Analysis of xx-top500-011-base.sdk
Contents
Original Sudoku
level: medium
position: 1..5..3.....3.6...2........6.......2....3..4....7.......3...78..4..12............ initial
Autosolve
position: 1..5273.44.73.621.23.4.1.7.67415..32...23.6473.27641..92364578174..12..3....7342. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C3: 6 => CTR => C3: 5,9 * PRF # B5: 5,9 => SOL * DIS # I2: 5 => CTR => I2: 8,9 * DIS # I3: 8,9 => CTR => I3: 5,6 * DIS # I3: 5,8 => CTR => I3: 6,9 * DIS # C1: 6,9 => CTR => C1: 8 * DIS # H8: 5 => CTR => H8: 6,9 * DIS # B5: 5,8 => CTR => B5: 1,9 * DIS # C5: 5,8 => CTR => C5: 1,9 * PRF # B5: 8,9 => SOL * DIS # I6: 5 => CTR => I6: 8,9 * DIS # B1: 8,9 => CTR => B1: 6 * PRF # B1: 6 => SOL * PRF # B5: 8,9 => SOL * DIS # I6: 5 => CTR => I6: 8,9 * DIS # I6: 8 => CTR => I6: 5,9 * DIS # H8: 5,9 => CTR => H8: 6 * DIS # B9: 5,8 => CTR => B9: 1,6 * DIS # C9: 5,8 => CTR => C9: 1,6 * DIS # H8: 5,9 => CTR => H8: 6 * DIS # G3: 8 => CTR => G3: 5,9 * CNT 21 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C3: 6 => CTR => C3: 5,9 * PRF C3: 5,9 # B5: 5,9 => SOL * STA C3: 5,9 + B5: 5,9 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1..5..3.....3.6...2........6.......2....3..4....7.......3...78..4..12............ | initial |
| 1..5273.44.73.621.23.4.1.7.67415..32...23.6473.27641..92364578174..12..3....7342. | autosolve |
| 168527394457396218239481576674159832591238647382764159923645781745812963816973425 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) B2: 5,9 E2: 8,9 E3: 8,9 H1: 6,9 A5: 5,8 B6: 8,9 F4: 8,9 F5: 8,9 G4: 8,9 H6: 5,9 A9: 5,8 D8: 8,9 D9: 8,9 G8: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B5,C5: 1.. / B5 = 1 => 14 pairs (_) / C5 = 1 => 0 pairs (*) B9,C9: 1.. / B9 = 1 => 0 pairs (*) / C9 = 1 => 0 pairs (X) B5,B9: 1.. / B5 = 1 => 14 pairs (_) / B9 = 1 => 0 pairs (*) C5,C9: 1.. / C5 = 1 => 0 pairs (*) / C9 = 1 => 0 pairs (X) B2,C3: 5.. / B2 = 5 => 15 pairs (_) / C3 = 5 => 0 pairs (X) H6,I6: 5.. / H6 = 5 => 15 pairs (_) / I6 = 5 => 0 pairs (X) B2,I2: 5.. / B2 = 5 => 15 pairs (_) / I2 = 5 => 0 pairs (X) A5,A9: 5.. / A5 = 5 => 12 pairs (_) / A9 = 5 => 0 pairs (X) G3,G8: 5.. / G3 = 5 => 14 pairs (_) / G8 = 5 => 19 pairs (_) H6,H8: 5.. / H6 = 5 => 15 pairs (_) / H8 = 5 => 0 pairs (X) H1,I3: 6.. / H1 = 6 => 0 pairs (X) / I3 = 6 => 22 pairs (_) H8,I9: 6.. / H8 = 6 => 22 pairs (_) / I9 = 6 => 0 pairs (X) C3,I3: 6.. / C3 = 6 => 0 pairs (X) / I3 = 6 => 22 pairs (_) C8,H8: 6.. / C8 = 6 => 0 pairs (X) / H8 = 6 => 22 pairs (_) B1,B9: 6.. / B1 = 6 => 0 pairs (*) / B9 = 6 => 0 pairs (X) H1,H8: 6.. / H1 = 6 => 0 pairs (X) / H8 = 6 => 22 pairs (_) I3,I9: 6.. / I3 = 6 => 22 pairs (_) / I9 = 6 => 0 pairs (X) B1,C1: 8.. / B1 = 8 => 0 pairs (X) / C1 = 8 => 15 pairs (_) E2,E3: 8.. / E2 = 8 => 15 pairs (_) / E3 = 8 => 12 pairs (_) F4,F5: 8.. / F4 = 8 => 0 pairs (X) / F5 = 8 => 13 pairs (_) G4,I6: 8.. / G4 = 8 => 13 pairs (_) / I6 = 8 => 0 pairs (X) D8,D9: 8.. / D8 = 8 => 14 pairs (_) / D9 = 8 => 0 pairs (X) E2,I2: 8.. / E2 = 8 => 15 pairs (_) / I2 = 8 => 12 pairs (_) F4,G4: 8.. / F4 = 8 => 0 pairs (X) / G4 = 8 => 13 pairs (_) B6,I6: 8.. / B6 = 8 => 13 pairs (_) / I6 = 8 => 0 pairs (X) C8,D8: 8.. / C8 = 8 => 0 pairs (X) / D8 = 8 => 14 pairs (_) A5,A9: 8.. / A5 = 8 => 0 pairs (X) / A9 = 8 => 12 pairs (_) G3,G4: 8.. / G3 = 8 => 0 pairs (X) / G4 = 8 => 13 pairs (_) E2,E3: 9.. / E2 = 9 => 12 pairs (_) / E3 = 9 => 15 pairs (_) F4,F5: 9.. / F4 = 9 => 13 pairs (_) / F5 = 9 => 0 pairs (X) D8,D9: 9.. / D8 = 9 => 0 pairs (X) / D9 = 9 => 14 pairs (_) F4,G4: 9.. / F4 = 9 => 13 pairs (_) / G4 = 9 => 0 pairs (X) D9,I9: 9.. / D9 = 9 => 14 pairs (_) / I9 = 9 => 0 pairs (X) * DURATION: 0:00:57.353748 START: 02:58:19.461278 END: 02:59:16.815026 2017-05-04 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A9,B2,B6,D8,D9,E2,E3,F4,F5,G4,G8,H1,H6) * 1..5273.44.73.621.23.4.1.7.67415..32...23.6473.27641..92364578174..12..3....7342. * PAIR B2: 5,9 BLK 1 C3: 5,9,6 # reduction candidate for 5,9 C3: 6 => CTR * 1..5273.44573.621.2364.1.7.67415..32...23.6473.27641..92364578174..12.63.61.7342. C3: 5,9 # 22 pairs * PAIR B2: 5,9 ROW 2 I2: 5,9,8 # reduction candidate for 5,9 I2: 5,9 # 15 pairs I2: 8 # 12 pairs * PAIR B2: 5,9 COL B B5: 5,9,1,8 # reduction candidate for 5,9 B5: 5,9 => SOLVED * 168527394457396218239481576674159832591238647382764159923645781745812963816973425 B5: 1,8 # 15 pairs * PAIR E2: 8,9 ROW 2 I2: 8,9,5 # reduction candidate for 8,9 I2: 5 => CTR * 1..5273.44.7386215235491876674158932...2396473927641..92364578174..12..3....7342. I2: 8,9 # 15 pairs * PAIR E3: 8,9 ROW 3 G3: 8,9,5 # reduction candidate for 8,9 G3: 8,9 # 19 pairs I3: 8,9,5,6 # reduction candidate for 8,9 I3: 8,9 => CTR * 1..5273644.73.621.2364.157.67415.832...2386473827641..92364578174..129538...7342. I3: 5,6 # 15 pairs * PAIR H1: 6,9 BLK 3 I3: 6,9,5,8 # reduction candidate for 6,9 I3: 5,8 => CTR * 1..5273644.73.621.2364.1.7.67415..32...23.6473.27641..92364578174..12..3.61.7342. I3: 6,9 # 17 pairs * PAIR H1: 6,9 ROW 1 B1: 6,9,8 # reduction candidate for 6,9 B1: 6,9 # 15 pairs C1: 6,9,8 # reduction candidate for 6,9 C1: 6,9 => CTR * 18.5273.445738621923.49187.67415..32...23.64739276415892364578174..12..3.61.7342. C1: 8 # 15 pairs * PAIR H1: 6,9 COL H H8: 6,9,5 # reduction candidate for 6,9 H8: 5 => CTR * 1..5273644.73.621.2364.1.7.67415..32...23.6473.276419592364578174..12.53.61.73429 H8: 6,9 # 15 pairs * PAIR A5: 5,8 BLK 4 B5: 5,8,1,9 # reduction candidate for 5,8 B5: 5,8 => CTR * 1685273944573.621.23.4.1.7.67415..32..123964739276415892364578174..12..3.1..7342. B5: 1,9 # 15 pairs C5: 5,8,1,9 # reduction candidate for 5,8 C5: 5,8 => CTR * 16.5273.445738621923.491875674158932.1.23964739276415892364578174..125935.1973426 C5: 1,9 # 15 pairs * PAIR B6: 8,9 BLK 4 B5: 8,9,1,5 # reduction candidate for 8,9 B5: 8,9 => SOLVED * 168527394457396218239481576674159832591238647382764159923645781745812963816973425 B5: 1,5 # 15 pairs C5: 8,9,1,5 # reduction candidate for 8,9 C5: 8,9 # 14 pairs * PAIR B6: 8,9 ROW 6 I6: 8,9,5 # reduction candidate for 8,9 I6: 5 => CTR * 16.5273.44.73.621.23.4.1.7.67415.832...23864738276419592364578174..12.538..973426 I6: 8,9 # 15 pairs * PAIR B6: 8,9 COL B B1: 8,9,6 # reduction candidate for 8,9 B1: 8,9 => CTR * 1.652739445739621823948157667415.832.1.23.6473.27641..92364578174..12.63.61.7342. B1: 6 => SOLVED * 168527394457396218239481576674159832591238647382764159923645781745812963816973425 * PAIR F5: 8,9 ROW 5 B5: 8,9,1,5 # reduction candidate for 8,9 B5: 8,9 => SOLVED * 168527394457396218239481576674159832591238647382764159923645781745812963816973425 B5: 1,5 # 15 pairs C5: 8,9,1,5 # reduction candidate for 8,9 C5: 8,9 # 14 pairs * PAIR G4: 8,9 BLK 6 I6: 8,9,5 # reduction candidate for 8,9 I6: 5 => CTR * 16.5273.44.73.621.23.4.1.7.67415.832...23864738276419592364578174..12.538..973426 I6: 8,9 # 15 pairs * PAIR G4: 8,9 COL G G3: 8,9,5 # reduction candidate for 8,9 G3: 8,9 # 19 pairs G3: 5 # 14 pairs * PAIR H6: 5,9 BLK 6 I6: 5,9,8 # reduction candidate for 5,9 I6: 8 => CTR * 1.9527364457386219236491875674158932...2396473927641589236457817489125.3....7342. I6: 5,9 # 13 pairs * PAIR H6: 5,9 COL H H8: 5,9,6 # reduction candidate for 5,9 H8: 5,9 => CTR * 1..5273644.73.621.2364.1.7.67415..32...23.6473.27641..92364578174..12..3.61.7342. H8: 6 # 22 pairs * PAIR A9: 5,8 BLK 7 C8: 5,8,6 # reduction candidate for 5,8 C8: 5,8 # 22 pairs B9: 5,8,1,6 # reduction candidate for 5,8 B9: 5,8 => CTR * 1685273944.73.621.23.4.1.7667415..32.1.23.6473.276415.92364578174.812963....7342. B9: 1,6 # 15 pairs C9: 5,8,1,6 # reduction candidate for 5,8 C9: 5,8 => CTR * 1685273944.73.621.23948157.67415..32..123.6473.27641..92364578174..12..3.1..73426 C9: 1,6 # 15 pairs * PAIR G8: 5,9 BLK 9 H8: 5,9,6 # reduction candidate for 5,9 H8: 5,9 => CTR * 1..5273644.73.621.2364.1.7.67415..32...23.6473.27641..92364578174..12..3.61.7342. H8: 6 # 22 pairs I9: 5,9,6 # reduction candidate for 5,9 I9: 5,9 # 22 pairs * PAIR G8: 5,9 COL G G3: 5,9,8 # reduction candidate for 5,9 G3: 8 => CTR * 16.5273.445738621923.491875674158932...23964739276415892364578174..12593...973426 G3: 5,9 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-011-base-pr-000.dot * REASONING * DIS # C3: 6 => CTR => C3: 5,9 * PRF # B5: 5,9 => SOL * DIS # I2: 5 => CTR => I2: 8,9 * DIS # I3: 8,9 => CTR => I3: 5,6 * DIS # I3: 5,8 => CTR => I3: 6,9 * DIS # C1: 6,9 => CTR => C1: 8 * DIS # H8: 5 => CTR => H8: 6,9 * DIS # B5: 5,8 => CTR => B5: 1,9 * DIS # C5: 5,8 => CTR => C5: 1,9 * PRF # B5: 8,9 => SOL * DIS # I6: 5 => CTR => I6: 8,9 * DIS # B1: 8,9 => CTR => B1: 6 * PRF # B1: 6 => SOL * PRF # B5: 8,9 => SOL * DIS # I6: 5 => CTR => I6: 8,9 * DIS # I6: 8 => CTR => I6: 5,9 * DIS # H8: 5,9 => CTR => H8: 6 * DIS # B9: 5,8 => CTR => B9: 1,6 * DIS # C9: 5,8 => CTR => C9: 1,6 * DIS # H8: 5,9 => CTR => H8: 6 * DIS # G3: 8 => CTR => G3: 5,9 * CNT 21 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A9,B2,B6,D8,D9,E2,E3,F4,F5,G4,G8,H1,H6) * 1..5273.44.73.621.23.4.1.7.67415..32...23.6473.27641..92364578174..12..3....7342. * PAIR B2: 5,9 BLK 1 C3: 5,9,6 # reduction candidate for 5,9 C3: 6 => CTR * 1..5273.44573.621.2364.1.7.67415..32...23.6473.27641..92364578174..12.63.61.7342. * PAIR B2: 5,9 COL B B5: 5,9,1,8 # reduction candidate for 5,9 B5: 5,9 => SOLVED * 168527394457396218239481576674159832591238647382764159923645781745812963816973425 * DURATION: 0:00:03.974928 START: 03:00:03.459434 END: 03:00:07.434362 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-011-base-pr-001.dot * REASONING * DIS # C3: 6 => CTR => C3: 5,9 * PRF C3: 5,9 # B5: 5,9 => SOL * STA C3: 5,9 + B5: 5,9 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 011 solution: 168527394457396218239481576674159832591238647382764159923645781745812963816973425 info: 1308 FNBTWXY S8.f 25693 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 168527394457396218239481576674159832591238647382764159923645781745812963816973425 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 # C3: 5,9 => UNS * DIS # C3: 6 => CTR => C3: 5,9 * INC # I2: 5,9 => UNS * INC # I2: 8 => UNS * PRF # B5: 5,9 => SOL * INC # B5: 1,8 => UNS * INC # I2: 8,9 => UNS * DIS # I2: 5 => CTR => I2: 8,9 * INC # G3: 8,9 => UNS * DIS # I3: 8,9 => CTR => I3: 5,6 * INC # I3: 5,6 => UNS * INC # I3: 6,9 => UNS * DIS # I3: 5,8 => CTR => I3: 6,9 * INC # B1: 6,9 => UNS * DIS # C1: 6,9 => CTR => C1: 8 * INC # C1: 8 => UNS * INC # H8: 6,9 => UNS * DIS # H8: 5 => CTR => H8: 6,9 * DIS # B5: 5,8 => CTR => B5: 1,9 * INC # B5: 1,9 => UNS * DIS # C5: 5,8 => CTR => C5: 1,9 * INC # C5: 1,9 => UNS * PRF # B5: 8,9 => SOL * INC # B5: 1,5 => UNS * INC # C5: 8,9 => UNS * INC # I6: 8,9 => UNS * DIS # I6: 5 => CTR => I6: 8,9 * DIS # B1: 8,9 => CTR => B1: 6 * PRF # B1: 6 => SOL * PRF # B5: 8,9 => SOL * INC # B5: 1,5 => UNS * INC # C5: 8,9 => UNS * INC # I6: 8,9 => UNS * DIS # I6: 5 => CTR => I6: 8,9 * INC # G3: 8,9 => UNS * INC # G3: 5 => UNS * INC # I6: 5,9 => UNS * DIS # I6: 8 => CTR => I6: 5,9 * DIS # H8: 5,9 => CTR => H8: 6 * INC # H8: 6 => UNS * INC # C8: 5,8 => UNS * DIS # B9: 5,8 => CTR => B9: 1,6 * INC # B9: 1,6 => UNS * DIS # C9: 5,8 => CTR => C9: 1,6 * INC # C9: 1,6 => UNS * DIS # H8: 5,9 => CTR => H8: 6 * INC # H8: 6 => UNS * INC # I9: 5,9 => UNS * INC # G3: 5,9 => UNS * DIS # G3: 8 => CTR => G3: 5,9 * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C3: 5,9 => UNS * DIS # C3: 6 => CTR => C3: 5,9 * PRF C3: 5,9 # B5: 5,9 => SOL * STA C3: 5,9 + B5: 5,9 * CNT 3 HDP CHAINS / 3 HYP OPENED