Analysis of xx-top500-284-base.sdk
Contents
Original Sudoku
level: medium
position: .......51.7..3....8...........5.1.4..3....6.....8.....5..42......1...3........7.. initial
Autosolve
position: 3..78..51174.358..85.1...37.875.1.43.35.7.618.1.8.357.5.342718.7.16583.4.483197.5 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 2,6 => CTR => C1: 9 * PRF # F1: 4 => SOL * DIS # I2: 6 => CTR => I2: 2,9 * DIS # G3: 2 => CTR => G3: 4,9 * DIS # E6: 6 => CTR => E6: 4,9 * PRF # I2: 6,9 => SOL * DIS # I2: 2 => CTR => I2: 6,9 * DIS # A6: 2,6 => CTR => A6: 4,9 * DIS # A6: 2,6 => CTR => A6: 4,9 * DIS # C1: 2,6 => CTR => C1: 9 * DIS # E6: 6,9 => CTR => E6: 4 * PRF # E6: 4 => SOL * DIS # A4: 6,9 => CTR => A4: 2 * PRF # A4: 2 => SOL * DIS # F3: 2,4 => CTR => F3: 6 * DIS # A4: 6 => CTR => A4: 2,9 * PRF # G1: 2,9 => SOL * PRF # A6: 2,9 => SOL * DIS # I2: 6 => CTR => I2: 2,9 * DIS # A6: 2,6 => CTR => A6: 4,9 * PRF # I2: 6,9 => SOL * DIS # I2: 2 => CTR => I2: 6,9 * CNT 22 HDP CHAINS / 42 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 2,6 => CTR => C1: 9 * PRF C1: 9 # F1: 4 => SOL * STA C1: 9 + F1: 4 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .......51.7..3....8...........5.1.4..3....6.....8.....5..42......1...3........7.. | initial |
| 3..78..51174.358..85.1...37.875.1.43.35.7.618.1.8.357.5.342718.7.16583.4.483197.5 | autosolve |
| 369784251174235869852196437287561943435972618916843572593427186721658394648319725 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) B1: 2,6 D2: 2,9 E3: 4,9 H2: 6,9 A5: 4,9 C6: 2,6 E4: 6,9 D5: 2,9 F5: 2,4 G4: 2,9 I6: 2,9 B7: 6,9 B8: 2,9 A9: 2,6 I7: 6,9 H8: 2,9 H9: 2,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D5,F5: 2.. / D5 = 2 => 0 pairs (X) / F5 = 2 => 0 pairs (_) G4,I6: 2.. / G4 = 2 => 0 pairs (X) / I6 = 2 => 0 pairs (_) B8,A9: 2.. / B8 = 2 => 13 pairs (_) / A9 = 2 => 0 pairs (X) H8,H9: 2.. / H8 = 2 => 0 pairs (X) / H9 = 2 => 13 pairs (_) D2,I2: 2.. / D2 = 2 => 0 pairs (*) / I2 = 2 => 0 pairs (X) A4,G4: 2.. / A4 = 2 => 0 pairs (*) / G4 = 2 => 0 pairs (X) B8,H8: 2.. / B8 = 2 => 13 pairs (_) / H8 = 2 => 0 pairs (X) A9,H9: 2.. / A9 = 2 => 0 pairs (X) / H9 = 2 => 13 pairs (_) B1,B8: 2.. / B1 = 2 => 0 pairs (X) / B8 = 2 => 13 pairs (_) D2,D5: 2.. / D2 = 2 => 0 pairs (*) / D5 = 2 => 0 pairs (X) I2,I6: 2.. / I2 = 2 => 0 pairs (X) / I6 = 2 => 0 pairs (_) G1,G3: 4.. / G1 = 4 => 20 pairs (_) / G3 = 4 => 0 pairs (*) A5,A6: 4.. / A5 = 4 => 0 pairs (*) / A6 = 4 => 0 pairs (X) F5,E6: 4.. / F5 = 4 => 0 pairs (X) / E6 = 4 => 0 pairs (_) F1,G1: 4.. / F1 = 4 => 0 pairs (*) / G1 = 4 => 0 pairs (X) A5,F5: 4.. / A5 = 4 => 0 pairs (*) / F5 = 4 => 0 pairs (X) A6,E6: 4.. / A6 = 4 => 0 pairs (X) / E6 = 4 => 0 pairs (_) E3,E6: 4.. / E3 = 4 => 0 pairs (X) / E6 = 4 => 0 pairs (_) F1,F3: 6.. / F1 = 6 => 0 pairs (X) / F3 = 6 => 19 pairs (_) H2,I2: 6.. / H2 = 6 => 13 pairs (_) / I2 = 6 => 0 pairs (X) E4,E6: 6.. / E4 = 6 => 18 pairs (_) / E6 = 6 => 0 pairs (X) B7,A9: 6.. / B7 = 6 => 0 pairs (X) / A9 = 6 => 13 pairs (_) I7,H9: 6.. / I7 = 6 => 13 pairs (_) / H9 = 6 => 0 pairs (X) C3,F3: 6.. / C3 = 6 => 0 pairs (X) / F3 = 6 => 19 pairs (_) A4,E4: 6.. / A4 = 6 => 0 pairs (X) / E4 = 6 => 18 pairs (_) B7,I7: 6.. / B7 = 6 => 0 pairs (X) / I7 = 6 => 13 pairs (_) A9,H9: 6.. / A9 = 6 => 13 pairs (_) / H9 = 6 => 0 pairs (X) B1,B7: 6.. / B1 = 6 => 13 pairs (_) / B7 = 6 => 0 pairs (X) H2,H9: 6.. / H2 = 6 => 13 pairs (_) / H9 = 6 => 0 pairs (X) I2,I7: 6.. / I2 = 6 => 0 pairs (X) / I7 = 6 => 13 pairs (_) C1,C3: 9.. / C1 = 9 => 19 pairs (_) / C3 = 9 => 0 pairs (X) D2,E3: 9.. / D2 = 9 => 0 pairs (X) / E3 = 9 => 0 pairs (_) G4,I6: 9.. / G4 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) B7,B8: 9.. / B7 = 9 => 13 pairs (_) / B8 = 9 => 0 pairs (X) I7,H8: 9.. / I7 = 9 => 0 pairs (X) / H8 = 9 => 13 pairs (_) C1,G1: 9.. / C1 = 9 => 19 pairs (_) / G1 = 9 => 0 pairs (X) A5,D5: 9.. / A5 = 9 => 0 pairs (X) / D5 = 9 => 0 pairs (_) B7,I7: 9.. / B7 = 9 => 13 pairs (_) / I7 = 9 => 0 pairs (X) B8,H8: 9.. / B8 = 9 => 0 pairs (X) / H8 = 9 => 13 pairs (_) D2,D5: 9.. / D2 = 9 => 0 pairs (X) / D5 = 9 => 0 pairs (_) H2,H8: 9.. / H2 = 9 => 0 pairs (X) / H8 = 9 => 13 pairs (_) * DURATION: 0:01:17.786655 START: 12:37:29.330746 END: 12:38:47.117401 2017-05-04 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A9,B1,B7,B8,C6,D2,D5,E3,E4,F5,G4,H2,H8,H9,I6,I7) * 3..78..51174.358..85.1...37.875.1.43.35.7.618.1.8.357.5.342718.7.16583.4.483197.5 * PAIR B1: 2,6 BLK 1 C1: 2,6,9 # reduction candidate for 2,6 C1: 2,6 => CTR * 3..78.95117493586285914..37.875.1.43.35.7.618.1.8.357.5.342718.7.16583.4.483197.5 C1: 9 # 19 pairs C3: 2,6,9 # reduction candidate for 2,6 C3: 2,6 # 19 pairs * PAIR B1: 2,6 ROW 1 F1: 2,6,4 # reduction candidate for 2,6 F1: 4 => SOLVED * 369784251174235869852196437287561943435972618916843572593427186721658394648319725 F1: 2,6 # 20 pairs * PAIR D2: 2,9 ROW 2 I2: 2,9,6 # reduction candidate for 2,9 I2: 6 => CTR * 3..78..5117423589685.19..37.87561943.359726189168435725634271897916583242483197.5 I2: 2,9 # 13 pairs * PAIR E3: 4,9 ROW 3 G3: 4,9,2 # reduction candidate for 4,9 G3: 2 => CTR * 3..78.451174.358..85.1..237287561943.35.7.618.168.357.5.342718.7.16583.4.483197.5 G3: 4,9 # 21 pairs * PAIR E3: 4,9 COL E E6: 4,9,6 # reduction candidate for 4,9 E6: 6 => CTR * 3..78..51174.358..85.14..37.875912439352746184128635795934271867216583.4.483197.5 E6: 4,9 # 18 pairs * PAIR H2: 6,9 BLK 3 I2: 6,9,2 # reduction candidate for 6,9 I2: 6,9 => SOLVED * 369784251174235869852196437287561943435972618916843572593427186721658394648319725 I2: 2 => CTR * 3..78..51174.3586285.1...37.875.1243.3527461841286357959342718.7.16583.4.483197.5 * PAIR A5: 4,9 BLK 4 A6: 4,9,2,6 # reduction candidate for 4,9 A6: 2,6 => CTR * 3..78..51174.358..85.1...37.875.1.43435972618.1.843579593427186721658394.483197.5 A6: 4,9 # 19 pairs * PAIR C6: 2,6 BLK 4 A4: 2,6,9 # reduction candidate for 2,6 A4: 2,6 # 19 pairs A6: 2,6,4,9 # reduction candidate for 2,6 A6: 2,6 => CTR * 3..78..51174.358..85.1...37.875.1.43435972618.1.843579593427186721658394.483197.5 A6: 4,9 # 19 pairs * PAIR C6: 2,6 COL C C1: 2,6,9 # reduction candidate for 2,6 C1: 2,6 => CTR * 3..78.95117493586285914..37.875.1.43.35.7.618.1.8.357.5.342718.7.16583.4.483197.5 C1: 9 # 19 pairs C3: 2,6,9 # reduction candidate for 2,6 C3: 2,6 # 19 pairs * PAIR E4: 6,9 BLK 5 E6: 6,9,4 # reduction candidate for 6,9 E6: 6,9 => CTR * 3..78.45117493586285.14.937.875.1243935.7461841.8.357.5.342718.7.16583.4.483197.5 E6: 4 => SOLVED * 369784251174235869852196437287561943435972618916843572593427186721658394648319725 * PAIR E4: 6,9 ROW 4 A4: 6,9,2 # reduction candidate for 6,9 A4: 6,9 => CTR * 36.78..5117493586285.14..37.875.1243.35.7.618.1.8.3579593427186721658394648319725 A4: 2 => SOLVED * 369784251174235869852196437287561943435972618916843572593427186721658394648319725 * PAIR F5: 2,4 COL F F1: 2,4,6 # reduction candidate for 2,4 F1: 2,4 # 19 pairs F3: 2,4,6 # reduction candidate for 2,4 F3: 2,4 => CTR * 3..786451174.358..8561...37.875.1.43.35.7.618.128.35795.342718.7.16583.4.483197.5 F3: 6 # 19 pairs * PAIR G4: 2,9 ROW 4 A4: 2,9,6 # reduction candidate for 2,9 A4: 6 => CTR * 3..78..51174.358..85.1...376875912439352746184128635795.342718.7.16583.4.483197.5 A4: 2,9 # 18 pairs * PAIR G4: 2,9 COL G G1: 2,9,4 # reduction candidate for 2,9 G1: 2,9 => SOLVED * 369784251174235869852196437287561943435972618916843572593427186721658394648319725 G1: 4 # 20 pairs G3: 2,9,4 # reduction candidate for 2,9 G3: 2,9 # 20 pairs * PAIR I6: 2,9 ROW 6 A6: 2,9,4,6 # reduction candidate for 2,9 A6: 2,9 => SOLVED * 369784251174235869852196437287561943435972618916843572593427186721658394648319725 A6: 4,6 # 18 pairs * PAIR I6: 2,9 COL I I2: 2,9,6 # reduction candidate for 2,9 I2: 6 => CTR * 3..78..5117423589685.19..37.87561943.359726189168435725634271897916583242483197.5 I2: 2,9 # 13 pairs * PAIR A9: 2,6 COL A A4: 2,6,9 # reduction candidate for 2,6 A4: 2,6 # 19 pairs A6: 2,6,4,9 # reduction candidate for 2,6 A6: 2,6 => CTR * 3..78..51174.358..85.1...37.875.1.43435972618.1.843579593427186721658394.483197.5 A6: 4,9 # 19 pairs * PAIR I7: 6,9 COL I I2: 6,9,2 # reduction candidate for 6,9 I2: 6,9 => SOLVED * 369784251174235869852196437287561943435972618916843572593427186721658394648319725 I2: 2 => CTR * 3..78..51174.3586285.1...37.875.1243.3527461841286357959342718.7.16583.4.483197.5 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-284-base-pr-000.dot * REASONING * DIS # C1: 2,6 => CTR => C1: 9 * PRF # F1: 4 => SOL * DIS # I2: 6 => CTR => I2: 2,9 * DIS # G3: 2 => CTR => G3: 4,9 * DIS # E6: 6 => CTR => E6: 4,9 * PRF # I2: 6,9 => SOL * DIS # I2: 2 => CTR => I2: 6,9 * DIS # A6: 2,6 => CTR => A6: 4,9 * DIS # A6: 2,6 => CTR => A6: 4,9 * DIS # C1: 2,6 => CTR => C1: 9 * DIS # E6: 6,9 => CTR => E6: 4 * PRF # E6: 4 => SOL * DIS # A4: 6,9 => CTR => A4: 2 * PRF # A4: 2 => SOL * DIS # F3: 2,4 => CTR => F3: 6 * DIS # A4: 6 => CTR => A4: 2,9 * PRF # G1: 2,9 => SOL * PRF # A6: 2,9 => SOL * DIS # I2: 6 => CTR => I2: 2,9 * DIS # A6: 2,6 => CTR => A6: 4,9 * PRF # I2: 6,9 => SOL * DIS # I2: 2 => CTR => I2: 6,9 * CNT 22 HDP CHAINS / 42 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A9,B1,B7,B8,C6,D2,D5,E3,E4,F5,G4,H2,H8,H9,I6,I7) * 3..78..51174.358..85.1...37.875.1.43.35.7.618.1.8.357.5.342718.7.16583.4.483197.5 * PAIR B1: 2,6 BLK 1 C1: 2,6,9 # reduction candidate for 2,6 C1: 2,6 => CTR * 3..78.95117493586285914..37.875.1.43.35.7.618.1.8.357.5.342718.7.16583.4.483197.5 * RESTART * PAIR B1: 2,6 ROW 1 F1: 2,6,4 # reduction candidate for 2,6 F1: 4 => SOLVED * 369784251174235869852196437287561943435972618916843572593427186721658394648319725 * DURATION: 0:00:04.124824 START: 12:39:31.253350 END: 12:39:35.378174 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-284-base-pr-001.dot * REASONING * DIS # C1: 2,6 => CTR => C1: 9 * PRF C1: 9 # F1: 4 => SOL * STA C1: 9 + F1: 4 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 284 solution: 369784251174235869852196437287561943435972618916843572593427186721658394648319725 info: 2332 FNBTWXY S8.f 416 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 369784251174235869852196437287561943435972618916843572593427186721658394648319725 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 # C1: 2,6 => CTR => C1: 9 * INC # C1: 9 => UNS * INC # C3: 2,6 => UNS * INC # F1: 2,6 => UNS * PRF # F1: 4 => SOL * INC # I2: 2,9 => UNS * DIS # I2: 6 => CTR => I2: 2,9 * INC # G3: 4,9 => UNS * DIS # G3: 2 => CTR => G3: 4,9 * INC # E6: 4,9 => UNS * DIS # E6: 6 => CTR => E6: 4,9 * PRF # I2: 6,9 => SOL * DIS # I2: 2 => CTR => I2: 6,9 * INC # A6: 4,9 => UNS * DIS # A6: 2,6 => CTR => A6: 4,9 * INC # A4: 2,6 => UNS * DIS # A6: 2,6 => CTR => A6: 4,9 * INC # A6: 4,9 => UNS * DIS # C1: 2,6 => CTR => C1: 9 * INC # C1: 9 => UNS * INC # C3: 2,6 => UNS * DIS # E6: 6,9 => CTR => E6: 4 * PRF # E6: 4 => SOL * DIS # A4: 6,9 => CTR => A4: 2 * PRF # A4: 2 => SOL * INC # F1: 2,4 => UNS * DIS # F3: 2,4 => CTR => F3: 6 * INC # F3: 6 => UNS * INC # A4: 2,9 => UNS * DIS # A4: 6 => CTR => A4: 2,9 * PRF # G1: 2,9 => SOL * INC # G1: 4 => UNS * INC # G3: 2,9 => UNS * PRF # A6: 2,9 => SOL * INC # A6: 4,6 => UNS * INC # I2: 2,9 => UNS * DIS # I2: 6 => CTR => I2: 2,9 * INC # A4: 2,6 => UNS * DIS # A6: 2,6 => CTR => A6: 4,9 * INC # A6: 4,9 => UNS * PRF # I2: 6,9 => SOL * DIS # I2: 2 => CTR => I2: 6,9 * CNT 42 HDP CHAINS / 42 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C1: 2,6 => CTR => C1: 9 * INC C1: 9 # F1: 2,6 => UNS * PRF C1: 9 # F1: 4 => SOL * STA C1: 9 + F1: 4 * CNT 3 HDP CHAINS / 3 HYP OPENED