Analysis of xx-top95-011-base.sdk
Contents
Original Sudoku
level: medium
position: 6..3.2....5.....1..........7.26............543.........8.15........4.2........7.. initial
Autosolve
position: 6..3.25...5.....12.2.5.....7426.5..........543.5....2728.15........4.2........7.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # G2: 8,9 => SOL * DIS # I3: 8,9 => CTR => I3: 3,6 * DIS # C1: 8,9 => CTR => C1: 1,4,7 * DIS # I4: 3 => CTR => I4: 8,9 * DIS # G4: 3,9 => CTR => G4: 1,8 * DIS # I4: 3,9 => CTR => I4: 8 * DIS # E4: 1,8 => CTR => E4: 3,9 * PRF # H3: 3,9 => SOL * DIS # A8: 9 => CTR => A8: 1,5 * DIS # A9: 1,5 => CTR => A9: 4,9 * CNT 10 HDP CHAINS / 26 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # G2: 8,9 => SOL * STA G2: 8,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6..3.2....5.....1..........7.26............543.........8.15........4.2........7.. | initial |
| 6..3.25...5.....12.2.5.....7426.5..........543.5....2728.15........4.2........7.. | autosolve |
| 614382579953764812827591436742635198168279354395418627286157943579843261431926785 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (4) I1: 8,9 H4: 3,9 I8: 1,5 I9: 1,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I8,I9: 1.. / I8 = 1 => 2 pairs (_) / I9 = 1 => 0 pairs (X) E4,G4: 1.. / E4 = 1 => 0 pairs (X) / G4 = 1 => 4 pairs (_) D5,E5: 2.. / D5 = 2 => 5 pairs (_) / E5 = 2 => 5 pairs (_) D9,E9: 2.. / D9 = 2 => 5 pairs (_) / E9 = 2 => 5 pairs (_) D5,D9: 2.. / D5 = 2 => 5 pairs (_) / D9 = 2 => 5 pairs (_) E5,E9: 2.. / E5 = 2 => 5 pairs (_) / E9 = 2 => 5 pairs (_) C2,C3: 3.. / C2 = 3 => 0 pairs (*) / C3 = 3 => 0 pairs (X) B8,B9: 3.. / B8 = 3 => 0 pairs (X) / B9 = 3 => 4 pairs (_) C2,G2: 3.. / C2 = 3 => 0 pairs (*) / G2 = 3 => 0 pairs (X) D6,F6: 4.. / D6 = 4 => 4 pairs (_) / F6 = 4 => 6 pairs (_) C1,H1: 4.. / C1 = 4 => 4 pairs (_) / H1 = 4 => 0 pairs (X) D2,D6: 4.. / D2 = 4 => 6 pairs (_) / D6 = 4 => 4 pairs (_) A8,A9: 5.. / A8 = 5 => 2 pairs (_) / A9 = 5 => 0 pairs (X) I8,I9: 5.. / I8 = 5 => 0 pairs (X) / I9 = 5 => 2 pairs (_) A8,I8: 5.. / A8 = 5 => 2 pairs (_) / I8 = 5 => 0 pairs (X) A9,I9: 5.. / A9 = 5 => 0 pairs (X) / I9 = 5 => 2 pairs (_) E2,F2: 6.. / E2 = 6 => 4 pairs (_) / F2 = 6 => 0 pairs (X) H3,I3: 6.. / H3 = 6 => 0 pairs (X) / I3 = 6 => 5 pairs (_) G5,G6: 6.. / G5 = 6 => 0 pairs (X) / G6 = 6 => 5 pairs (_) B6,G6: 6.. / B6 = 6 => 0 pairs (X) / G6 = 6 => 5 pairs (_) E2,E9: 6.. / E2 = 6 => 4 pairs (_) / E9 = 6 => 0 pairs (X) I3,I7: 6.. / I3 = 6 => 5 pairs (_) / I7 = 6 => 0 pairs (X) H1,H3: 7.. / H1 = 7 => 0 pairs (*) / H3 = 7 => 0 pairs (X) C7,F7: 7.. / C7 = 7 => 0 pairs (X) / F7 = 7 => 7 pairs (_) B1,B8: 7.. / B1 = 7 => 0 pairs (X) / B8 = 7 => 0 pairs (_) A5,C5: 8.. / A5 = 8 => 5 pairs (_) / C5 = 8 => 5 pairs (_) H8,H9: 8.. / H8 = 8 => 5 pairs (_) / H9 = 8 => 5 pairs (_) * DURATION: 0:00:40.948072 START: 23:04:12.367592 END: 23:04:53.315664 2017-05-03 * CP COUNT: (27) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (H4,I1,I8,I9) * 6..3.25...5.....12.2.5.....7426.5..........543.5....2728.15........4.2........7.. * PAIR I1: 8,9 BLK 3 G2: 8,9,3,4 # reduction candidate for 8,9 G2: 8,9 => SOLVED * 614382579953764812827591436742635198168279354395418627286157943579843261431926785 G2: 3,4 # 5 pairs G3: 8,9,3,4 # reduction candidate for 8,9 G3: 8,9 # 8 pairs I3: 8,9,3,6 # reduction candidate for 8,9 I3: 8,9 => CTR * 6.43.257..5.....12.2.5...6.7426.5.93....3..543.5....27289157..6.7..4328.43....7.. I3: 3,6 # 5 pairs * PAIR I1: 8,9 ROW 1 C1: 8,9,1,4,7 # reduction candidate for 8,9 C1: 8,9 => CTR * 61.37254..57.6.312.235...767426.5..........543.5....2728.1574...7..4.2...34.2.7.. C1: 1,4,7 # 4 pairs E1: 8,9,1,7 # reduction candidate for 8,9 E1: 8,9 # 7 pairs * PAIR I1: 8,9 COL I I4: 8,9,3 # reduction candidate for 8,9 I4: 3 => CTR * 6..3.25...57.6.312.235.....7426.5.93.......543.5....2728.157.3..7..432........7.. I4: 8,9 # 7 pairs * PAIR H4: 3,9 BLK 6 G4: 3,9,1,8 # reduction candidate for 3,9 G4: 3,9 => CTR * 6..3.25.9.57.6.312.235.18.6742615938.......543.5....2728.1574.3.7..432........7.. G4: 1,8 # 5 pairs I4: 3,9,8 # reduction candidate for 3,9 I4: 3,9 => CTR * 6..3.25...57.6.312.235.....7426.5..........543.5....2728.157....7..4.2...3..2.7.. I4: 8 # 7 pairs G5: 3,9,1,6 # reduction candidate for 3,9 G5: 3,9 # 10 pairs * PAIR H4: 3,9 ROW 4 E4: 3,9,1,8 # reduction candidate for 3,9 E4: 1,8 => CTR * 6..3.25...57.6.312.235.....7426.5..........543.5....2728.157....7..4.2...3..2.7.. E4: 3,9 # 9 pairs * PAIR H4: 3,9 COL H H3: 3,9,4,6,7 # reduction candidate for 3,9 H3: 3,9 => SOLVED * 614382579953764812827591436742635198168279354395418627286157943579843261431926785 H3: 4,6,7 # 4 pairs H7: 3,9,4,6 # reduction candidate for 3,9 H7: 3,9 # 8 pairs H8: 3,9,6,8 # reduction candidate for 3,9 H8: 3,9 # 9 pairs H9: 3,9,4,6,8 # reduction candidate for 3,9 H9: 3,9 # 9 pairs * PAIR I8: 1,5 ROW 8 A8: 1,5,9 # reduction candidate for 1,5 A8: 9 => CTR * 6..37254..57.6.312.235...767426.5..........543.5....272861574..97184.2.5534.2.781 A8: 1,5 # 5 pairs * PAIR I9: 1,5 ROW 9 A9: 1,5,4,9 # reduction candidate for 1,5 A9: 1,5 => CTR * 6..37254..57.6.312.235...767426.5..........543.5....2728.1574...7..4.2...34.2.7.. A9: 4,9 # 3 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-011-base-pr-000.dot * REASONING * PRF # G2: 8,9 => SOL * DIS # I3: 8,9 => CTR => I3: 3,6 * DIS # C1: 8,9 => CTR => C1: 1,4,7 * DIS # I4: 3 => CTR => I4: 8,9 * DIS # G4: 3,9 => CTR => G4: 1,8 * DIS # I4: 3,9 => CTR => I4: 8 * DIS # E4: 1,8 => CTR => E4: 3,9 * PRF # H3: 3,9 => SOL * DIS # A8: 9 => CTR => A8: 1,5 * DIS # A9: 1,5 => CTR => A9: 4,9 * CNT 10 HDP CHAINS / 26 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (H4,I1,I8,I9) * 6..3.25...5.....12.2.5.....7426.5..........543.5....2728.15........4.2........7.. * PAIR I1: 8,9 BLK 3 G2: 8,9,3,4 # reduction candidate for 8,9 G2: 8,9 => SOLVED * 614382579953764812827591436742635198168279354395418627286157943579843261431926785 * DURATION: 0:00:02.729172 START: 23:05:15.724247 END: 23:05:18.453419 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-011-base-pr-001.dot * REASONING * PRF # G2: 8,9 => SOL * STA G2: 8,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 95 Sudokus 011 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 614382579953764812827591436742635198168279354395418627286157943579843261431926785 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 # G2: 8,9 => SOL * INC # G2: 3,4 => UNS * INC # G3: 8,9 => UNS * DIS # I3: 8,9 => CTR => I3: 3,6 * INC # I3: 3,6 => UNS * DIS # C1: 8,9 => CTR => C1: 1,4,7 * INC # C1: 1,4,7 => UNS * INC # E1: 8,9 => UNS * INC # I4: 8,9 => UNS * DIS # I4: 3 => CTR => I4: 8,9 * DIS # G4: 3,9 => CTR => G4: 1,8 * INC # G4: 1,8 => UNS * DIS # I4: 3,9 => CTR => I4: 8 * INC # I4: 8 => UNS * INC # G5: 3,9 => UNS * INC # E4: 3,9 => UNS * DIS # E4: 1,8 => CTR => E4: 3,9 * PRF # H3: 3,9 => SOL * INC # H3: 4,6,7 => UNS * INC # H7: 3,9 => UNS * INC # H8: 3,9 => UNS * INC # H9: 3,9 => UNS * INC # A8: 1,5 => UNS * DIS # A8: 9 => CTR => A8: 1,5 * DIS # A9: 1,5 => CTR => A9: 4,9 * INC # A9: 4,9 => UNS * CNT 26 HDP CHAINS / 26 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # G2: 8,9 => SOL * STA G2: 8,9 * CNT 1 HDP CHAINS / 1 HYP OPENED