Analysis of xx-top95-092-base.sdk
Contents
Original Sudoku
level: medium
position: .2.3.......6..8.9.83.5........2...8.7.9..5........6..4.......1...1...4.22..7..8.9 initial
Autosolve
position: 92.3....8..64.8.9.83.5........2...8.7.9..5.....2..6..4..8....1...1...4.22..7..8.9 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A4: 1,5 => CTR => A4: 3,4,6 * DIS # E3: 2,7 => CTR => E3: 1,6,9 * DIS # G4: 3,5 => CTR => G4: 1,6,7,9 * DIS # A7: 3,5 => CTR => A7: 4,6 * DIS # E9: 3,5 => CTR => E9: 1,4 * PRF # F7: 3,9 => SOL * CNT 6 HDP CHAINS / 46 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A4: 1,5 => CTR => A4: 3,4,6 * DIS A4: 3,4,6 # A6: 3 => CTR => A6: 1,5 * DIS A4: 3,4,6 + A6: 1,5 # B6: 1,5 => CTR => B6: 8 * DIS A4: 3,4,6 + A6: 1,5 + B6: 8 # E1: 1,7 => CTR => E1: 6 * DIS A4: 3,4,6 + A6: 1,5 + B6: 8 + E1: 6 # E3: 1,7 => CTR => E3: 2,9 * PRF A4: 3,4,6 + A6: 1,5 + B6: 8 + E1: 6 + E3: 2,9 # G1: 1,7 => SOL * STA A4: 3,4,6 + A6: 1,5 + B6: 8 + E1: 6 + E3: 2,9 + G1: 1,7 * CNT 6 HDP CHAINS / 20 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2.3.......6..8.9.83.5........2...8.7.9..5........6..4.......1...1...4.22..7..8.9 | initial |
| 92.3....8..64.8.9.83.5........2...8.7.9..5.....2..6..4..8....1...1...4.22..7..8.9 | autosolve |
| 924361758156478293837592641613247985749185326582936174498623517371859462265714839 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) C1: 4,7 A2: 1,5 B2: 1,5 C3: 4,7 F1: 1,7 E2: 2,7 I2: 3,7 C4: 3,5 D5: 1,8 B7: 7,9 B8: 7,9 C9: 3,5 D7: 6,9 F8: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,B2: 1.. / A2 = 1 => 16 pairs (_) / B2 = 1 => 16 pairs (_) D5,D6: 1.. / D5 = 1 => 18 pairs (_) / D6 = 1 => 18 pairs (_) E9,F9: 1.. / E9 = 1 => 16 pairs (_) / F9 = 1 => 0 pairs (X) G5,H5: 2.. / G5 = 2 => 17 pairs (_) / H5 = 2 => 14 pairs (_) E7,F7: 2.. / E7 = 2 => 0 pairs (*) / F7 = 2 => 0 pairs (X) E2,G2: 2.. / E2 = 2 => 15 pairs (_) / G2 = 2 => 16 pairs (_) F3,F7: 2.. / F3 = 2 => 0 pairs (*) / F7 = 2 => 0 pairs (X) H3,H5: 2.. / H3 = 2 => 17 pairs (_) / H5 = 2 => 14 pairs (_) G2,I2: 3.. / G2 = 3 => 13 pairs (_) / I2 = 3 => 15 pairs (_) C4,C9: 3.. / C4 = 3 => 18 pairs (_) / C9 = 3 => 23 pairs (_) C1,C3: 4.. / C1 = 4 => 13 pairs (_) / C3 = 4 => 12 pairs (_) H1,H3: 4.. / H1 = 4 => 12 pairs (_) / H3 = 4 => 13 pairs (_) A7,B9: 4.. / A7 = 4 => 17 pairs (_) / B9 = 4 => 0 pairs (X) C1,H1: 4.. / C1 = 4 => 13 pairs (_) / H1 = 4 => 12 pairs (_) C3,H3: 4.. / C3 = 4 => 12 pairs (_) / H3 = 4 => 13 pairs (_) B5,E5: 4.. / B5 = 4 => 19 pairs (_) / E5 = 4 => 15 pairs (_) A4,A7: 4.. / A4 = 4 => 0 pairs (X) / A7 = 4 => 17 pairs (_) A2,B2: 5.. / A2 = 5 => 16 pairs (_) / B2 = 5 => 16 pairs (_) G1,H1: 5.. / G1 = 5 => 14 pairs (_) / H1 = 5 => 15 pairs (_) C4,C9: 5.. / C4 = 5 => 23 pairs (_) / C9 = 5 => 18 pairs (_) I4,I7: 5.. / I4 = 5 => 19 pairs (_) / I7 = 5 => 15 pairs (_) E1,E3: 6.. / E1 = 6 => 14 pairs (_) / E3 = 6 => 18 pairs (_) D7,D8: 6.. / D7 = 6 => 15 pairs (_) / D8 = 6 => 0 pairs (X) B9,H9: 6.. / B9 = 6 => 18 pairs (_) / H9 = 6 => 16 pairs (_) C1,C3: 7.. / C1 = 7 => 12 pairs (_) / C3 = 7 => 13 pairs (_) B7,B8: 7.. / B7 = 7 => 16 pairs (_) / B8 = 7 => 13 pairs (_) B8,H8: 7.. / B8 = 7 => 13 pairs (_) / H8 = 7 => 16 pairs (_) B5,B6: 8.. / B5 = 8 => 20 pairs (_) / B6 = 8 => 15 pairs (_) D8,E8: 8.. / D8 = 8 => 17 pairs (_) / E8 = 8 => 19 pairs (_) E3,F3: 9.. / E3 = 9 => 15 pairs (_) / F3 = 9 => 16 pairs (_) G4,G6: 9.. / G4 = 9 => 14 pairs (_) / G6 = 9 => 20 pairs (_) B7,B8: 9.. / B7 = 9 => 13 pairs (_) / B8 = 9 => 16 pairs (_) * DURATION: 0:00:45.431826 START: 01:09:23.586809 END: 01:10:09.018635 2017-05-04 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B2,B7,B8,C1,C3,C4,C9,D5,D7,E2,F1,F8,I2) * 92.3....8..64.8.9.83.5........2...8.7.9..5.....2..6..4..8....1...1...4.22..7..8.9 * PAIR C1: 4,7 ROW 1 H1: 4,7,5,6 # reduction candidate for 4,7 H1: 4,7 # 15 pairs H1: 5,6 # 14 pairs * PAIR A2: 1,5 COL A A4: 1,5,3,4,6 # reduction candidate for 1,5 A4: 1,5 => CTR * 92.3615.851642879383.5976211652..9877491852363829761544.86.2.156.185.4.22537..869 A4: 3,4,6 # 14 pairs A6: 1,5,3 # reduction candidate for 1,5 A6: 1,5 # 18 pairs * PAIR B2: 1,5 COL B B4: 1,5,4,6 # reduction candidate for 1,5 B4: 1,5 # 19 pairs B6: 1,5,8 # reduction candidate for 1,5 B6: 1,5 # 20 pairs * PAIR C3: 4,7 ROW 3 H3: 4,7,2,6 # reduction candidate for 4,7 H3: 4,7 # 16 pairs H3: 2,6 # 13 pairs * PAIR F1: 1,7 BLK 2 E1: 1,7,6 # reduction candidate for 1,7 E1: 1,7 # 18 pairs E3: 1,7,2,6,9 # reduction candidate for 1,7 E3: 1,7 # 20 pairs F3: 1,7,2,9 # reduction candidate for 1,7 F3: 1,7 # 19 pairs * PAIR F1: 1,7 ROW 1 G1: 1,7,5,6 # reduction candidate for 1,7 G1: 1,7 # 16 pairs G1: 5,6 # 15 pairs * PAIR E2: 2,7 BLK 2 E3: 2,7,1,6,9 # reduction candidate for 2,7 E3: 2,7 => CTR * 92.361..85164.8.9383.5.9..7..52.798.7.9..5....82..6..44.8692315691853472253714869 E3: 1,6,9 # 14 pairs F3: 2,7,1,9 # reduction candidate for 2,7 F3: 2,7 # 16 pairs * PAIR E2: 2,7 ROW 2 G2: 2,7,3 # reduction candidate for 2,7 G2: 2,7 # 15 pairs G2: 3 # 13 pairs * PAIR I2: 3,7 BLK 3 G2: 3,7,2 # reduction candidate for 3,7 G2: 2 # 16 pairs G2: 3,7 # 15 pairs * PAIR I2: 3,7 COL I I4: 3,7,1,5,6 # reduction candidate for 3,7 I4: 3,7 # 18 pairs I7: 3,7,5,6 # reduction candidate for 3,7 I7: 3,7 # 22 pairs * PAIR C4: 3,5 BLK 4 A4: 3,5,1,4,6 # reduction candidate for 3,5 A4: 3,5 # 23 pairs A6: 3,5,1 # reduction candidate for 3,5 A6: 3,5 # 16 pairs * PAIR C4: 3,5 ROW 4 G4: 3,5,1,6,7,9 # reduction candidate for 3,5 G4: 3,5 => CTR * 92.3.7..8156428.9.8375.9.4...5294387749..5.....2..69.4..8....155.1.834.22.3751869 G4: 1,6,7,9 # 14 pairs I4: 3,5,1,6,7 # reduction candidate for 3,5 I4: 3,5 # 15 pairs * PAIR D5: 1,8 BLK 5 D6: 1,8,9 # reduction candidate for 1,8 D6: 1,8 # 19 pairs D6: 9 # 17 pairs * PAIR D5: 1,8 ROW 5 B5: 1,8,4,6 # reduction candidate for 1,8 B5: 1,8 # 20 pairs B5: 4,6 # 16 pairs * PAIR C9: 3,5 BLK 7 A7: 3,5,4,6 # reduction candidate for 3,5 A7: 3,5 => CTR * 92.3....8..647829383.592...4..23798.7.9.4532.3.2986..459862471.6.1...4.224.7..869 A7: 4,6 # 15 pairs A8: 3,5,6 # reduction candidate for 3,5 A8: 3,5 # 18 pairs * PAIR C9: 3,5 ROW 9 E9: 3,5,1,4 # reduction candidate for 3,5 E9: 3,5 => CTR * 9243.7.58..6428.9.8375.924.4..2...8.7.9..5.2...2..6..4..8..2.1...1..34.224.751869 E9: 1,4 # 15 pairs H9: 3,5,6 # reduction candidate for 3,5 H9: 3,5 # 18 pairs * PAIR D7: 6,9 BLK 8 D8: 6,9,8 # reduction candidate for 6,9 D8: 6,9 # 19 pairs D8: 8 # 17 pairs * PAIR F8: 3,9 BLK 8 E7: 3,9,2,4,5 # reduction candidate for 3,9 E7: 3,9 # 23 pairs F7: 3,9,2,4 # reduction candidate for 3,9 F7: 3,9 => SOLVED * 924361758156478293837592641613247985749185326582936174498623517371859462265714839 F7: 2,4 # 15 pairs E8: 3,9,5,8 # reduction candidate for 3,9 E8: 3,9 # 20 pairs * PAIR F8: 3,9 COL F F4: 3,9,4,7 # reduction candidate for 3,9 F4: 3,9 # 21 pairs F4: 4,7 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-092-base-pr-000.dot * REASONING * DIS # A4: 1,5 => CTR => A4: 3,4,6 * DIS # E3: 2,7 => CTR => E3: 1,6,9 * DIS # G4: 3,5 => CTR => G4: 1,6,7,9 * DIS # A7: 3,5 => CTR => A7: 4,6 * DIS # E9: 3,5 => CTR => E9: 1,4 * PRF # F7: 3,9 => SOL * CNT 6 HDP CHAINS / 46 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B2,B7,B8,C1,C3,C4,C9,D5,D7,E2,F1,F8,I2) * 92.3....8..64.8.9.83.5........2...8.7.9..5.....2..6..4..8....1...1...4.22..7..8.9 * PAIR C1: 4,7 ROW 1 H1: 4,7,5,6 # reduction candidate for 4,7 H1: 4,7 # 15 pairs H1: 5,6 # 14 pairs * PAIR A2: 1,5 COL A A4: 1,5,3,4,6 # reduction candidate for 1,5 A4: 1,5 => CTR * 92.3615.851642879383.5976211652..9877491852363829761544.86.2.156.185.4.22537..869 A6: 1,5,3 # reduction candidate for 1,5 A6: 1,5 # 18 pairs * RESTART * PAIR A2: 1,5 COL A A6: 1,5,3 # reduction candidate for 1,5 A6: 3 => CTR * 92.3.7..8156428.9.8375.9.4...52...8.7.9..5.2.3.2..6..46.89.2.155916..4.22.3751869 * PAIR RESTART * PAIR B2: 1,5 COL B B4: 1,5,4,6 # reduction candidate for 1,5 B4: 1,5 # 21 pairs B6: 1,5,8 # reduction candidate for 1,5 B6: 1,5 => CTR * 92.3..5.8..64.8.9.83.5........2...85789145.....2836974..8.52.1..71.8.4522.5714839 * RESTART * PAIR B2: 1,5 COL B B4: 1,5,4,6 # reduction candidate for 1,5 B4: 4,6 # 25 pairs B4: 1,5 # 21 pairs * PAIR RESTART * PAIR B2: 1,5 COL B B4: 1,5,4,6 # reduction candidate for 1,5 B4: 4,6 # 25 pairs B4: 1,5 # 21 pairs * PAIR C3: 4,7 ROW 3 H3: 4,7,2,6 # reduction candidate for 4,7 H3: 4,7 # 21 pairs H3: 2,6 # 19 pairs * PAIR F1: 1,7 BLK 2 E1: 1,7,6 # reduction candidate for 1,7 E1: 1,7 => CTR * 92.3..658..6428.9.83.569.4....2...8.7.9..5.2..82..6.34..86.2.1.6.1.534722.37..869 E3: 1,7,2,9 # reduction candidate for 1,7 E3: 1,7 => CTR * 92.36...8516428.9.83.5.9...3.52..9817.9185...1829367544786923156.18534722537..869 F3: 1,7,2,9 # reduction candidate for 1,7 F3: 1,7 # 28 pairs * RESTART * PAIR F1: 1,7 BLK 2 F3: 1,7,2,9 # reduction candidate for 1,7 F3: 1,7 # 28 pairs F3: 2,9 # 22 pairs * PAIR F1: 1,7 ROW 1 G1: 1,7,5 # reduction candidate for 1,7 G1: 1,7 => SOLVED * 924361758156478293837592641613247985749185326582936174498623517371859462265714839 * DURATION: 0:00:20.842279 START: 01:10:46.818064 END: 01:11:07.660343 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-092-base-pr-001.dot * REASONING * DIS # A4: 1,5 => CTR => A4: 3,4,6 * DIS A4: 3,4,6 # A6: 3 => CTR => A6: 1,5 * DIS A4: 3,4,6 + A6: 1,5 # B6: 1,5 => CTR => B6: 8 * DIS A4: 3,4,6 + A6: 1,5 + B6: 8 # E1: 1,7 => CTR => E1: 6 * DIS A4: 3,4,6 + A6: 1,5 + B6: 8 + E1: 6 # E3: 1,7 => CTR => E3: 2,9 * PRF A4: 3,4,6 + A6: 1,5 + B6: 8 + E1: 6 + E3: 2,9 # G1: 1,7 => SOL * STA A4: 3,4,6 + A6: 1,5 + B6: 8 + E1: 6 + E3: 2,9 + G1: 1,7 * CNT 6 HDP CHAINS / 20 HYP OPENED
Header Info
Top 95 Sudokus 092 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 924361758156478293837592641613247985749185326582936174498623517371859462265714839 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 # H1: 4,7 => UNS * INC # H1: 5,6 => UNS * DIS # A4: 1,5 => CTR => A4: 3,4,6 * INC # A4: 3,4,6 => UNS * INC # A6: 1,5 => UNS * INC # B4: 1,5 => UNS * INC # B6: 1,5 => UNS * INC # H3: 4,7 => UNS * INC # H3: 2,6 => UNS * INC # E1: 1,7 => UNS * INC # E3: 1,7 => UNS * INC # F3: 1,7 => UNS * INC # G1: 1,7 => UNS * INC # G1: 5,6 => UNS * DIS # E3: 2,7 => CTR => E3: 1,6,9 * INC # E3: 1,6,9 => UNS * INC # F3: 2,7 => UNS * INC # G2: 2,7 => UNS * INC # G2: 3 => UNS * INC # G2: 3,7 => UNS * INC # G2: 2 => UNS * INC # I4: 3,7 => UNS * INC # I7: 3,7 => UNS * INC # A4: 3,5 => UNS * INC # A6: 3,5 => UNS * DIS # G4: 3,5 => CTR => G4: 1,6,7,9 * INC # G4: 1,6,7,9 => UNS * INC # I4: 3,5 => UNS * INC # D6: 1,8 => UNS * INC # D6: 9 => UNS * INC # B5: 1,8 => UNS * INC # B5: 4,6 => UNS * DIS # A7: 3,5 => CTR => A7: 4,6 * INC # A7: 4,6 => UNS * INC # A8: 3,5 => UNS * DIS # E9: 3,5 => CTR => E9: 1,4 * INC # E9: 1,4 => UNS * INC # H9: 3,5 => UNS * INC # D8: 6,9 => UNS * INC # D8: 8 => UNS * INC # E7: 3,9 => UNS * PRF # F7: 3,9 => SOL * INC # F7: 2,4 => UNS * INC # E8: 3,9 => UNS * INC # F4: 3,9 => UNS * INC # F4: 4,7 => UNS * CNT 46 HDP CHAINS / 46 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # H1: 4,7 => UNS * INC # H1: 5,6 => UNS * DIS # A4: 1,5 => CTR => A4: 3,4,6 * INC A4: 3,4,6 # A6: 1,5 => UNS * INC A4: 3,4,6 # A6: 1,5 => UNS * DIS A4: 3,4,6 # A6: 3 => CTR => A6: 1,5 * INC A4: 3,4,6 + A6: 1,5 # B4: 1,5 => UNS * DIS A4: 3,4,6 + A6: 1,5 # B6: 1,5 => CTR => B6: 8 * INC A4: 3,4,6 + A6: 1,5 + B6: 8 # B4: 1,5 => UNS * INC A4: 3,4,6 + A6: 1,5 + B6: 8 # B4: 4,6 => UNS * INC A4: 3,4,6 + A6: 1,5 + B6: 8 # B4: 1,5 => UNS * INC A4: 3,4,6 + A6: 1,5 + B6: 8 # B4: 4,6 => UNS * INC A4: 3,4,6 + A6: 1,5 + B6: 8 # H3: 4,7 => UNS * INC A4: 3,4,6 + A6: 1,5 + B6: 8 # H3: 2,6 => UNS * DIS A4: 3,4,6 + A6: 1,5 + B6: 8 # E1: 1,7 => CTR => E1: 6 * DIS A4: 3,4,6 + A6: 1,5 + B6: 8 + E1: 6 # E3: 1,7 => CTR => E3: 2,9 * INC A4: 3,4,6 + A6: 1,5 + B6: 8 + E1: 6 + E3: 2,9 # F3: 1,7 => UNS * INC A4: 3,4,6 + A6: 1,5 + B6: 8 + E1: 6 + E3: 2,9 # F3: 1,7 => UNS * INC A4: 3,4,6 + A6: 1,5 + B6: 8 + E1: 6 + E3: 2,9 # F3: 2,9 => UNS * PRF A4: 3,4,6 + A6: 1,5 + B6: 8 + E1: 6 + E3: 2,9 # G1: 1,7 => SOL * STA A4: 3,4,6 + A6: 1,5 + B6: 8 + E1: 6 + E3: 2,9 + G1: 1,7 * CNT 20 HDP CHAINS / 20 HYP OPENED