Analysis of xx-top500-426-base.sdk
Contents
Original Sudoku
level: medium
position: 84.....6....7.2......3.....5...8....1.......9......2......3..4...7...3...2.9..... initial
Autosolve
position: 843.9.7629..7.2...27.3.8.9.5.2.89.7.1.4.27..97.9..32..6.823.9474978.632.32.974... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I2: 1,5 => CTR => I2: 3,4,8 * DIS # D6: 5,6 => CTR => D6: 1,4 * DIS # I6: 1,5 => CTR => I6: 4,6,8 * PRF # I9: 1,5 => SOL * PRF # I9: 1,5 => SOL * DIS # I2: 1,5 => CTR => I2: 3,4,8 * DIS # I6: 1,5 => CTR => I6: 4,6,8 * CNT 7 HDP CHAINS / 40 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I2: 1,5 => CTR => I2: 3,4,8 * DIS I2: 3,4,8 # D6: 5,6 => CTR => D6: 1,4 * DIS I2: 3,4,8 + D6: 1,4 # I6: 1,5 => CTR => I6: 4,6,8 * DIS I2: 3,4,8 + D6: 1,4 + I6: 4,6,8 # H6: 8 => CTR => H6: 1,5 * PRF I2: 3,4,8 + D6: 1,4 + I6: 4,6,8 + H6: 1,5 # I9: 1,5 => SOL * STA I2: 3,4,8 + D6: 1,4 + I6: 4,6,8 + H6: 1,5 + I9: 1,5 * CNT 5 HDP CHAINS / 29 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 84.....6....7.2......3.....5...8....1.......9......2......3..4...7...3...2.9..... | initial |
| 843.9.7629..7.2...27.3.8.9.5.2.89.7.1.4.27..97.9..32..6.823.9474978.632.32.974... | autosolve |
| 843591762956742138271368594562189473134627859789453216618235947497816325325974681 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) B2: 1,5 D1: 1,5 F1: 1,5 E2: 4,6 E3: 4,6 B4: 3,6 B6: 6,8 D5: 5,6 E6: 1,5 B7: 1,5 C9: 1,5 F7: 1,5 E8: 1,5 I8: 1,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,F1: 1.. / D1 = 1 => 0 pairs (X) / F1 = 1 => 0 pairs (_) B7,C9: 1.. / B7 = 1 => 0 pairs (*) / C9 = 1 => 0 pairs (X) F7,E8: 1.. / F7 = 1 => 0 pairs (X) / E8 = 1 => 0 pairs (_) B7,F7: 1.. / B7 = 1 => 0 pairs (*) / F7 = 1 => 0 pairs (X) E8,I8: 1.. / E8 = 1 => 0 pairs (*) / I8 = 1 => 0 pairs (X) B2,B7: 1.. / B2 = 1 => 0 pairs (X) / B7 = 1 => 0 pairs (_) E6,E8: 1.. / E6 = 1 => 0 pairs (X) / E8 = 1 => 0 pairs (_) F1,F7: 1.. / F1 = 1 => 0 pairs (*) / F7 = 1 => 0 pairs (X) H2,I2: 3.. / H2 = 3 => 18 pairs (_) / I2 = 3 => 14 pairs (_) B4,B5: 3.. / B4 = 3 => 14 pairs (_) / B5 = 3 => 18 pairs (_) I4,H5: 3.. / I4 = 3 => 18 pairs (_) / H5 = 3 => 14 pairs (_) B4,I4: 3.. / B4 = 3 => 14 pairs (_) / I4 = 3 => 18 pairs (_) B5,H5: 3.. / B5 = 3 => 18 pairs (_) / H5 = 3 => 14 pairs (_) H2,H5: 3.. / H2 = 3 => 18 pairs (_) / H5 = 3 => 14 pairs (_) I2,I4: 3.. / I2 = 3 => 14 pairs (_) / I4 = 3 => 18 pairs (_) E2,E3: 4.. / E2 = 4 => 13 pairs (_) / E3 = 4 => 18 pairs (_) D4,D6: 4.. / D4 = 4 => 20 pairs (_) / D6 = 4 => 15 pairs (_) D6,I6: 4.. / D6 = 4 => 15 pairs (_) / I6 = 4 => 20 pairs (_) D1,F1: 5.. / D1 = 5 => 0 pairs (*) / F1 = 5 => 0 pairs (X) B7,C9: 5.. / B7 = 5 => 0 pairs (X) / C9 = 5 => 0 pairs (_) F7,E8: 5.. / F7 = 5 => 0 pairs (*) / E8 = 5 => 0 pairs (X) B7,F7: 5.. / B7 = 5 => 0 pairs (X) / F7 = 5 => 0 pairs (_) E8,I8: 5.. / E8 = 5 => 0 pairs (X) / I8 = 5 => 0 pairs (_) B2,B7: 5.. / B2 = 5 => 0 pairs (*) / B7 = 5 => 0 pairs (X) E6,E8: 5.. / E6 = 5 => 0 pairs (*) / E8 = 5 => 0 pairs (X) F1,F7: 5.. / F1 = 5 => 0 pairs (X) / F7 = 5 => 0 pairs (_) C2,C3: 6.. / C2 = 6 => 13 pairs (_) / C3 = 6 => 18 pairs (_) E2,E3: 6.. / E2 = 6 => 18 pairs (_) / E3 = 6 => 13 pairs (_) G9,I9: 6.. / G9 = 6 => 16 pairs (_) / I9 = 6 => 14 pairs (_) C2,E2: 6.. / C2 = 6 => 13 pairs (_) / E2 = 6 => 18 pairs (_) C3,E3: 6.. / C3 = 6 => 18 pairs (_) / E3 = 6 => 13 pairs (_) B5,B6: 8.. / B5 = 8 => 13 pairs (_) / B6 = 8 => 17 pairs (_) * DURATION: 0:00:58.359582 START: 17:20:52.844761 END: 17:21:51.204343 2017-05-04 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B4,B6,B7,C9,D1,D5,E2,E3,E6,E8,F1,F7,I8) * 843.9.7629..7.2...27.3.8.9.5.2.89.7.1.4.27..97.9..32..6.823.9474978.632.32.974... * PAIR B2: 1,5 BLK 1 C2: 1,5,6 # reduction candidate for 1,5 C2: 1,5 # 18 pairs C3: 1,5,6 # reduction candidate for 1,5 C3: 1,5 # 13 pairs * PAIR B2: 1,5 ROW 2 G2: 1,5,4,8 # reduction candidate for 1,5 G2: 1,5 # 16 pairs H2: 1,5,3,8 # reduction candidate for 1,5 H2: 1,5 # 13 pairs I2: 1,5,3,4,8 # reduction candidate for 1,5 I2: 1,5 => CTR * 843.9.7629..74283.27.368.94562.894731346275897894532166.823594749781632.32.9746.8 I2: 3,4,8 # 14 pairs * PAIR D1: 1,5 COL D D6: 1,5,4,6 # reduction candidate for 1,5 D6: 4,6 # 15 pairs D6: 1,5 # 14 pairs * PAIR B4: 3,6 BLK 4 B5: 3,6,8 # reduction candidate for 3,6 B5: 3,6 # 17 pairs B5: 8 # 13 pairs * PAIR B4: 3,6 ROW 4 I4: 3,6,1,4 # reduction candidate for 3,6 I4: 1,4 # 19 pairs I4: 3,6 # 17 pairs * PAIR B6: 6,8 BLK 4 B5: 6,8,3 # reduction candidate for 6,8 B5: 3 # 18 pairs B5: 6,8 # 14 pairs * PAIR B6: 6,8 ROW 6 I6: 6,8,1,4,5 # reduction candidate for 6,8 I6: 1,4,5 # 19 pairs I6: 6,8 # 17 pairs * PAIR D5: 5,6 BLK 5 D6: 5,6,1,4 # reduction candidate for 5,6 D6: 5,6 => CTR * 84319576291.7.2...27.3.81955.24896731.4.27..97.9.132.46.8231947497856321321974... D6: 1,4 # 15 pairs * PAIR D5: 5,6 ROW 5 G5: 5,6,8 # reduction candidate for 5,6 G5: 8 # 21 pairs G5: 5,6 # 17 pairs * PAIR E6: 1,5 BLK 5 D6: 1,5,4,6 # reduction candidate for 1,5 D6: 4,6 # 15 pairs D6: 1,5 # 14 pairs * PAIR E6: 1,5 ROW 6 H6: 1,5,8 # reduction candidate for 1,5 H6: 1,5 # 16 pairs I6: 1,5,4,6,8 # reduction candidate for 1,5 I6: 1,5 => CTR * 843.9.7629..7.28.327.3.8.9.532.89.761846275397694532816.8235947497816325325974618 I6: 4,6,8 # 14 pairs * PAIR C9: 1,5 ROW 9 G9: 1,5,6,8 # reduction candidate for 1,5 G9: 1,5 # 19 pairs H9: 1,5,8 # reduction candidate for 1,5 H9: 1,5 # 17 pairs I9: 1,5,6,8 # reduction candidate for 1,5 I9: 1,5 => SOLVED * 843591762956742138271368594562189473134627859789453216618235947497816325325974681 I9: 6,8 # 15 pairs * PAIR C9: 1,5 COL C C2: 1,5,6 # reduction candidate for 1,5 C2: 1,5 # 18 pairs C3: 1,5,6 # reduction candidate for 1,5 C3: 1,5 # 13 pairs * PAIR I8: 1,5 BLK 9 G9: 1,5,6,8 # reduction candidate for 1,5 G9: 1,5 # 19 pairs H9: 1,5,8 # reduction candidate for 1,5 H9: 1,5 # 17 pairs I9: 1,5,6,8 # reduction candidate for 1,5 I9: 1,5 => SOLVED * 843591762956742138271368594562189473134627859789453216618235947497816325325974681 I9: 6,8 # 15 pairs * PAIR I8: 1,5 COL I I2: 1,5,3,4,8 # reduction candidate for 1,5 I2: 1,5 => CTR * 843.9.7629..74283.27.368.94562.894731346275897894532166.823594749781632.32.9746.8 I2: 3,4,8 # 14 pairs I3: 1,5,4 # reduction candidate for 1,5 I3: 1,5 # 16 pairs I6: 1,5,4,6,8 # reduction candidate for 1,5 I6: 1,5 => CTR * 843.9.7629..7.28.327.3.8.9.532.89.761846275397694532816.8235947497816325325974618 I6: 4,6,8 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-426-base-pr-000.dot * REASONING * DIS # I2: 1,5 => CTR => I2: 3,4,8 * DIS # D6: 5,6 => CTR => D6: 1,4 * DIS # I6: 1,5 => CTR => I6: 4,6,8 * PRF # I9: 1,5 => SOL * PRF # I9: 1,5 => SOL * DIS # I2: 1,5 => CTR => I2: 3,4,8 * DIS # I6: 1,5 => CTR => I6: 4,6,8 * CNT 7 HDP CHAINS / 40 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B4,B6,B7,C9,D1,D5,E2,E3,E6,E8,F1,F7,I8) * 843.9.7629..7.2...27.3.8.9.5.2.89.7.1.4.27..97.9..32..6.823.9474978.632.32.974... * PAIR B2: 1,5 BLK 1 C2: 1,5,6 # reduction candidate for 1,5 C2: 1,5 # 18 pairs C3: 1,5,6 # reduction candidate for 1,5 C3: 1,5 # 13 pairs * PAIR B2: 1,5 ROW 2 G2: 1,5,4,8 # reduction candidate for 1,5 G2: 1,5 # 16 pairs H2: 1,5,3,8 # reduction candidate for 1,5 H2: 1,5 # 13 pairs I2: 1,5,3,4,8 # reduction candidate for 1,5 I2: 1,5 => CTR * 843.9.7629..74283.27.368.94562.894731346275897894532166.823594749781632.32.9746.8 * PAIR RESTART * PAIR B2: 1,5 BLK 1 C2: 1,5,6 # reduction candidate for 1,5 C2: 1,5 # 18 pairs C3: 1,5,6 # reduction candidate for 1,5 C3: 1,5 # 14 pairs * PAIR B2: 1,5 ROW 2 G2: 1,5,4,8 # reduction candidate for 1,5 G2: 1,5 # 16 pairs H2: 1,5,3,8 # reduction candidate for 1,5 H2: 1,5 # 13 pairs * PAIR D1: 1,5 COL D D6: 1,5,4,6 # reduction candidate for 1,5 D6: 4,6 # 15 pairs D6: 1,5 # 14 pairs * PAIR B4: 3,6 BLK 4 B5: 3,6,8 # reduction candidate for 3,6 B5: 3,6 # 17 pairs B5: 8 # 13 pairs * PAIR B4: 3,6 ROW 4 I4: 3,6,1,4 # reduction candidate for 3,6 I4: 1,4 # 19 pairs I4: 3,6 # 17 pairs * PAIR B6: 6,8 BLK 4 B5: 6,8,3 # reduction candidate for 6,8 B5: 3 # 19 pairs B5: 6,8 # 14 pairs * PAIR B6: 6,8 ROW 6 I6: 6,8,1,4,5 # reduction candidate for 6,8 I6: 1,4,5 # 19 pairs I6: 6,8 # 17 pairs * PAIR D5: 5,6 BLK 5 D6: 5,6,1,4 # reduction candidate for 5,6 D6: 5,6 => CTR * 84319576291.7.2...27.3.81955.24896731.4.27..97.9.132.46.8231947497856321321974... * PAIR D5: 5,6 ROW 5 G5: 5,6,8 # reduction candidate for 5,6 G5: 8 # 22 pairs G5: 5,6 # 18 pairs * PAIR E6: 1,5 ROW 6 H6: 1,5,8 # reduction candidate for 1,5 H6: 1,5 # 17 pairs I6: 1,5,4,6,8 # reduction candidate for 1,5 I6: 1,5 => CTR * 843.9.7629..7.28.327.3.8.9.532.89.761846275397694532816.8235947497816325325974618 * RESTART * PAIR E6: 1,5 ROW 6 H6: 1,5,8 # reduction candidate for 1,5 H6: 8 => CTR * 84359176295.7.2.3.27.3.859.5.2.89.731.4.27..97.9.5328.6.8235947497816325325974.1. * PAIR RESTART * PAIR C9: 1,5 ROW 9 G9: 1,5,6,8 # reduction candidate for 1,5 G9: 1,5 # 17 pairs H9: 1,5,8 # reduction candidate for 1,5 H9: 1,5 # 23 pairs I9: 1,5,6,8 # reduction candidate for 1,5 I9: 1,5 => SOLVED * 843591762956742138271368594562189473134627859789453216618235947497816325325974681 * DURATION: 0:00:32.574642 START: 17:22:32.023938 END: 17:23:04.598580 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-426-base-pr-001.dot * REASONING * DIS # I2: 1,5 => CTR => I2: 3,4,8 * DIS I2: 3,4,8 # D6: 5,6 => CTR => D6: 1,4 * DIS I2: 3,4,8 + D6: 1,4 # I6: 1,5 => CTR => I6: 4,6,8 * DIS I2: 3,4,8 + D6: 1,4 + I6: 4,6,8 # H6: 8 => CTR => H6: 1,5 * PRF I2: 3,4,8 + D6: 1,4 + I6: 4,6,8 + H6: 1,5 # I9: 1,5 => SOL * STA I2: 3,4,8 + D6: 1,4 + I6: 4,6,8 + H6: 1,5 + I9: 1,5 * CNT 5 HDP CHAINS / 29 HYP OPENED
Header Info
Top 500 Minimum 17 426 solution: 843591762956742138271368594562189473134627859789453216618235947497816325325974681 info: 95181 FNBYK S8.f 38718 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 843591762956742138271368594562189473134627859789453216618235947497816325325974681 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 # C2: 1,5 => UNS * INC # C3: 1,5 => UNS * INC # G2: 1,5 => UNS * INC # H2: 1,5 => UNS * DIS # I2: 1,5 => CTR => I2: 3,4,8 * INC # I2: 3,4,8 => UNS * INC # D6: 1,5 => UNS * INC # D6: 4,6 => UNS * INC # B5: 3,6 => UNS * INC # B5: 8 => UNS * INC # I4: 3,6 => UNS * INC # I4: 1,4 => UNS * INC # B5: 6,8 => UNS * INC # B5: 3 => UNS * INC # I6: 6,8 => UNS * INC # I6: 1,4,5 => UNS * DIS # D6: 5,6 => CTR => D6: 1,4 * INC # D6: 1,4 => UNS * INC # G5: 5,6 => UNS * INC # G5: 8 => UNS * INC # D6: 1,5 => UNS * INC # D6: 4,6 => UNS * INC # H6: 1,5 => UNS * DIS # I6: 1,5 => CTR => I6: 4,6,8 * INC # I6: 4,6,8 => UNS * INC # G9: 1,5 => UNS * INC # H9: 1,5 => UNS * PRF # I9: 1,5 => SOL * INC # I9: 6,8 => UNS * INC # C2: 1,5 => UNS * INC # C3: 1,5 => UNS * INC # G9: 1,5 => UNS * INC # H9: 1,5 => UNS * PRF # I9: 1,5 => SOL * INC # I9: 6,8 => UNS * DIS # I2: 1,5 => CTR => I2: 3,4,8 * INC # I2: 3,4,8 => UNS * INC # I3: 1,5 => UNS * DIS # I6: 1,5 => CTR => I6: 4,6,8 * INC # I6: 4,6,8 => UNS * CNT 40 HDP CHAINS / 40 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C2: 1,5 => UNS * INC # C3: 1,5 => UNS * INC # G2: 1,5 => UNS * INC # H2: 1,5 => UNS * DIS # I2: 1,5 => CTR => I2: 3,4,8 * INC I2: 3,4,8 # C2: 1,5 => UNS * INC I2: 3,4,8 # C3: 1,5 => UNS * INC I2: 3,4,8 # G2: 1,5 => UNS * INC I2: 3,4,8 # H2: 1,5 => UNS * INC I2: 3,4,8 # D6: 1,5 => UNS * INC I2: 3,4,8 # D6: 4,6 => UNS * INC I2: 3,4,8 # B5: 3,6 => UNS * INC I2: 3,4,8 # B5: 8 => UNS * INC I2: 3,4,8 # I4: 3,6 => UNS * INC I2: 3,4,8 # I4: 1,4 => UNS * INC I2: 3,4,8 # B5: 6,8 => UNS * INC I2: 3,4,8 # B5: 3 => UNS * INC I2: 3,4,8 # I6: 6,8 => UNS * INC I2: 3,4,8 # I6: 1,4,5 => UNS * DIS I2: 3,4,8 # D6: 5,6 => CTR => D6: 1,4 * INC I2: 3,4,8 + D6: 1,4 # G5: 5,6 => UNS * INC I2: 3,4,8 + D6: 1,4 # G5: 8 => UNS * INC I2: 3,4,8 + D6: 1,4 # H6: 1,5 => UNS * DIS I2: 3,4,8 + D6: 1,4 # I6: 1,5 => CTR => I6: 4,6,8 * INC I2: 3,4,8 + D6: 1,4 + I6: 4,6,8 # H6: 1,5 => UNS * DIS I2: 3,4,8 + D6: 1,4 + I6: 4,6,8 # H6: 8 => CTR => H6: 1,5 * INC I2: 3,4,8 + D6: 1,4 + I6: 4,6,8 + H6: 1,5 # G9: 1,5 => UNS * INC I2: 3,4,8 + D6: 1,4 + I6: 4,6,8 + H6: 1,5 # H9: 1,5 => UNS * PRF I2: 3,4,8 + D6: 1,4 + I6: 4,6,8 + H6: 1,5 # I9: 1,5 => SOL * STA I2: 3,4,8 + D6: 1,4 + I6: 4,6,8 + H6: 1,5 + I9: 1,5 * CNT 29 HDP CHAINS / 29 HYP OPENED