Analysis of xx-top500-342-base.sdk
Contents
Original Sudoku
level: medium
position: 9..8...21.4..5...........6....9.2....7....3.......1...2.1..........3.4....6...... initial
Autosolve
position: 9..8...21.4..5...........64...9.2....7....3.....3.1...2.1.9........3.4..4.6...... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B6: 5,6 => CTR => B6: 2,8,9 * DIS # F1: 4,6 => CTR => F1: 3,7 * DIS # D3: 1,2 => CTR => D3: 7 * DIS # B3: 5,8 => CTR => B3: 1,2 * DIS # C1: 3 => CTR => C1: 5,7 * DIS # D9: 1,2 => CTR => D9: 5,7 * DIS # G9: 7,8,9 => CTR => G9: 1,2 * CNT 7 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B6: 5,6 => CTR => B6: 2,8,9 * DIS B6: 2,8,9 # F1: 4,6 => CTR => F1: 3,7 * PRF B6: 2,8,9 + F1: 3,7 # D2: 1,2 => SOL * STA B6: 2,8,9 + F1: 3,7 + D2: 1,2 * CNT 3 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 9..8...21.4..5...........6....9.2....7....3.......1...2.1..........3.4....6...... | initial |
| 9..8...21.4..5...........64...9.2....7....3.....3.1...2.1.9........3.4..4.6...... | autosolve |
| 965843721742156938318729564653982147179465382824371659231694875597238416486517293 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) B1: 5,6 E1: 4,6 E3: 1,2 G1: 5,7 E9: 1,2 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,D2: 1.. / A2 = 1 => 0 pairs (X) / D2 = 1 => 9 pairs (_) A5,H5: 1.. / A5 = 1 => 9 pairs (_) / H5 = 1 => 0 pairs (X) D8,H8: 1.. / D8 = 1 => 0 pairs (X) / H8 = 1 => 9 pairs (_) B3,B4: 1.. / B3 = 1 => 9 pairs (_) / B4 = 1 => 0 pairs (X) E3,E9: 1.. / E3 = 1 => 0 pairs (X) / E9 = 1 => 9 pairs (_) G4,G9: 1.. / G4 = 1 => 9 pairs (_) / G9 = 1 => 0 pairs (X) C2,D2: 2.. / C2 = 2 => 9 pairs (_) / D2 = 2 => 0 pairs (X) C5,I5: 2.. / C5 = 2 => 0 pairs (X) / I5 = 2 => 9 pairs (_) D8,I8: 2.. / D8 = 2 => 9 pairs (_) / I8 = 2 => 0 pairs (X) B3,B6: 2.. / B3 = 2 => 0 pairs (X) / B6 = 2 => 9 pairs (_) E3,E9: 2.. / E3 = 2 => 9 pairs (_) / E9 = 2 => 0 pairs (X) G6,G9: 2.. / G6 = 2 => 0 pairs (X) / G9 = 2 => 9 pairs (_) F1,F3: 3.. / F1 = 3 => 8 pairs (_) / F3 = 3 => 0 pairs (X) H2,I2: 3.. / H2 = 3 => 5 pairs (_) / I2 = 3 => 5 pairs (_) A4,C4: 3.. / A4 = 3 => 5 pairs (_) / C4 = 3 => 10 pairs (_) B7,B9: 3.. / B7 = 3 => 5 pairs (_) / B9 = 3 => 6 pairs (_) C1,F1: 3.. / C1 = 3 => 0 pairs (X) / F1 = 3 => 8 pairs (_) A3,A4: 3.. / A3 = 3 => 10 pairs (_) / A4 = 3 => 5 pairs (_) E1,F1: 4.. / E1 = 4 => 7 pairs (_) / F1 = 4 => 0 pairs (X) D7,F7: 4.. / D7 = 4 => 6 pairs (_) / F7 = 4 => 7 pairs (_) D5,D7: 4.. / D5 = 4 => 7 pairs (_) / D7 = 4 => 6 pairs (_) G1,G3: 5.. / G1 = 5 => 7 pairs (_) / G3 = 5 => 10 pairs (_) D5,F5: 5.. / D5 = 5 => 6 pairs (_) / F5 = 5 => 8 pairs (_) B1,A2: 6.. / B1 = 6 => 7 pairs (_) / A2 = 6 => 0 pairs (X) E4,E6: 7.. / E4 = 7 => 5 pairs (_) / E6 = 7 => 5 pairs (_) A8,C8: 7.. / A8 = 7 => 5 pairs (_) / C8 = 7 => 8 pairs (_) F2,F3: 9.. / F2 = 9 => 0 pairs (X) / F3 = 9 => 8 pairs (_) F3,G3: 9.. / F3 = 9 => 8 pairs (_) / G3 = 9 => 0 pairs (X) * DURATION: 0:00:39.379525 START: 14:25:38.852891 END: 14:26:18.232416 2017-05-04 * CP COUNT: (28) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,E1,E3,E9,G1) * 9..8...21.4..5...........64...9.2....7....3.....3.1...2.1.9........3.4..4.6...... * PAIR B1: 5,6 COL B B4: 5,6,1,8 # reduction candidate for 5,6 B4: 5,6 # 14 pairs B6: 5,6,2,8,9 # reduction candidate for 5,6 B6: 5,6 => CTR * 9..8...2114.256....2.719.64.1.9.2....72...319..93.12..2.1694...7..13.4.24.65271.. B6: 2,8,9 # 5 pairs * PAIR E1: 4,6 BLK 2 F1: 4,6,3,7 # reduction candidate for 4,6 F1: 4,6 => CTR * 9.38..721.4..5.........3.64...9.2....7....3.....3.1...2.1.9........3.4..4.6...... F1: 3,7 # 7 pairs * PAIR E1: 4,6 COL E E4: 4,6,7,8 # reduction candidate for 4,6 E4: 4,6 # 7 pairs E5: 4,6,8 # reduction candidate for 4,6 E5: 4,6 # 9 pairs E6: 4,6,7,8 # reduction candidate for 4,6 E6: 4,6 # 7 pairs * PAIR E3: 1,2 BLK 2 D2: 1,2,6,7 # reduction candidate for 1,2 D2: 1,2 # 8 pairs D3: 1,2,7 # reduction candidate for 1,2 D3: 1,2 => CTR * 9..8...21142.5...........64.1.9.2....7....312.2.3.1...2.1.9........3.4..4.6...... D3: 7 # 8 pairs * PAIR E3: 1,2 ROW 3 B3: 1,2,5,8 # reduction candidate for 1,2 B3: 5,8 => CTR * 9..8...21.4..5...........64.1.9.2....7....31..2.3.1...2.1.9.......13.4.24.6...... B3: 1,2 # 9 pairs * PAIR G1: 5,7 BLK 3 G3: 5,7,8,9 # reduction candidate for 5,7 G3: 5,7 # 13 pairs G3: 8,9 # 11 pairs * PAIR G1: 5,7 ROW 1 C1: 5,7,3 # reduction candidate for 5,7 C1: 3 => CTR * 963847521142659........396431.9.2....7....312.2.3.1...2.1.9........3.4..4.6...... C1: 5,7 # 8 pairs * PAIR E9: 1,2 BLK 8 D8: 1,2,5,6 # reduction candidate for 1,2 D8: 1,2 # 7 pairs D9: 1,2,5,7 # reduction candidate for 1,2 D9: 1,2 => CTR * 9..8...21.4..5...........64...9.21..17....3.....3.12..2.1.9.6......3.4124.6...... D9: 5,7 # 7 pairs * PAIR E9: 1,2 ROW 9 G9: 1,2,7,8,9 # reduction candidate for 1,2 G9: 7,8,9 => CTR * 9..8...21.4..5...........64...9.21..17....3.....3.12..2.1.9.6......3.4..4.6...... G9: 1,2 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-342-base-pr-000.dot * REASONING * DIS # B6: 5,6 => CTR => B6: 2,8,9 * DIS # F1: 4,6 => CTR => F1: 3,7 * DIS # D3: 1,2 => CTR => D3: 7 * DIS # B3: 5,8 => CTR => B3: 1,2 * DIS # C1: 3 => CTR => C1: 5,7 * DIS # D9: 1,2 => CTR => D9: 5,7 * DIS # G9: 7,8,9 => CTR => G9: 1,2 * CNT 7 HDP CHAINS / 22 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,E1,E3,E9,G1) * 9..8...21.4..5...........64...9.2....7....3.....3.1...2.1.9........3.4..4.6...... * PAIR B1: 5,6 COL B B4: 5,6,1,8 # reduction candidate for 5,6 B4: 5,6 # 14 pairs B6: 5,6,2,8,9 # reduction candidate for 5,6 B6: 5,6 => CTR * 9..8...2114.256....2.719.64.1.9.2....72...319..93.12..2.1694...7..13.4.24.65271.. * RESTART * PAIR B1: 5,6 COL B B4: 5,6,1,8 # reduction candidate for 5,6 B4: 5,6 # 14 pairs B4: 1,8 # 8 pairs * PAIR RESTART * PAIR B1: 5,6 COL B B4: 5,6,1,8 # reduction candidate for 5,6 B4: 5,6 # 14 pairs B4: 1,8 # 8 pairs * PAIR E1: 4,6 BLK 2 F1: 4,6,3,7 # reduction candidate for 4,6 F1: 4,6 => CTR * 9.38..721.4..5.........3.64...9.2....7....3.....3.1...2.1.9........3.4..4.6...... * PAIR E3: 1,2 BLK 2 D2: 1,2,6,7 # reduction candidate for 1,2 D2: 1,2 => SOLVED * 965843721742156938318729564653982147179465382824371659231694875597238416486517293 * DURATION: 0:00:09.521639 START: 14:26:34.574925 END: 14:26:44.096564 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-342-base-pr-001.dot * REASONING * DIS # B6: 5,6 => CTR => B6: 2,8,9 * DIS B6: 2,8,9 # F1: 4,6 => CTR => F1: 3,7 * PRF B6: 2,8,9 + F1: 3,7 # D2: 1,2 => SOL * STA B6: 2,8,9 + F1: 3,7 + D2: 1,2 * CNT 3 HDP CHAINS / 8 HYP OPENED
Header Info
Top 500 Minimum 17 342 solution: 965843721742156938318729564653982147179465382824371659231694875597238416486517293 info: 3295 FNBTHWXY S8.f 39082 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 965843721742156938318729564653982147179465382824371659231694875597238416486517293 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 # B4: 5,6 => UNS * DIS # B6: 5,6 => CTR => B6: 2,8,9 * INC # B6: 2,8,9 => UNS * DIS # F1: 4,6 => CTR => F1: 3,7 * INC # F1: 3,7 => UNS * INC # E4: 4,6 => UNS * INC # E5: 4,6 => UNS * INC # E6: 4,6 => UNS * INC # D2: 1,2 => UNS * DIS # D3: 1,2 => CTR => D3: 7 * INC # D3: 7 => UNS * INC # B3: 1,2 => UNS * DIS # B3: 5,8 => CTR => B3: 1,2 * INC # G3: 5,7 => UNS * INC # G3: 8,9 => UNS * INC # C1: 5,7 => UNS * DIS # C1: 3 => CTR => C1: 5,7 * INC # D8: 1,2 => UNS * DIS # D9: 1,2 => CTR => D9: 5,7 * INC # D9: 5,7 => UNS * INC # G9: 1,2 => UNS * DIS # G9: 7,8,9 => CTR => G9: 1,2 * CNT 22 HDP CHAINS / 22 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B4: 5,6 => UNS * DIS # B6: 5,6 => CTR => B6: 2,8,9 * INC B6: 2,8,9 # B4: 5,6 => UNS * INC B6: 2,8,9 # B4: 1,8 => UNS * INC B6: 2,8,9 # B4: 5,6 => UNS * INC B6: 2,8,9 # B4: 1,8 => UNS * DIS B6: 2,8,9 # F1: 4,6 => CTR => F1: 3,7 * PRF B6: 2,8,9 + F1: 3,7 # D2: 1,2 => SOL * STA B6: 2,8,9 + F1: 3,7 + D2: 1,2 * CNT 8 HDP CHAINS / 8 HYP OPENED