Analysis of xx-top95-050-base.sdk
Contents
Original Sudoku
level: medium
position: 6..3.2....1.....5..........7.26............843.........8.15........8.2........7.. initial
Autosolve
position: 6..3.28...1.....52.2.......7.26.8..........843.8....2728.15........8.2.5......7.8 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I3: 1,9 => CTR => I3: 3,6 * DIS # E1: 4,7 => CTR => E1: 1,9 * DIS # I4: 3 => CTR => I4: 1,9 * DIS # G4: 3,9 => CTR => G4: 1,5 * DIS # I4: 3,9 => CTR => I4: 1 * DIS # E4: 1,4 => CTR => E4: 3,9 * PRF # H3: 3,9 => SOL * CNT 7 HDP CHAINS / 19 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I3: 1,9 => CTR => I3: 3,6 * DIS I3: 3,6 # G3: 3,4 => CTR => G3: 1,9 * DIS I3: 3,6 + G3: 1,9 # E1: 4,7 => CTR => E1: 1,9 * DIS I3: 3,6 + G3: 1,9 + E1: 1,9 # I4: 3 => CTR => I4: 1,9 * DIS I3: 3,6 + G3: 1,9 + E1: 1,9 + I4: 1,9 # G4: 3,9 => CTR => G4: 1,5 * DIS I3: 3,6 + G3: 1,9 + E1: 1,9 + I4: 1,9 + G4: 1,5 # G5: 5,6 => CTR => G5: 3,9 * DIS I3: 3,6 + G3: 1,9 + E1: 1,9 + I4: 1,9 + G4: 1,5 + G5: 3,9 # E4: 4 => CTR => E4: 3,9 * DIS I3: 3,6 + G3: 1,9 + E1: 1,9 + I4: 1,9 + G4: 1,5 + G5: 3,9 + E4: 3,9 # C1: 5,7 => CTR => C1: 4 * PRF I3: 3,6 + G3: 1,9 + E1: 1,9 + I4: 1,9 + G4: 1,5 + G5: 3,9 + E4: 3,9 + C1: 4 => SOL * STA I3: 3,6 + G3: 1,9 + E1: 1,9 + I4: 1,9 + G4: 1,5 + G5: 3,9 + E4: 3,9 + C1: 4 * CNT 9 HDP CHAINS / 21 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6..3.2....1.....5..........7.26............843.........8.15........8.2........7.. | initial |
| 6..3.28...1.....52.2.......7.26.8..........843.8....2728.15........8.2.5......7.8 | autosolve |
| 654312879913876452827495136742638591165729384398541627286157943471983265539264718 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (2) I1: 1,9 H4: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A5,C5: 1.. / A5 = 1 => 3 pairs (_) / C5 = 1 => 3 pairs (_) H8,H9: 1.. / H8 = 1 => 5 pairs (_) / H9 = 1 => 2 pairs (_) E1,I1: 1.. / E1 = 1 => 7 pairs (_) / I1 = 1 => 0 pairs (X) F3,F6: 1.. / F3 = 1 => 0 pairs (X) / F6 = 1 => 3 pairs (_) D5,E5: 2.. / D5 = 2 => 3 pairs (_) / E5 = 2 => 2 pairs (_) D9,E9: 2.. / D9 = 2 => 2 pairs (_) / E9 = 2 => 3 pairs (_) D5,D9: 2.. / D5 = 2 => 3 pairs (_) / D9 = 2 => 2 pairs (_) E5,E9: 2.. / E5 = 2 => 2 pairs (_) / E9 = 2 => 3 pairs (_) C2,C3: 3.. / C2 = 3 => 0 pairs (*) / C3 = 3 => 0 pairs (X) B8,B9: 3.. / B8 = 3 => 0 pairs (X) / B9 = 3 => 2 pairs (_) C2,G2: 3.. / C2 = 3 => 0 pairs (*) / G2 = 3 => 0 pairs (X) B4,B6: 4.. / B4 = 4 => 2 pairs (_) / B6 = 4 => 0 pairs (X) B4,E4: 4.. / B4 = 4 => 2 pairs (_) / E4 = 4 => 0 pairs (X) B1,C1: 5.. / B1 = 5 => 0 pairs (*) / C1 = 5 => 0 pairs (X) D3,F3: 5.. / D3 = 5 => 4 pairs (_) / F3 = 5 => 3 pairs (_) B4,G4: 5.. / B4 = 5 => 0 pairs (X) / G4 = 5 => 3 pairs (_) A5,A9: 5.. / A5 = 5 => 9 pairs (_) / A9 = 5 => 3 pairs (_) E2,F2: 6.. / E2 = 6 => 2 pairs (_) / F2 = 6 => 0 pairs (*) H3,I3: 6.. / H3 = 6 => 0 pairs (X) / I3 = 6 => 3 pairs (_) G5,G6: 6.. / G5 = 6 => 0 pairs (X) / G6 = 6 => 2 pairs (_) B6,G6: 6.. / B6 = 6 => 0 pairs (X) / G6 = 6 => 2 pairs (_) E2,E9: 6.. / E2 = 6 => 2 pairs (_) / E9 = 6 => 0 pairs (*) I3,I7: 6.. / I3 = 6 => 3 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 => 5 pairs (_) B1,B8: 7.. / B1 = 7 => 0 pairs (X) / B8 = 7 => 0 pairs (_) A2,A3: 8.. / A2 = 8 => 4 pairs (_) / A3 = 8 => 3 pairs (_) D2,D3: 8.. / D2 = 8 => 3 pairs (_) / D3 = 8 => 4 pairs (_) A2,D2: 8.. / A2 = 8 => 4 pairs (_) / D2 = 8 => 3 pairs (_) A3,D3: 8.. / A3 = 8 => 3 pairs (_) / D3 = 8 => 4 pairs (_) * DURATION: 0:00:43.102873 START: 23:52:02.584777 END: 23:52:45.687650 2017-05-03 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (H4,I1) * 6..3.28...1.....52.2.......7.26.8..........843.8....2728.15........8.2.5......7.8 * PAIR I1: 1,9 BLK 3 G3: 1,9,3,4 # reduction candidate for 1,9 G3: 1,9 # 6 pairs I3: 1,9,3,6 # reduction candidate for 1,9 I3: 1,9 => CTR * 6..3.287..1.....52.2.....6.7.26.8.93....3..843.8....2728.157936.7..832.5.3..267.8 I3: 3,6 # 3 pairs * PAIR I1: 1,9 ROW 1 E1: 1,9,4,7 # reduction candidate for 1,9 E1: 4,7 => CTR * 6..3.28.1.17.6.352.23......7.26.8..........843.8....2728.157....7..8.2.5.3..2.7.8 E1: 1,9 # 5 pairs * PAIR I1: 1,9 COL I I4: 1,9,3 # reduction candidate for 1,9 I4: 3 => CTR * 6..3.28...17.6.352.23......7.26.8.93.......843.8....2728.157.3..7..832.5......7.8 I4: 1,9 # 5 pairs * PAIR H4: 3,9 BLK 6 G4: 3,9,1,5 # reduction candidate for 3,9 G4: 3,9 => CTR * 6.5312849.1....352.23...176752648931......584348.9.62728.15........8.2.55.....7.8 G4: 1,5 # 3 pairs I4: 3,9,1 # reduction candidate for 3,9 I4: 3,9 => CTR * 6..3.28...17.6.352.23......7.26.8..........843.8....2728.157....7..8.2.5.3..2.7.8 I4: 1 # 7 pairs G5: 3,9,5,6 # reduction candidate for 3,9 G5: 3,9 # 9 pairs * PAIR H4: 3,9 ROW 4 E4: 3,9,1,4 # reduction candidate for 3,9 E4: 1,4 => CTR * 6..3.28...17.6.352.23......7.26.8..........843.8....2728.157....7..8.2.5.3..2.7.8 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 * 654312879913876452827495136742638591165729384398541627286157943471983265539264718 H3: 4,6,7 # 2 pairs H7: 3,9,4,6 # reduction candidate for 3,9 H7: 3,9 # 4 pairs H8: 3,9,1,4,6 # reduction candidate for 3,9 H8: 3,9 # 6 pairs H9: 3,9,1,4,6 # reduction candidate for 3,9 H9: 3,9 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-050-base-pr-000.dot * REASONING * DIS # I3: 1,9 => CTR => I3: 3,6 * DIS # E1: 4,7 => CTR => E1: 1,9 * DIS # I4: 3 => CTR => I4: 1,9 * DIS # G4: 3,9 => CTR => G4: 1,5 * DIS # I4: 3,9 => CTR => I4: 1 * DIS # E4: 1,4 => CTR => E4: 3,9 * PRF # H3: 3,9 => SOL * CNT 7 HDP CHAINS / 19 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (H4,I1) * 6..3.28...1.....52.2.......7.26.8..........843.8....2728.15........8.2.5......7.8 * PAIR I1: 1,9 BLK 3 G3: 1,9,3,4 # reduction candidate for 1,9 G3: 1,9 # 6 pairs I3: 1,9,3,6 # reduction candidate for 1,9 I3: 1,9 => CTR * 6..3.287..1.....52.2.....6.7.26.8.93....3..843.8....2728.157936.7..832.5.3..267.8 * RESTART * PAIR I1: 1,9 BLK 3 G3: 1,9,3,4 # reduction candidate for 1,9 G3: 3,4 => CTR * 6..3.28.1.17.6.352.23...4.67.26.8..........843.8....2728.1579.3.7..832.5......7.8 * PAIR I1: 1,9 ROW 1 E1: 1,9,4,7 # reduction candidate for 1,9 E1: 4,7 => CTR * 6..3.28.1.1..6..52.2....9..7.26.8..........843.8.9..2728.157....7..8.2.5.3..2.7.8 * PAIR I1: 1,9 COL I I4: 1,9,3 # reduction candidate for 1,9 I4: 3 => CTR * 6..392871.17.64352.235719467.26.8.93.......843.89.5.2728.157439.7.4832.5......7.8 * PAIR RESTART * PAIR H4: 3,9 BLK 6 G4: 3,9,1,5 # reduction candidate for 3,9 G4: 3,9 => CTR * 675312849.1....352.23...176752648931......584348.9.62728.15........8.2.55.....7.8 G5: 3,9,5,6 # reduction candidate for 3,9 G5: 3,9 # 9 pairs * RESTART * PAIR H4: 3,9 BLK 6 G5: 3,9,5,6 # reduction candidate for 3,9 G5: 5,6 => CTR * 6..3.287..17.6.352.23.7..467.26.8.3........843.8....2728.1574.3.7..832.5......7.8 * PAIR H4: 3,9 ROW 4 E4: 3,9,4 # reduction candidate for 3,9 E4: 4 => CTR * 6..312879.17.6.352.23.75146792648531......98434859162728.1574.3.7..832.5......7.8 * PAIR H4: 3,9 COL H H7: 3,9,4,6 # reduction candidate for 3,9 H7: 3,9 # 11 pairs H8: 3,9,1,4,6 # reduction candidate for 3,9 H8: 3,9 # 13 pairs H9: 3,9,1,4,6 # reduction candidate for 3,9 H9: 3,9 # 16 pairs * PAIR RESTART * PAIR H4: 3,9 COL H H7: 3,9,4,6 # reduction candidate for 3,9 H7: 3,9 # 11 pairs H8: 3,9,1,4,6 # reduction candidate for 3,9 H8: 3,9 # 13 pairs H9: 3,9,1,4,6 # reduction candidate for 3,9 H9: 3,9 # 16 pairs * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (B1,B6,E4,E6,G2,G5,H1,H4,I3,I7) * 6..3128.9.1.....52.2....1..7426.85.1.......843.8..162728.15........8.2.5......7.8 * PAIR B1: 5,7 BLK 1 C1: 5,7,4 # reduction candidate for 5,7 C1: 5,7 => CTR * 6..312849.1....352.23...1767426.8531......98439854162728.15.4.3....8.2.5......7.8 C1: 4 => SOLVED * 654312879913876452827495136742638591165729384398541627286157943471983265539264718 * DURATION: 0:00:22.030724 START: 23:53:00.663311 END: 23:53:22.694035 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-050-base-pr-001.dot * REASONING * DIS # I3: 1,9 => CTR => I3: 3,6 * DIS I3: 3,6 # G3: 3,4 => CTR => G3: 1,9 * DIS I3: 3,6 + G3: 1,9 # E1: 4,7 => CTR => E1: 1,9 * DIS I3: 3,6 + G3: 1,9 + E1: 1,9 # I4: 3 => CTR => I4: 1,9 * DIS I3: 3,6 + G3: 1,9 + E1: 1,9 + I4: 1,9 # G4: 3,9 => CTR => G4: 1,5 * DIS I3: 3,6 + G3: 1,9 + E1: 1,9 + I4: 1,9 + G4: 1,5 # G5: 5,6 => CTR => G5: 3,9 * DIS I3: 3,6 + G3: 1,9 + E1: 1,9 + I4: 1,9 + G4: 1,5 + G5: 3,9 # E4: 4 => CTR => E4: 3,9 * DIS I3: 3,6 + G3: 1,9 + E1: 1,9 + I4: 1,9 + G4: 1,5 + G5: 3,9 + E4: 3,9 # C1: 5,7 => CTR => C1: 4 * PRF I3: 3,6 + G3: 1,9 + E1: 1,9 + I4: 1,9 + G4: 1,5 + G5: 3,9 + E4: 3,9 + C1: 4 => SOL * STA I3: 3,6 + G3: 1,9 + E1: 1,9 + I4: 1,9 + G4: 1,5 + G5: 3,9 + E4: 3,9 + C1: 4 * CNT 9 HDP CHAINS / 21 HYP OPENED
Header Info
Top 95 Sudokus 050 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 654312879913876452827495136742638591165729384398541627286157943471983265539264718 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 # G3: 1,9 => UNS * DIS # I3: 1,9 => CTR => I3: 3,6 * INC # I3: 3,6 => UNS * INC # E1: 1,9 => UNS * DIS # E1: 4,7 => CTR => E1: 1,9 * INC # I4: 1,9 => UNS * DIS # I4: 3 => CTR => I4: 1,9 * DIS # G4: 3,9 => CTR => G4: 1,5 * INC # G4: 1,5 => UNS * DIS # I4: 3,9 => CTR => I4: 1 * INC # I4: 1 => UNS * INC # G5: 3,9 => UNS * INC # E4: 3,9 => UNS * DIS # E4: 1,4 => 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 * CNT 19 HDP CHAINS / 19 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G3: 1,9 => UNS * DIS # I3: 1,9 => CTR => I3: 3,6 * INC I3: 3,6 # G3: 1,9 => UNS * DIS I3: 3,6 # G3: 3,4 => CTR => G3: 1,9 * INC I3: 3,6 + G3: 1,9 # E1: 1,9 => UNS * DIS I3: 3,6 + G3: 1,9 # E1: 4,7 => CTR => E1: 1,9 * INC I3: 3,6 + G3: 1,9 + E1: 1,9 # I4: 1,9 => UNS * DIS I3: 3,6 + G3: 1,9 + E1: 1,9 # I4: 3 => CTR => I4: 1,9 * DIS I3: 3,6 + G3: 1,9 + E1: 1,9 + I4: 1,9 # G4: 3,9 => CTR => G4: 1,5 * INC I3: 3,6 + G3: 1,9 + E1: 1,9 + I4: 1,9 + G4: 1,5 # G5: 3,9 => UNS * INC I3: 3,6 + G3: 1,9 + E1: 1,9 + I4: 1,9 + G4: 1,5 # G5: 3,9 => UNS * DIS I3: 3,6 + G3: 1,9 + E1: 1,9 + I4: 1,9 + G4: 1,5 # G5: 5,6 => CTR => G5: 3,9 * INC I3: 3,6 + G3: 1,9 + E1: 1,9 + I4: 1,9 + G4: 1,5 + G5: 3,9 # E4: 3,9 => UNS * DIS I3: 3,6 + G3: 1,9 + E1: 1,9 + I4: 1,9 + G4: 1,5 + G5: 3,9 # E4: 4 => CTR => E4: 3,9 * INC I3: 3,6 + G3: 1,9 + E1: 1,9 + I4: 1,9 + G4: 1,5 + G5: 3,9 + E4: 3,9 # H7: 3,9 => UNS * INC I3: 3,6 + G3: 1,9 + E1: 1,9 + I4: 1,9 + G4: 1,5 + G5: 3,9 + E4: 3,9 # H8: 3,9 => UNS * INC I3: 3,6 + G3: 1,9 + E1: 1,9 + I4: 1,9 + G4: 1,5 + G5: 3,9 + E4: 3,9 # H9: 3,9 => UNS * INC I3: 3,6 + G3: 1,9 + E1: 1,9 + I4: 1,9 + G4: 1,5 + G5: 3,9 + E4: 3,9 # H7: 3,9 => UNS * INC I3: 3,6 + G3: 1,9 + E1: 1,9 + I4: 1,9 + G4: 1,5 + G5: 3,9 + E4: 3,9 # H8: 3,9 => UNS * INC I3: 3,6 + G3: 1,9 + E1: 1,9 + I4: 1,9 + G4: 1,5 + G5: 3,9 + E4: 3,9 # H9: 3,9 => UNS * DIS I3: 3,6 + G3: 1,9 + E1: 1,9 + I4: 1,9 + G4: 1,5 + G5: 3,9 + E4: 3,9 # C1: 5,7 => CTR => C1: 4 * PRF I3: 3,6 + G3: 1,9 + E1: 1,9 + I4: 1,9 + G4: 1,5 + G5: 3,9 + E4: 3,9 + C1: 4 => SOL * STA I3: 3,6 + G3: 1,9 + E1: 1,9 + I4: 1,9 + G4: 1,5 + G5: 3,9 + E4: 3,9 + C1: 4 * CNT 22 HDP CHAINS / 21 HYP OPENED