Analysis of xx-top95-017-base.sdk
Contents
Original Sudoku
level: medium
position: ....3..9....2....1.5.9..............1.2.8.4.6.8.5...2..75......4.1..6..3.....4.6. initial
Autosolve
position: .1..3..9....2....1.5.9.....5........1.2.8.456.8.5...2.675......4.1..6..3.....4.6. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 4,6 => CTR => C2: 3,7,8,9 * PRF # E2: 7 => SOL * PRF # E3: 4,6 => SOL * DIS # C2: 4,6 => CTR => C2: 3,7,8,9 * PRF # E3: 4,6 => SOL * DIS # I7: 2,9 => CTR => I7: 4,8 * CNT 6 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C2: 4,6 => CTR => C2: 3,7,8,9 * PRF C2: 3,7,8,9 # E2: 7 => SOL * STA C2: 3,7,8,9 + E2: 7 * CNT 2 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....3..9....2....1.5.9..............1.2.8.4.6.8.5...2..75......4.1..6..3.....4.6. | initial |
| .1..3..9....2....1.5.9.....5........1.2.8.456.8.5...2.675......4.1..6..3.....4.6. | autosolve |
| 718435692963278541254961378547612839192387456386549127675893214421756983839124765 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) B2: 4,6 D1: 4,6 B4: 4,6 B5: 3,9 C6: 4,6 D4: 4,6 D5: 3,7 E6: 4,6 I6: 7,9 B8: 2,9 E7: 2,9 D8: 7,8 D9: 1,7 H8: 7,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E3,F3: 1.. / E3 = 1 => 19 pairs (_) / F3 = 1 => 21 pairs (_) D7,D9: 1.. / D7 = 1 => 0 pairs (X) / D9 = 1 => 14 pairs (_) F6,G6: 1.. / F6 = 1 => 19 pairs (_) / G6 = 1 => 19 pairs (_) D9,G9: 1.. / D9 = 1 => 14 pairs (_) / G9 = 1 => 0 pairs (X) E3,E4: 1.. / E3 = 1 => 19 pairs (_) / E4 = 1 => 21 pairs (_) H4,H7: 1.. / H4 = 1 => 19 pairs (_) / H7 = 1 => 14 pairs (_) A1,A3: 2.. / A1 = 2 => 14 pairs (_) / A3 = 2 => 15 pairs (_) E4,F4: 2.. / E4 = 2 => 16 pairs (_) / F4 = 2 => 16 pairs (_) B8,B9: 2.. / B8 = 2 => 16 pairs (_) / B9 = 2 => 21 pairs (_) F4,F7: 2.. / F4 = 2 => 16 pairs (_) / F7 = 2 => 16 pairs (_) D7,F7: 3.. / D7 = 3 => 19 pairs (_) / F7 = 3 => 21 pairs (_) B5,B9: 3.. / B5 = 3 => 22 pairs (_) / B9 = 3 => 20 pairs (_) D5,D7: 3.. / D5 = 3 => 21 pairs (_) / D7 = 3 => 19 pairs (_) B4,C6: 4.. / B4 = 4 => 0 pairs (*) / C6 = 4 => 0 pairs (X) D4,E6: 4.. / D4 = 4 => 0 pairs (X) / E6 = 4 => 0 pairs (_) H7,I7: 4.. / H7 = 4 => 23 pairs (_) / I7 = 4 => 15 pairs (_) B4,D4: 4.. / B4 = 4 => 0 pairs (*) / D4 = 4 => 0 pairs (X) C6,E6: 4.. / C6 = 4 => 0 pairs (X) / E6 = 4 => 0 pairs (_) B2,B4: 4.. / B2 = 4 => 0 pairs (X) / B4 = 4 => 0 pairs (_) D1,D4: 4.. / D1 = 4 => 0 pairs (*) / D4 = 4 => 0 pairs (X) F1,F2: 5.. / F1 = 5 => 16 pairs (_) / F2 = 5 => 15 pairs (_) E8,E9: 5.. / E8 = 5 => 15 pairs (_) / E9 = 5 => 14 pairs (_) F2,G2: 5.. / F2 = 5 => 15 pairs (_) / G2 = 5 => 16 pairs (_) E8,G8: 5.. / E8 = 5 => 15 pairs (_) / G8 = 5 => 14 pairs (_) I1,I9: 5.. / I1 = 5 => 15 pairs (_) / I9 = 5 => 15 pairs (_) B4,C6: 6.. / B4 = 6 => 0 pairs (X) / C6 = 6 => 0 pairs (_) D4,E6: 6.. / D4 = 6 => 0 pairs (*) / E6 = 6 => 0 pairs (X) B4,D4: 6.. / B4 = 6 => 0 pairs (X) / D4 = 6 => 0 pairs (_) C6,E6: 6.. / C6 = 6 => 0 pairs (*) / E6 = 6 => 0 pairs (X) B2,B4: 6.. / B2 = 6 => 0 pairs (*) / B4 = 6 => 0 pairs (X) D1,D4: 6.. / D1 = 6 => 0 pairs (X) / D4 = 6 => 0 pairs (_) C4,A6: 7.. / C4 = 7 => 16 pairs (_) / A6 = 7 => 18 pairs (_) D5,F5: 7.. / D5 = 7 => 19 pairs (_) / F5 = 7 => 21 pairs (_) D8,H8: 7.. / D8 = 7 => 21 pairs (_) / H8 = 7 => 13 pairs (_) A9,C9: 8.. / A9 = 8 => 16 pairs (_) / C9 = 8 => 15 pairs (_) D7,D8: 8.. / D7 = 8 => 21 pairs (_) / D8 = 8 => 13 pairs (_) D8,H8: 8.. / D8 = 8 => 13 pairs (_) / H8 = 8 => 21 pairs (_) A2,C2: 9.. / A2 = 9 => 16 pairs (_) / C2 = 9 => 16 pairs (_) B5,F5: 9.. / B5 = 9 => 20 pairs (_) / F5 = 9 => 22 pairs (_) * DURATION: 0:01:10.491654 START: 23:12:31.312868 END: 23:13:41.804522 2017-05-03 * CP COUNT: (39) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B4,B5,B8,C6,D1,D4,D5,D8,D9,E6,E7,H8,I6) * .1..3..9....2....1.5.9.....5........1.2.8.456.8.5...2.675......4.1..6..3.....4.6. * PAIR B2: 4,6 BLK 1 C1: 4,6,7,8 # reduction candidate for 4,6 C1: 4,6 # 15 pairs C2: 4,6,3,7,8,9 # reduction candidate for 4,6 C2: 4,6 => CTR * .1..3..9.9..27...1.5.9.1...5...12...1.2.87456.8.5.9127675..3.144.1..6..3...1.476. C2: 3,7,8,9 # 14 pairs C3: 4,6,3,7,8 # reduction candidate for 4,6 C3: 4,6 # 16 pairs * PAIR B2: 4,6 ROW 2 E2: 4,6,7 # reduction candidate for 4,6 E2: 7 => SOLVED * 718435692963278541254961378547612839192387456386549127675893214421756983839124765 E2: 4,6 # 16 pairs * PAIR D1: 4,6 BLK 2 E2: 4,6,7 # reduction candidate for 4,6 E2: 4,6 # 16 pairs E3: 4,6,1,7 # reduction candidate for 4,6 E3: 4,6 => SOLVED * 718435692963278541254961378547612839192387456386549127675893214421756983839124765 E3: 1,7 # 16 pairs * PAIR D1: 4,6 ROW 1 C1: 4,6,7,8 # reduction candidate for 4,6 C1: 7,8 # 15 pairs C1: 4,6 # 15 pairs * PAIR B5: 3,9 BLK 4 C4: 3,9,7 # reduction candidate for 3,9 C4: 3,9 # 18 pairs A6: 3,9,7 # reduction candidate for 3,9 A6: 3,9 # 16 pairs * PAIR B5: 3,9 ROW 5 F5: 3,9,7 # reduction candidate for 3,9 F5: 7 # 21 pairs F5: 3,9 # 19 pairs * PAIR B5: 3,9 COL B B9: 3,9,2 # reduction candidate for 3,9 B9: 2 # 21 pairs B9: 3,9 # 16 pairs * PAIR C6: 4,6 COL C C1: 4,6,7,8 # reduction candidate for 4,6 C1: 4,6 # 15 pairs C2: 4,6,3,7,8,9 # reduction candidate for 4,6 C2: 4,6 => CTR * .1..3..9.9..27...1.5.9.1...5...12...1.2.87456.8.5.9127675..3.144.1..6..3...1.476. C2: 3,7,8,9 # 14 pairs C3: 4,6,3,7,8 # reduction candidate for 4,6 C3: 4,6 # 16 pairs * PAIR D5: 3,7 BLK 5 F5: 3,7,9 # reduction candidate for 3,7 F5: 9 # 22 pairs F5: 3,7 # 20 pairs * PAIR E6: 4,6 COL E E2: 4,6,7 # reduction candidate for 4,6 E2: 4,6 # 16 pairs E3: 4,6,1,7 # reduction candidate for 4,6 E3: 4,6 => SOLVED * 718435692963278541254961378547612839192387456386549127675893214421756983839124765 E3: 1,7 # 16 pairs * PAIR I6: 7,9 BLK 6 G4: 7,9,1,3,8 # reduction candidate for 7,9 G4: 7,9 # 17 pairs I4: 7,9,8 # reduction candidate for 7,9 I4: 7,9 # 17 pairs G6: 7,9,1,3 # reduction candidate for 7,9 G6: 7,9 # 24 pairs * PAIR I6: 7,9 ROW 6 A6: 7,9,3 # reduction candidate for 7,9 A6: 3 # 19 pairs A6: 7,9 # 17 pairs * PAIR I6: 7,9 COL I I9: 7,9,2,5 # reduction candidate for 7,9 I9: 7,9 # 18 pairs I9: 2,5 # 15 pairs * PAIR B8: 2,9 BLK 7 B9: 2,9,3 # reduction candidate for 2,9 B9: 2,9 # 22 pairs B9: 3 # 20 pairs * PAIR B8: 2,9 ROW 8 E8: 2,9,5 # reduction candidate for 2,9 E8: 2,9 # 14 pairs G8: 2,9,5 # reduction candidate for 2,9 G8: 2,9 # 15 pairs * PAIR E7: 2,9 BLK 8 F7: 2,9,3 # reduction candidate for 2,9 F7: 2,9 # 19 pairs E8: 2,9,5 # reduction candidate for 2,9 E8: 2,9 # 14 pairs E9: 2,9,5,7 # reduction candidate for 2,9 E9: 2,9 # 15 pairs * PAIR E7: 2,9 ROW 7 G7: 2,9,1,8 # reduction candidate for 2,9 G7: 2,9 # 21 pairs I7: 2,9,4,8 # reduction candidate for 2,9 I7: 2,9 => CTR * .1..3..9....2....1.5.91....5......1.1.2.8.456.8.5.1.2.675....4.4.1..6..3.....4.6. I7: 4,8 # 15 pairs * PAIR E7: 2,9 COL E E4: 2,9,1 # reduction candidate for 2,9 E4: 1 # 21 pairs E4: 2,9 # 19 pairs * PAIR D9: 1,7 ROW 9 G9: 1,7,2,5,9 # reduction candidate for 1,7 G9: 1,7 # 21 pairs G9: 2,5,9 # 14 pairs * PAIR H8: 7,8 COL H H2: 7,8,3,4 # reduction candidate for 7,8 H2: 7,8 # 18 pairs H3: 7,8,3,4 # reduction candidate for 7,8 H3: 7,8 # 18 pairs H4: 7,8,1,3 # reduction candidate for 7,8 H4: 7,8 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-017-base-pr-000.dot * REASONING * DIS # C2: 4,6 => CTR => C2: 3,7,8,9 * PRF # E2: 7 => SOL * PRF # E3: 4,6 => SOL * DIS # C2: 4,6 => CTR => C2: 3,7,8,9 * PRF # E3: 4,6 => SOL * DIS # I7: 2,9 => CTR => I7: 4,8 * CNT 6 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B4,B5,B8,C6,D1,D4,D5,D8,D9,E6,E7,H8,I6) * .1..3..9....2....1.5.9.....5........1.2.8.456.8.5...2.675......4.1..6..3.....4.6. * PAIR B2: 4,6 BLK 1 C1: 4,6,7,8 # reduction candidate for 4,6 C1: 4,6 # 15 pairs C2: 4,6,3,7,8,9 # reduction candidate for 4,6 C2: 4,6 => CTR * .1..3..9.9..27...1.5.9.1...5...12...1.2.87456.8.5.9127675..3.144.1..6..3...1.476. C3: 4,6,3,7,8 # reduction candidate for 4,6 C3: 4,6 # 16 pairs * PAIR B2: 4,6 ROW 2 E2: 4,6,7 # reduction candidate for 4,6 E2: 7 => SOLVED * 718435692963278541254961378547612839192387456386549127675893214421756983839124765 * DURATION: 0:00:06.233229 START: 23:14:30.261969 END: 23:14:36.495198 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-017-base-pr-001.dot * REASONING * DIS # C2: 4,6 => CTR => C2: 3,7,8,9 * PRF C2: 3,7,8,9 # E2: 7 => SOL * STA C2: 3,7,8,9 + E2: 7 * CNT 2 HDP CHAINS / 5 HYP OPENED
Header Info
Top 95 Sudokus 017 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 718435692963278541254961378547612839192387456386549127675893214421756983839124765 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 # C1: 4,6 => UNS * DIS # C2: 4,6 => CTR => C2: 3,7,8,9 * INC # C2: 3,7,8,9 => UNS * INC # C3: 4,6 => UNS * INC # E2: 4,6 => UNS * PRF # E2: 7 => SOL * INC # E2: 4,6 => UNS * PRF # E3: 4,6 => SOL * INC # E3: 1,7 => UNS * INC # C1: 4,6 => UNS * INC # C1: 7,8 => UNS * INC # C4: 3,9 => UNS * INC # A6: 3,9 => UNS * INC # F5: 3,9 => UNS * INC # F5: 7 => UNS * INC # B9: 3,9 => UNS * INC # B9: 2 => UNS * INC # C1: 4,6 => UNS * DIS # C2: 4,6 => CTR => C2: 3,7,8,9 * INC # C2: 3,7,8,9 => UNS * INC # C3: 4,6 => UNS * INC # F5: 3,7 => UNS * INC # F5: 9 => UNS * INC # E2: 4,6 => UNS * PRF # E3: 4,6 => SOL * INC # E3: 1,7 => UNS * INC # G4: 7,9 => UNS * INC # I4: 7,9 => UNS * INC # G6: 7,9 => UNS * INC # A6: 7,9 => UNS * INC # A6: 3 => UNS * INC # I9: 7,9 => UNS * INC # I9: 2,5 => UNS * INC # B9: 2,9 => UNS * INC # B9: 3 => UNS * INC # E8: 2,9 => UNS * INC # G8: 2,9 => UNS * INC # F7: 2,9 => UNS * INC # E8: 2,9 => UNS * INC # E9: 2,9 => UNS * INC # G7: 2,9 => UNS * DIS # I7: 2,9 => CTR => I7: 4,8 * INC # I7: 4,8 => UNS * INC # E4: 2,9 => UNS * INC # E4: 1 => UNS * INC # G9: 1,7 => UNS * INC # G9: 2,5,9 => UNS * INC # H2: 7,8 => UNS * INC # H3: 7,8 => UNS * INC # H4: 7,8 => UNS * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 4,6 => UNS * DIS # C2: 4,6 => CTR => C2: 3,7,8,9 * INC C2: 3,7,8,9 # C3: 4,6 => UNS * INC C2: 3,7,8,9 # E2: 4,6 => UNS * PRF C2: 3,7,8,9 # E2: 7 => SOL * STA C2: 3,7,8,9 + E2: 7 * CNT 5 HDP CHAINS / 5 HYP OPENED