7.. / F6 = 7 => 0 pairs (X) / H6 = 7 => 0 pairs (_) I5,I7: 7.. / I5 = 7 => 0 pairs (X) / I7 = 7 => 20 pairs (_) D7,D9: 8.. / D7 = 8 => 0 pairs (*) / D9 = 8 => 0 pairs (X) G7,G9: 8.. / G7 = 8 => 18 pairs (_) / G9 = 8 => 0 pairs (*) D7,G7: 8.. / D7 = 8 => 0 pairs (*) / G7 = 8 => 0 pairs (X) D9,G9: 8.. / D9 = 8 => 18 pairs (_) / G9 = 8 => 0 pairs (*) * DURATION: 0:01:22.926905 START: 03:59:49.164087 END: 04:01:12.090992 2017-05-04 * CP COUNT: (43) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B6,B7,C1,C6,C8,D3,D4,D9,F2,F5,F6,F8,G9,H4,H6,I2) * 6..94278332875.49.947.38.2.783.192.459248.3..4..32.9.82.4.93...83.27..49179.64.32 * PAIR D3: 1,6 ROW 3 G3: 1,6,5 # reduction candidate for 1,6 G3: 1,6 # 18 pairs I3: 1,6,5 # reduction candidate for 1,6 I3: 1,6 => CTR * 65194278332875649194713852678361925459248.3..4..32.9.82.4.93..5835271649179564832 I3: 5 # 18 pairs * PAIR I2: 1,6 BLK 3 G3: 1,6,5 # reduction candidate for 1,6 G3: 1,6 # 18 pairs I3: 1,6,5 # reduction candidate for 1,6 I3: 1,6 => CTR * 65194278332875649194713852678361925459248.3..4..32.9.82.4.93..5835271649179564832 I3: 5 # 18 pairs * PAIR I2: 1,6 COL I I5: 1,6,7 # reduction candidate for 1,6 I5: 1,6 # 20 pairs I7: 1,6,5,7 # reduction candidate for 1,6 I7: 1,6 => CTR * 6.5942783328751496947.38.25783.192.459248.3.74..3279582.4.93.7.83.275149179864532 I7: 5,7 # 18 pairs * PAIR F5: 6,7 ROW 5 H5: 6,7,1 # reduction candidate for 6,7 H5: 6,7 => CTR * 6..94278332875.49.947.38.2.783.192.459248.3.14..32.9.82.4.93.1783.271.49179.64.32 H5: 1 # 19 pairs I5: 6,7,1 # reduction candidate for 6,7 I5: 6,7 # 19 pairs * PAIR B7: 5,6 ROW 7 G7: 5,6,1,8 # reduction candidate for 5,6 G7: 5,6 => CTR * 6..942783328756491947138.2.7836192545924873164..3259782.4893.67836271549179564832 G7: 1,8 # 18 pairs I7: 5,6,1,7 # reduction candidate for 5,6 I7: 5,6 => CTR * 6.5942783328751496947.38.2.783.192.459248.3.74..3279582.4.93.7.83.275149179864532 I7: 1,7 # 19 pairs * PAIR C8: 5,6 ROW 8 G8: 5,6,1 # reduction candidate for 5,6 G8: 5,6 => SOLVED * 615942783328756491947138625783619254592487316461325978254893167836271549179564832 G8: 1 => CTR * 6.5942783328751496947.38.2.783.192.459248.3..4..32.9.82.4.93...836275149179864532 * PAIR F8: 1,5 BLK 8 D7: 1,5,8 # reduction candidate for 1,5 D7: 8 => SOLVED * 615942783328756491947138625783619254592487316461325978254893167836271549179564832 D7: 1,5 # 18 pairs * PAIR F8: 1,5 ROW 8 G8: 1,5,6 # reduction candidate for 1,5 G8: 6 => CTR * 6..94278332875649194713852678361925459248.3..4..32.9.82.4.93...83.271649179.64.32 G8: 1,5 # 14 pairs * PAIR D9: 5,8 BLK 8 D7: 5,8,1 # reduction candidate for 5,8 D7: 5,8 => SOLVED * 615942783328756491947138625783619254592487316461325978254893167836271549179564832 D7: 1 => CTR * 6..94278332875.49.947.38.2.783.192.459248.3..4..32.9.82.41938..83.275149179864532 * PAIR G9: 5,8 BLK 9 G7: 5,8,1,6 # reduction candidate for 5,8 G7: 1,6 => SOLVED * 615942783328756491947138625783619254592487316461325978254893167836271549179564832 G7: 5,8 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-039-base-pr-000.dot * REASONING * DIS # I3: 1,6 => CTR => I3: 5 * DIS # I3: 1,6 => CTR => I3: 5 * DIS # I7: 1,6 => CTR => I7: 5,7 * DIS # H5: 6,7 => CTR => H5: 1 * DIS # G7: 5,6 => CTR => G7: 1,8 * DIS # I7: 5,6 => CTR => I7: 1,7 * PRF # G8: 5,6 => SOL * DIS # G8: 1 => CTR => G8: 5,6 * PRF # D7: 8 => SOL * DIS # G8: 6 => CTR => G8: 1,5 * PRF # D7: 5,8 => SOL * DIS # D7: 1 => CTR => D7: 5,8 * PRF # G7: 1,6 => SOL * CNT 13 HDP CHAINS / 26 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B6,B7,C1,C6,C8,D3,D4,D9,F2,F5,F6,F8,G9,H4,H6,I2) * 6..94278332875.49.947.38.2.783.192.459248.3..4..32.9.82.4.93...83.27..49179.64.32 * PAIR D3: 1,6 ROW 3 G3: 1,6,5 # reduction candidate for 1,6 G3: 1,6 # 18 pairs I3: 1,6,5 # reduction candidate for 1,6 I3: 1,6 => CTR * 65194278332875649194713852678361925459248.3..4..32.9.82.4.93..5835271649179564832 * RESTART * PAIR RESTART * PAIR I2: 1,6 COL I I5: 1,6,7 # reduction candidate for 1,6 I5: 1,6 # 20 pairs I7: 1,6,7 # reduction candidate for 1,6 I7: 1,6 => CTR * 6.5942783328751496947.38.25783.192.459248.3.74..3279582.4.93.7.83.275149179864532 * RESTART * PAIR RESTART * PAIR F5: 6,7 ROW 5 H5: 6,7,1 # reduction candidate for 6,7 H5: 6,7 => CTR * 6..94278332875.49.947.38.25783.192.459248.3.14..32.9.82.4.93.1783.271.49179.64.32 H5: 1 => SOLVED * 615942783328756491947138625783619254592487316461325978254893167836271549179564832 * DURATION: 0:00:08.029012 START: 04:01:42.061779 END: 04:01:50.090791 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-039-base-pr-001.dot * REASONING * DIS # I3: 1,6 => CTR => I3: 5 * DIS I3: 5 # I7: 1,6 => CTR => I7: 7 * DIS I3: 5 + I7: 7 # H5: 6,7 => CTR => H5: 1 * PRF I3: 5 + I7: 7 + H5: 1 => SOL * STA I3: 5 + I7: 7 + H5: 1 * CNT 4 HDP CHAINS / 5 HYP OPENED
Header Info
Top 500 Minimum 17 039 solution: 615942783328756491947138625783619254592487316461325978254893167836271549179564832 info: 1370 FNBHWXY S8.f 34423 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 615942783328756491947138625783619254592487316461325978254893167836271549179564832 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 # G3: 1,6 => UNS * DIS # I3: 1,6 => CTR => I3: 5 * INC # I3: 5 => UNS * INC # G3: 1,6 => UNS * DIS # I3: 1,6 => CTR => I3: 5 * INC # I3: 5 => UNS * INC # I5: 1,6 => UNS * DIS # I7: 1,6 => CTR => I7: 5,7 * INC # I7: 5,7 => UNS * DIS # H5: 6,7 => CTR => H5: 1 * INC # H5: 1 => UNS * INC # I5: 6,7 => UNS * DIS # G7: 5,6 => CTR => G7: 1,8 * INC # G7: 1,8 => UNS * DIS # I7: 5,6 => CTR => I7: 1,7 * INC # I7: 1,7 => UNS * PRF # G8: 5,6 => SOL * DIS # G8: 1 => CTR => G8: 5,6 * INC # D7: 1,5 => UNS * PRF # D7: 8 => SOL * INC # G8: 1,5 => UNS * DIS # G8: 6 => CTR => G8: 1,5 * PRF # D7: 5,8 => SOL * DIS # D7: 1 => CTR => D7: 5,8 * INC # G7: 5,8 => UNS * PRF # G7: 1,6 => SOL * CNT 26 HDP CHAINS / 26 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G3: 1,6 => UNS * DIS # I3: 1,6 => CTR => I3: 5 * INC I3: 5 # I5: 1,6 => UNS * DIS I3: 5 # I7: 1,6 => CTR => I7: 7 * DIS I3: 5 + I7: 7 # H5: 6,7 => CTR => H5: 1 * PRF I3: 5 + I7: 7 + H5: 1 => SOL * STA I3: 5 + I7: 7 + H5: 1 * CNT 6 HDP CHAINS / 5 HYP OPENED