Analysis of xx-top95-077-base.sdk
Contents
Original Sudoku
level: medium
position: 1.......3.6.3..7...7...5..121.7...9...7........8.1..2....8.64....9.2..6....4..... initial
Autosolve
position: 1...78..3.6.3.17...73..5..12157..89...758213...8.1.527..18.647...912736.7.64...1. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # E3: 4,9 => SOL * DIS # E3: 6 => CTR => E3: 4,9 * PRF # G1: 2,9 => SOL * DIS # I9: 2,9 => CTR => I9: 5,8 * PRF # A5: 4,9 => SOL * DIS # A5: 6 => CTR => A5: 4,9 * DIS # A6: 3,4 => CTR => A6: 6 * PRF # A6: 6 => SOL * DIS # D3: 6,9 => CTR => D3: 2 * PRF # A5: 4,6 => SOL * DIS # A5: 9 => CTR => A5: 4,6 * DIS # B7: 3,5 => CTR => B7: 2 * DIS # B9: 3,5 => CTR => B9: 2,8 * PRF # E7: 3,5 => SOL * DIS # E7: 9 => CTR => E7: 3,5 * PRF # E9: 3,9 => SOL * DIS # I9: 2,9 => CTR => I9: 5,8 * PRF # B8: 4 => SOL * DIS # I9: 2,9 => CTR => I9: 5,8 * PRF # G1: 2,9 => SOL * CNT 20 HDP CHAINS / 38 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # E3: 4,9 => SOL * STA E3: 4,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1.......3.6.3..7...7...5..121.7...9...7........8.1..2....8.64....9.2..6....4..... | initial |
| 1...78..3.6.3.17...73..5..12157..89...758213...8.1.527..18.647...912736.7.64...1. | autosolve |
| 152678943864391752973245681215763894497582136638914527321856479549127368786439215 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (23) B1: 5,9 C1: 2,4 A2: 5,8 C2: 2,4 A3: 8,9 E2: 4,9 H1: 4,5 H2: 5,8 I2: 2,9 H3: 4,8 B5: 4,9 B6: 3,4 E4: 3,6 F4: 3,4 D6: 6,9 F6: 4,9 I4: 4,6 I5: 4,6 A7: 3,5 A8: 4,5 F9: 3,9 I8: 5,8 G9: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,C2: 2.. / C1 = 2 => 0 pairs (*) / C2 = 2 => 0 pairs (X) D1,D3: 2.. / D1 = 2 => 0 pairs (X) / D3 = 2 => 25 pairs (_) B7,B9: 2.. / B7 = 2 => 24 pairs (_) / B9 = 2 => 0 pairs (X) C2,I2: 2.. / C2 = 2 => 0 pairs (X) / I2 = 2 => 0 pairs (_) D3,G3: 2.. / D3 = 2 => 25 pairs (_) / G3 = 2 => 0 pairs (X) B7,I7: 2.. / B7 = 2 => 24 pairs (_) / I7 = 2 => 0 pairs (X) A6,B6: 3.. / A6 = 3 => 0 pairs (X) / B6 = 3 => 24 pairs (_) E4,F4: 3.. / E4 = 3 => 0 pairs (X) / F4 = 3 => 0 pairs (_) A6,A7: 3.. / A6 = 3 => 0 pairs (X) / A7 = 3 => 24 pairs (_) F4,F9: 3.. / F4 = 3 => 0 pairs (*) / F9 = 3 => 0 pairs (X) C1,C2: 4.. / C1 = 4 => 0 pairs (X) / C2 = 4 => 0 pairs (_) E2,E3: 4.. / E2 = 4 => 0 pairs (X) / E3 = 4 => 0 pairs (_) H1,H3: 4.. / H1 = 4 => 0 pairs (*) / H3 = 4 => 0 pairs (X) F4,F6: 4.. / F4 = 4 => 0 pairs (X) / F6 = 4 => 0 pairs (_) I4,I5: 4.. / I4 = 4 => 0 pairs (*) / I5 = 4 => 0 pairs (X) A8,B8: 4.. / A8 = 4 => 25 pairs (_) / B8 = 4 => 0 pairs (*) C1,H1: 4.. / C1 = 4 => 0 pairs (X) / H1 = 4 => 0 pairs (_) C2,E2: 4.. / C2 = 4 => 0 pairs (*) / E2 = 4 => 0 pairs (X) E3,H3: 4.. / E3 = 4 => 0 pairs (*) / H3 = 4 => 0 pairs (X) F4,I4: 4.. / F4 = 4 => 0 pairs (X) / I4 = 4 => 0 pairs (_) B1,A2: 5.. / B1 = 5 => 0 pairs (*) / A2 = 5 => 0 pairs (X) H1,H2: 5.. / H1 = 5 => 0 pairs (X) / H2 = 5 => 0 pairs (_) E7,E9: 5.. / E7 = 5 => 0 pairs (*) / E9 = 5 => 0 pairs (X) B1,H1: 5.. / B1 = 5 => 0 pairs (*) / H1 = 5 => 0 pairs (X) A2,H2: 5.. / A2 = 5 => 0 pairs (X) / H2 = 5 => 0 pairs (_) G1,G3: 6.. / G1 = 6 => 25 pairs (_) / G3 = 6 => 0 pairs (*) A5,A6: 6.. / A5 = 6 => 0 pairs (X) / A6 = 6 => 0 pairs (_) E4,D6: 6.. / E4 = 6 => 0 pairs (*) / D6 = 6 => 0 pairs (X) I4,I5: 6.. / I4 = 6 => 0 pairs (X) / I5 = 6 => 0 pairs (_) D1,G1: 6.. / D1 = 6 => 0 pairs (*) / G1 = 6 => 0 pairs (X) E4,I4: 6.. / E4 = 6 => 0 pairs (*) / I4 = 6 => 0 pairs (X) A5,I5: 6.. / A5 = 6 => 0 pairs (X) / I5 = 6 => 0 pairs (_) A6,D6: 6.. / A6 = 6 => 0 pairs (*) / D6 = 6 => 0 pairs (X) E3,E4: 6.. / E3 = 6 => 0 pairs (X) / E4 = 6 => 0 pairs (_) A2,A3: 8.. / A2 = 8 => 0 pairs (*) / A3 = 8 => 0 pairs (X) H2,H3: 8.. / H2 = 8 => 0 pairs (X) / H3 = 8 => 0 pairs (_) B8,B9: 8.. / B8 = 8 => 24 pairs (_) / B9 = 8 => 24 pairs (_) I8,I9: 8.. / I8 = 8 => 24 pairs (_) / I9 = 8 => 24 pairs (_) A2,H2: 8.. / A2 = 8 => 0 pairs (*) / H2 = 8 => 0 pairs (X) A3,H3: 8.. / A3 = 8 => 0 pairs (X) / H3 = 8 => 0 pairs (_) B8,I8: 8.. / B8 = 8 => 24 pairs (_) / I8 = 8 => 24 pairs (_) B9,I9: 8.. / B9 = 8 => 24 pairs (_) / I9 = 8 => 24 pairs (_) B1,A3: 9.. / B1 = 9 => 0 pairs (X) / A3 = 9 => 0 pairs (_) A5,B5: 9.. / A5 = 9 => 0 pairs (X) / B5 = 9 => 0 pairs (_) D6,F6: 9.. / D6 = 9 => 0 pairs (*) / F6 = 9 => 0 pairs (X) E2,I2: 9.. / E2 = 9 => 0 pairs (*) / I2 = 9 => 0 pairs (X) E7,I7: 9.. / E7 = 9 => 0 pairs (X) / I7 = 9 => 0 pairs (_) A3,A5: 9.. / A3 = 9 => 0 pairs (*) / A5 = 9 => 0 pairs (X) B1,B5: 9.. / B1 = 9 => 0 pairs (X) / B5 = 9 => 0 pairs (_) F6,F9: 9.. / F6 = 9 => 0 pairs (X) / F9 = 9 => 0 pairs (_) * DURATION: 0:01:52.645095 START: 00:42:46.481606 END: 00:44:39.126701 2017-05-04 * CP COUNT: (50) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A7,A8,B1,B5,B6,C1,C2,D6,E2,E4,F4,F6,F9,G9,H1,H2,H3,I2,I4,I5,I8) * 1...78..3.6.3.17...73..5..12157..89...758213...8.1.527..18.647...912736.7.64...1. * PAIR E2: 4,9 BLK 2 E3: 4,9,6 # reduction candidate for 4,9 E3: 4,9 => SOLVED * 152678943864391752973245681215763894497582136638914527321856479549127368786439215 E3: 6 => CTR * 1...78..3.6.3417.9.73.65241215734896697582134..861.527..18.647...912736.7.64...1. * PAIR I2: 2,9 BLK 3 G1: 2,9,6 # reduction candidate for 2,9 G1: 2,9 => SOLVED * 152678943864391752973245681215763894497582136638914527321856479549127368786439215 G1: 6 # 25 pairs G3: 2,9,6 # reduction candidate for 2,9 G3: 2,9 # 25 pairs * PAIR I2: 2,9 COL I I7: 2,9,5 # reduction candidate for 2,9 I7: 2,9 # 25 pairs I9: 2,9,5,8 # reduction candidate for 2,9 I9: 2,9 => CTR * 15..786438643.17...73..5..1215734896697582134..8619527.21896475..9127368786453.1. I9: 5,8 # 25 pairs * PAIR B5: 4,9 BLK 4 A5: 4,9,6 # reduction candidate for 4,9 A5: 4,9 => SOLVED * 152678943864391752973245681215763894497582136638914527321856479549127368786439215 A5: 6 => CTR * 1...78..3.6.3.17..973..5.812157..89.697582134..8619527..18.647...912736.7.64.3.1. * PAIR B6: 3,4 BLK 4 A6: 3,4,6 # reduction candidate for 3,4 A6: 3,4 => CTR * 15..786438643917...73..5..12157..89.697582134..8619527..18.647...912736.7.64.3.1. A6: 6 => SOLVED * 152678943864391752973245681215763894497582136638914527321856479549127368786439215 * PAIR D6: 6,9 COL D D1: 6,9,2 # reduction candidate for 6,9 D1: 6,9 # 25 pairs D3: 6,9,2 # reduction candidate for 6,9 D3: 6,9 => CTR * 194278653562341789873965241215734896..758213...8.1.527..189647...912736.7.645391. D3: 2 # 25 pairs * PAIR I5: 4,6 ROW 5 A5: 4,6,9 # reduction candidate for 4,6 A5: 4,6 => SOLVED * 152678943864391752973245681215763894497582136638914527321856479549127368786439215 A5: 9 => CTR * 19..7865356.3.1782873..5..12157..89.9475821366389145273.18.647.4.912736.7.64.921. * PAIR A7: 3,5 BLK 7 B7: 3,5,2 # reduction candidate for 3,5 B7: 3,5 => CTR * 1.4.78.53562341789873965241215734896..758213...8.19527..1896472.89127365726453918 B7: 2 # 24 pairs B9: 3,5,2,8 # reduction candidate for 3,5 B9: 3,5 => CTR * 1.2.78.43.64391752.73245681215763894.47582136638.1.527.218.64794891273657.64..218 B9: 2,8 # 25 pairs * PAIR A7: 3,5 ROW 7 E7: 3,5,9 # reduction candidate for 3,5 E7: 3,5 => SOLVED * 152678943864391752973245681215763894497582136638914527321856479549127368786439215 E7: 9 => CTR * 1...78..3.6.3417.9.73.65241215734896697582134..861.527..189647...912736.7.6453.1. * PAIR A8: 4,5 BLK 7 B8: 4,5,8 # reduction candidate for 4,5 B8: 8 # 24 pairs B8: 4,5 # 24 pairs * PAIR F9: 3,9 BLK 8 E7: 3,9,5 # reduction candidate for 3,9 E7: 3,9 # 24 pairs E9: 3,9,5 # reduction candidate for 3,9 E9: 3,9 => SOLVED * 152678943864391752973245681215763894497582136638914527321856479549127368786439215 E9: 5 # 24 pairs * PAIR I8: 5,8 BLK 9 I9: 5,8,2,9 # reduction candidate for 5,8 I9: 2,9 => CTR * 15..786438643.17...73..5..1215734896697582134..8619527.21896475..9127368786453.1. I9: 5,8 # 25 pairs * PAIR I8: 5,8 ROW 8 B8: 5,8,4 # reduction candidate for 5,8 B8: 4 => SOLVED * 152678943864391752973245681215763894497582136638914527321856479549127368786439215 B8: 5,8 # 25 pairs * PAIR G9: 2,9 BLK 9 I7: 2,9,5 # reduction candidate for 2,9 I7: 2,9 # 25 pairs I9: 2,9,5,8 # reduction candidate for 2,9 I9: 2,9 => CTR * 15..786438643.17...73..5..1215734896697582134..8619527.21896475..9127368786453.1. I9: 5,8 # 25 pairs * PAIR G9: 2,9 COL G G1: 2,9,6 # reduction candidate for 2,9 G1: 2,9 => SOLVED * 152678943864391752973245681215763894497582136638914527321856479549127368786439215 G1: 6 # 25 pairs G3: 2,9,6 # reduction candidate for 2,9 G3: 2,9 # 25 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-077-base-pr-000.dot * REASONING * PRF # E3: 4,9 => SOL * DIS # E3: 6 => CTR => E3: 4,9 * PRF # G1: 2,9 => SOL * DIS # I9: 2,9 => CTR => I9: 5,8 * PRF # A5: 4,9 => SOL * DIS # A5: 6 => CTR => A5: 4,9 * DIS # A6: 3,4 => CTR => A6: 6 * PRF # A6: 6 => SOL * DIS # D3: 6,9 => CTR => D3: 2 * PRF # A5: 4,6 => SOL * DIS # A5: 9 => CTR => A5: 4,6 * DIS # B7: 3,5 => CTR => B7: 2 * DIS # B9: 3,5 => CTR => B9: 2,8 * PRF # E7: 3,5 => SOL * DIS # E7: 9 => CTR => E7: 3,5 * PRF # E9: 3,9 => SOL * DIS # I9: 2,9 => CTR => I9: 5,8 * PRF # B8: 4 => SOL * DIS # I9: 2,9 => CTR => I9: 5,8 * PRF # G1: 2,9 => SOL * CNT 20 HDP CHAINS / 38 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A7,A8,B1,B5,B6,C1,C2,D6,E2,E4,F4,F6,F9,G9,H1,H2,H3,I2,I4,I5,I8) * 1...78..3.6.3.17...73..5..12157..89...758213...8.1.527..18.647...912736.7.64...1. * PAIR E2: 4,9 BLK 2 E3: 4,9,6 # reduction candidate for 4,9 E3: 4,9 => SOLVED * 152678943864391752973245681215763894497582136638914527321856479549127368786439215 * DURATION: 0:00:02.659457 START: 00:45:28.739097 END: 00:45:31.398554 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-077-base-pr-001.dot * REASONING * PRF # E3: 4,9 => SOL * STA E3: 4,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 95 Sudokus 077 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 152678943864391752973245681215763894497582136638914527321856479549127368786439215 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:
* PRF # E3: 4,9 => SOL * DIS # E3: 6 => CTR => E3: 4,9 * PRF # G1: 2,9 => SOL * INC # G1: 6 => UNS * INC # G3: 2,9 => UNS * INC # I7: 2,9 => UNS * DIS # I9: 2,9 => CTR => I9: 5,8 * INC # I9: 5,8 => UNS * PRF # A5: 4,9 => SOL * DIS # A5: 6 => CTR => A5: 4,9 * DIS # A6: 3,4 => CTR => A6: 6 * PRF # A6: 6 => SOL * INC # D1: 6,9 => UNS * DIS # D3: 6,9 => CTR => D3: 2 * INC # D3: 2 => UNS * PRF # A5: 4,6 => SOL * DIS # A5: 9 => CTR => A5: 4,6 * DIS # B7: 3,5 => CTR => B7: 2 * INC # B7: 2 => UNS * DIS # B9: 3,5 => CTR => B9: 2,8 * INC # B9: 2,8 => UNS * PRF # E7: 3,5 => SOL * DIS # E7: 9 => CTR => E7: 3,5 * INC # B8: 4,5 => UNS * INC # B8: 8 => UNS * INC # E7: 3,9 => UNS * PRF # E9: 3,9 => SOL * INC # E9: 5 => UNS * INC # I9: 5,8 => UNS * DIS # I9: 2,9 => CTR => I9: 5,8 * INC # B8: 5,8 => UNS * PRF # B8: 4 => SOL * INC # I7: 2,9 => UNS * DIS # I9: 2,9 => CTR => I9: 5,8 * INC # I9: 5,8 => UNS * PRF # G1: 2,9 => SOL * INC # G1: 6 => UNS * INC # G3: 2,9 => UNS * CNT 38 HDP CHAINS / 38 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # E3: 4,9 => SOL * STA E3: 4,9 * CNT 1 HDP CHAINS / 1 HYP OPENED