Analysis of xx-top95-020-base.sdk
Contents
Original Sudoku
level: medium
position: ..84...3....3.....9....157479...8........7..514.....2...9.6...2.5....4......9..56 initial
Autosolve
position: ..84...3....3.....9....157479...8........7..514.9...2...9.6...265....4......9..56 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 2,5 => CTR => A2: 4 * PRF # A2: 4 => SOL * DIS # F1: 2,5 => CTR => F1: 6,9 * PRF # D3: 2,8 => SOL * DIS # D3: 6 => CTR => D3: 2,8 * DIS # I2: 1,9 => CTR => I2: 8 * DIS # I8: 1,9 => CTR => I8: 3,7,8 * DIS # E4: 3,5 => CTR => E4: 1,2,4 * PRF # F6: 3,5 => SOL * DIS # F6: 6 => CTR => F6: 3,5 * DIS # C6: 3,5 => CTR => C6: 6 * PRF # C6: 6 => SOL * DIS # G5: 1,3 => CTR => G5: 6,9 * DIS # I8: 7,8,9 => CTR => I8: 1,3 * DIS # I8: 7,8 => CTR => I8: 1,3,9 * PRF # B7: 1,7 => SOL * DIS # B9: 1,7 => CTR => B9: 2,3,8 * DIS # C9: 1,7 => CTR => C9: 4 * PRF # C9: 4 => SOL * DIS # I8: 1,7 => CTR => I8: 3,8,9 * PRF # C2: 1,7 => SOL * DIS # C2: 4 => CTR => C2: 1,7 * DIS # E8: 2,3 => CTR => E8: 1,8 * PRF # F7: 3,4 => SOL * DIS # F7: 5 => CTR => F7: 3,4 * DIS # A9: 3,4 => CTR => A9: 2,8 * DIS # H8: 1,8 => CTR => H8: 9 * DIS # I8: 1,8 => CTR => I8: 3,7,9 * DIS # D7: 1,8 => CTR => D7: 5,7 * CNT 29 HDP CHAINS / 61 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A2: 2,5 => CTR => A2: 4 * PRF A2: 4 => SOL * STA A2: 4 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..84...3....3.....9....157479...8........7..514.....2...9.6...2.5....4......9..56 | initial |
| ..84...3....3.....9....157479...8........7..514.9...2...9.6...265....4......9..56 | autosolve |
| 518476239427359618963821574795248361832617945146935827379564182651782493284193756 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) A1: 2,5 E3: 2,8 I1: 1,9 E6: 3,5 I4: 1,3 G6: 7,8 I6: 7,8 C8: 1,7 F8: 2,3 F9: 3,4 H7: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G1,G2: 2.. / G1 = 2 => 14 pairs (_) / G2 = 2 => 13 pairs (_) A9,B9: 2.. / A9 = 2 => 0 pairs (*) / B9 = 2 => 0 pairs (X) B3,C3: 3.. / B3 = 3 => 13 pairs (_) / C3 = 3 => 16 pairs (_) I4,I8: 3.. / I4 = 3 => 0 pairs (X) / I8 = 3 => 0 pairs (_) A2,C2: 4.. / A2 = 4 => 0 pairs (*) / C2 = 4 => 0 pairs (X) E4,E5: 4.. / E4 = 4 => 14 pairs (_) / E5 = 4 => 11 pairs (_) H4,H5: 4.. / H4 = 4 => 11 pairs (_) / H5 = 4 => 14 pairs (_) F7,F9: 4.. / F7 = 4 => 0 pairs (*) / F9 = 4 => 0 pairs (X) E4,H4: 4.. / E4 = 4 => 14 pairs (_) / H4 = 4 => 11 pairs (_) E5,H5: 4.. / E5 = 4 => 11 pairs (_) / H5 = 4 => 14 pairs (_) A7,F7: 4.. / A7 = 4 => 0 pairs (X) / F7 = 4 => 0 pairs (_) C2,C9: 4.. / C2 = 4 => 0 pairs (X) / C9 = 4 => 0 pairs (_) A1,A2: 5.. / A1 = 5 => 12 pairs (_) / A2 = 5 => 0 pairs (X) C4,C6: 5.. / C4 = 5 => 0 pairs (*) / C6 = 5 => 0 pairs (X) D7,F7: 5.. / D7 = 5 => 0 pairs (*) / F7 = 5 => 0 pairs (X) D4,D7: 5.. / D4 = 5 => 0 pairs (X) / D7 = 5 => 0 pairs (_) C6,F6: 6.. / C6 = 6 => 0 pairs (*) / F6 = 6 => 0 pairs (X) E1,E2: 7.. / E1 = 7 => 12 pairs (_) / E2 = 7 => 16 pairs (_) G6,I6: 7.. / G6 = 7 => 0 pairs (X) / I6 = 7 => 9 pairs (_) B1,E1: 7.. / B1 = 7 => 16 pairs (_) / E1 = 7 => 12 pairs (_) I6,I8: 7.. / I6 = 7 => 9 pairs (_) / I8 = 7 => 0 pairs (X) D3,E3: 8.. / D3 = 8 => 0 pairs (*) / E3 = 8 => 0 pairs (X) A5,B5: 8.. / A5 = 8 => 12 pairs (_) / B5 = 8 => 13 pairs (_) G6,I6: 8.. / G6 = 8 => 9 pairs (_) / I6 = 8 => 0 pairs (X) E3,E8: 8.. / E3 = 8 => 11 pairs (_) / E8 = 8 => 0 pairs (*) F1,F2: 9.. / F1 = 9 => 0 pairs (X) / F2 = 9 => 12 pairs (_) G5,H5: 9.. / G5 = 9 => 11 pairs (_) / H5 = 9 => 0 pairs (X) H8,I8: 9.. / H8 = 9 => 11 pairs (_) / I8 = 9 => 0 pairs (X) * DURATION: 0:00:43.608902 START: 23:17:11.457522 END: 23:17:55.066424 2017-05-03 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,C8,E3,E6,F8,F9,G6,H7,I1,I4,I6) * ..84...3....3.....9....157479...8........7..514.9...2...9.6...265....4......9..56 * PAIR A1: 2,5 BLK 1 A2: 2,5,4 # reduction candidate for 2,5 A2: 2,5 => CTR * ..84...3...43.....963..1574795..8..3..2..7..51469..827..956.71265..324...2..94356 A2: 4 => SOLVED * 518476239427359618963821574795248361832617945146935827379564182651782493284193756 * PAIR A1: 2,5 ROW 1 E1: 2,5,7 # reduction candidate for 2,5 E1: 2,5 # 16 pairs F1: 2,5,6,9 # reduction candidate for 2,5 F1: 2,5 => CTR * 5.84.2.3.4..3592..9..68157479.5.8........7..5145936.2...9.6...265....4......9..56 F1: 6,9 # 12 pairs * PAIR E3: 2,8 BLK 2 D3: 2,8,6 # reduction candidate for 2,8 D3: 2,8 => SOLVED * 518476239427359618963821574795248361832617945146935827379564182651782493284193756 D3: 6 => CTR * 5.84.9.314..3.5...9..68157479...8........7..514.9.6.2...9564..265...24.3..4.93.56 * PAIR E3: 2,8 COL E E8: 2,8,1,3 # reduction candidate for 2,8 E8: 2,8 # 22 pairs E8: 1,3 # 12 pairs * PAIR I1: 1,9 BLK 3 G1: 1,9,2,6 # reduction candidate for 1,9 G1: 1,9 # 14 pairs G2: 1,9,2,6,8 # reduction candidate for 1,9 G2: 1,9 # 14 pairs H2: 1,9,6,8 # reduction candidate for 1,9 H2: 1,9 # 15 pairs I2: 1,9,8 # reduction candidate for 1,9 I2: 1,9 => CTR * ..84...3...43.....9..68157479.5.8..3.....79.5145936.2.4.9.65..265...349.....94.56 I2: 8 # 9 pairs * PAIR I1: 1,9 COL I I8: 1,9,3,7,8 # reduction candidate for 1,9 I8: 1,9 => CTR * ..84...3...43....89..68157479.5.8..3.....7..51459368274.9.65..265...34......94.56 I8: 3,7,8 # 11 pairs * PAIR E6: 3,5 BLK 5 E4: 3,5,1,2,4 # reduction candidate for 3,5 E4: 3,5 => CTR * ..84...3...13....89..68157479...8.41....47..514.9.6827..9.6...2657812493...79.156 E4: 1,2,4 # 11 pairs F6: 3,5,6 # reduction candidate for 3,5 F6: 3,5 => SOLVED * 518476239427359618963821574795248361832617945146935827379564182651782493284193756 F6: 6 => CTR * 5.84.9.314..3.5...9..68157479...8........7..514.9.6.2...9564..265...24.3..4.93.56 * PAIR E6: 3,5 ROW 6 C6: 3,5,6 # reduction candidate for 3,5 C6: 3,5 => CTR * 5.84.9.314..3.5...9..68157479...8........7..514.9.6.2...9564..265...24.3..4.93.56 C6: 6 => SOLVED * 518476239427359618963821574795248361832617945146935827379564182651782493284193756 * PAIR I4: 1,3 BLK 6 G4: 1,3,6 # reduction candidate for 1,3 G4: 1,3 # 14 pairs G5: 1,3,6,9 # reduction candidate for 1,3 G5: 1,3 => CTR * ..84...31.1437..689....157479.518643...2471951459368274.9.65..265...34.9....94.56 G5: 6,9 # 12 pairs * PAIR I4: 1,3 ROW 4 E4: 1,3,2,4,5 # reduction candidate for 1,3 E4: 1,3 # 16 pairs E4: 2,4,5 # 11 pairs * PAIR I4: 1,3 COL I I8: 1,3,7,8,9 # reduction candidate for 1,3 I8: 7,8,9 => CTR * ..84...3...43.....9..68157479.5.8..3.....7..5145936.2.4.9.65..265...34......94.56 I8: 1,3 # 15 pairs * PAIR G6: 7,8 COL G G7: 7,8,1,3 # reduction candidate for 7,8 G7: 7,8 # 13 pairs G9: 7,8,1,3 # reduction candidate for 7,8 G9: 7,8 # 13 pairs * PAIR I6: 7,8 COL I I8: 7,8,1,3,9 # reduction candidate for 7,8 I8: 7,8 => CTR * ..84...3...43.....9..68157479.5.8..3.....79.5145936.2.4.9.65..265...349.....94.56 I8: 1,3,9 # 9 pairs * PAIR C8: 1,7 BLK 7 B7: 1,7,3,8 # reduction candidate for 1,7 B7: 1,7 => SOLVED * 518476239427359618963821574795248361832617945146935827379564182651782493284193756 B7: 3,8 # 12 pairs B9: 1,7,2,3,8 # reduction candidate for 1,7 B9: 1,7 => CTR * 5.84...394..3.9..89....157479...8..1.....79.514.9.5827..9564.8265...24932.4893.56 B9: 2,3,8 # 11 pairs C9: 1,7,4 # reduction candidate for 1,7 C9: 1,7 => CTR * ..84...3...43.....963..1574795..8..3..2..7..51469..827..956.71265..324...2..94356 C9: 4 => SOLVED * 518476239427359618963821574795248361832617945146935827379564182651782493284193756 * PAIR C8: 1,7 ROW 8 D8: 1,7,2,8 # reduction candidate for 1,7 D8: 1,7 # 19 pairs I8: 1,7,3,8,9 # reduction candidate for 1,7 I8: 1,7 => CTR * ..84...3...43.....9236815747925.8..3..62.79.5145936.2.4.9.65..265.82349.2...94.56 I8: 3,8,9 # 9 pairs * PAIR C8: 1,7 COL C C2: 1,7,4 # reduction candidate for 1,7 C2: 1,7 => SOLVED * 518476239427359618963821574795248361832617945146935827379564182651782493284193756 C2: 4 => CTR * ..84...3...43.....963..1574795..8..3..2..7..51469..827..956.71265..324...2..94356 * PAIR F8: 2,3 BLK 8 E8: 2,3,1,8 # reduction candidate for 2,3 E8: 2,3 => CTR * ..84...3...43.....9236815747925.8..3..62.7..5145936.2.4.9.65..265..234..2...94.56 E8: 1,8 # 13 pairs * PAIR F9: 3,4 BLK 8 F7: 3,4,5 # reduction candidate for 3,4 F7: 3,4 => SOLVED * 518476239427359618963821574795248361832617945146935827379564182651782493284193756 F7: 5 => CTR * ..84...3...43.....9..68157479.5.8..3.....7..5145936.2.4.9.65..265...34......94.56 * PAIR F9: 3,4 ROW 9 A9: 3,4,2,8 # reduction candidate for 3,4 A9: 3,4 => CTR * ..84...3...43.....9326815747965.8..38....7..5145936.2.48976531265...34..32..94.56 A9: 2,8 # 12 pairs * PAIR H7: 1,8 BLK 9 G7: 1,8,3,7 # reduction candidate for 1,8 G7: 1,8 # 22 pairs H8: 1,8,9 # reduction candidate for 1,8 H8: 1,8 => CTR * .7845.63151437.2989....157479.5.8..3.....7..51459368274.9.65..265...34.9....94.56 H8: 9 # 11 pairs I8: 1,8,3,7,9 # reduction candidate for 1,8 I8: 1,8 => CTR * ..84...3...43.....9..68157479.5.8..3.....79.51459368274.9.65..265...349.....94.56 I8: 3,7,9 # 11 pairs G9: 1,8,3,7 # reduction candidate for 1,8 G9: 1,8 # 15 pairs * PAIR H7: 1,8 ROW 7 B7: 1,8,3,7 # reduction candidate for 1,8 B7: 1,8 # 15 pairs D7: 1,8,5,7 # reduction candidate for 1,8 D7: 1,8 => CTR * ..84...3...43.....9..68157479.5.8..3.....7..5145936.2.4.9.65..265...34......94.56 D7: 5,7 # 12 pairs * PAIR H7: 1,8 COL H H2: 1,8,6,9 # reduction candidate for 1,8 H2: 1,8 # 17 pairs H2: 6,9 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-020-base-pr-000.dot * REASONING * DIS # A2: 2,5 => CTR => A2: 4 * PRF # A2: 4 => SOL * DIS # F1: 2,5 => CTR => F1: 6,9 * PRF # D3: 2,8 => SOL * DIS # D3: 6 => CTR => D3: 2,8 * DIS # I2: 1,9 => CTR => I2: 8 * DIS # I8: 1,9 => CTR => I8: 3,7,8 * DIS # E4: 3,5 => CTR => E4: 1,2,4 * PRF # F6: 3,5 => SOL * DIS # F6: 6 => CTR => F6: 3,5 * DIS # C6: 3,5 => CTR => C6: 6 * PRF # C6: 6 => SOL * DIS # G5: 1,3 => CTR => G5: 6,9 * DIS # I8: 7,8,9 => CTR => I8: 1,3 * DIS # I8: 7,8 => CTR => I8: 1,3,9 * PRF # B7: 1,7 => SOL * DIS # B9: 1,7 => CTR => B9: 2,3,8 * DIS # C9: 1,7 => CTR => C9: 4 * PRF # C9: 4 => SOL * DIS # I8: 1,7 => CTR => I8: 3,8,9 * PRF # C2: 1,7 => SOL * DIS # C2: 4 => CTR => C2: 1,7 * DIS # E8: 2,3 => CTR => E8: 1,8 * PRF # F7: 3,4 => SOL * DIS # F7: 5 => CTR => F7: 3,4 * DIS # A9: 3,4 => CTR => A9: 2,8 * DIS # H8: 1,8 => CTR => H8: 9 * DIS # I8: 1,8 => CTR => I8: 3,7,9 * DIS # D7: 1,8 => CTR => D7: 5,7 * CNT 29 HDP CHAINS / 61 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,C8,E3,E6,F8,F9,G6,H7,I1,I4,I6) * ..84...3....3.....9....157479...8........7..514.9...2...9.6...265....4......9..56 * PAIR A1: 2,5 BLK 1 A2: 2,5,4 # reduction candidate for 2,5 A2: 2,5 => CTR * ..84...3...43.....963..1574795..8..3..2..7..51469..827..956.71265..324...2..94356 A2: 4 => SOLVED * 518476239427359618963821574795248361832617945146935827379564182651782493284193756 * DURATION: 0:00:03.403839 START: 23:18:48.455544 END: 23:18:51.859383 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-020-base-pr-001.dot * REASONING * DIS # A2: 2,5 => CTR => A2: 4 * PRF A2: 4 => SOL * STA A2: 4 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 95 Sudokus 020 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 518476239427359618963821574795248361832617945146935827379564182651782493284193756 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 # A2: 2,5 => CTR => A2: 4 * PRF # A2: 4 => SOL * INC # E1: 2,5 => UNS * DIS # F1: 2,5 => CTR => F1: 6,9 * INC # F1: 6,9 => UNS * PRF # D3: 2,8 => SOL * DIS # D3: 6 => CTR => D3: 2,8 * INC # E8: 2,8 => UNS * INC # E8: 1,3 => UNS * INC # G1: 1,9 => UNS * INC # G2: 1,9 => UNS * INC # H2: 1,9 => UNS * DIS # I2: 1,9 => CTR => I2: 8 * INC # I2: 8 => UNS * DIS # I8: 1,9 => CTR => I8: 3,7,8 * INC # I8: 3,7,8 => UNS * DIS # E4: 3,5 => CTR => E4: 1,2,4 * INC # E4: 1,2,4 => UNS * PRF # F6: 3,5 => SOL * DIS # F6: 6 => CTR => F6: 3,5 * DIS # C6: 3,5 => CTR => C6: 6 * PRF # C6: 6 => SOL * INC # G4: 1,3 => UNS * DIS # G5: 1,3 => CTR => G5: 6,9 * INC # G5: 6,9 => UNS * INC # E4: 1,3 => UNS * INC # E4: 2,4,5 => UNS * INC # I8: 1,3 => UNS * DIS # I8: 7,8,9 => CTR => I8: 1,3 * INC # G7: 7,8 => UNS * INC # G9: 7,8 => UNS * DIS # I8: 7,8 => CTR => I8: 1,3,9 * INC # I8: 1,3,9 => UNS * PRF # B7: 1,7 => SOL * INC # B7: 3,8 => UNS * DIS # B9: 1,7 => CTR => B9: 2,3,8 * INC # B9: 2,3,8 => UNS * DIS # C9: 1,7 => CTR => C9: 4 * PRF # C9: 4 => SOL * INC # D8: 1,7 => UNS * DIS # I8: 1,7 => CTR => I8: 3,8,9 * INC # I8: 3,8,9 => UNS * PRF # C2: 1,7 => SOL * DIS # C2: 4 => CTR => C2: 1,7 * DIS # E8: 2,3 => CTR => E8: 1,8 * INC # E8: 1,8 => UNS * PRF # F7: 3,4 => SOL * DIS # F7: 5 => CTR => F7: 3,4 * DIS # A9: 3,4 => CTR => A9: 2,8 * INC # A9: 2,8 => UNS * INC # G7: 1,8 => UNS * DIS # H8: 1,8 => CTR => H8: 9 * INC # H8: 9 => UNS * DIS # I8: 1,8 => CTR => I8: 3,7,9 * INC # I8: 3,7,9 => UNS * INC # G9: 1,8 => UNS * INC # B7: 1,8 => UNS * DIS # D7: 1,8 => CTR => D7: 5,7 * INC # D7: 5,7 => UNS * INC # H2: 1,8 => UNS * INC # H2: 6,9 => UNS * CNT 61 HDP CHAINS / 61 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A2: 2,5 => CTR => A2: 4 * PRF A2: 4 => SOL * STA A2: 4 * CNT 2 HDP CHAINS / 1 HYP OPENED