Analysis of xx-top500-019-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 8..72........6..3.......6...3....5.....6..4..2..........41..........8.2..6.....7. initial

Autosolve

position: 8.672394.4...6.23.3.2..46..63..475.2.876.24.324.3..76.7241368....34781261682..374 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B2: 1,5 => CTR => B2: 7,9
* DIS # B3: 1,5 => CTR => B3: 7,9
* PRF # B2: 5,9 => SOL
* DIS # D2: 5,9 => CTR => D2: 8
* PRF # D2: 8 => SOL
* DIS # C6: 1 => CTR => C6: 5,9
* DIS # E3: 8 => CTR => E3: 1,9
* PRF # B2: 1,9 => SOL
* DIS # I2: 1,5 => CTR => I2: 7,8
* DIS # I3: 1,5 => CTR => I3: 7,8
* DIS # C6: 5 => CTR => C6: 1,9
* DIS # H4: 1,9 => CTR => H4: 8
* DIS # C6: 1 => CTR => C6: 5,9
* DIS # E6: 1,5 => CTR => E6: 8,9
* DIS # H4: 1 => CTR => H4: 8,9
* DIS # D3: 8,9 => CTR => D3: 5
* DIS # H4: 1,9 => CTR => H4: 8
* DIS # E5: 5 => CTR => E5: 1,9
* PRF # B2: 5,9 => SOL
* DIS # E6: 5,9 => CTR => E6: 1,8
* DIS # F6: 1 => CTR => F6: 5,9
* CNT  21 HDP CHAINS /  50 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* DIS # B2: 1,5 => CTR => B2: 7,9
* DIS B2: 7,9 # B3: 1,5 => CTR => B3: 7,9
* PRF B2: 7,9 + B3: 7,9 # E3: 1,9 => SOL
* STA B2: 7,9 + B3: 7,9 + E3: 1,9
* CNT   3 HDP CHAINS /   3 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Details

Positions

8..72........6..3.......6...3....5.....6..4..2..........41..........8.2..6.....7. initial
8.672394.4...6.23.3.2..46..63..475.2.876.24.324.3..76.7241368....34781261682..374 autosolve
816723945495861237372594618631947582587612493249385761724136859953478126168259374 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
B1: 1,5
C2: 5,9
F2: 1,9
I1: 1,5
C4: 1,9
A5: 5,9
D4: 8,9
H5: 1,9
A8: 5,9
B8: 5,9
E9: 5,9
F9: 5,9
H7: 5,9
I7: 5,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F2,E3: 1.. / F2 = 1  => 15 pairs (_) / E3 = 1  =>  0 pairs (X)
C4,C6: 1.. / C4 = 1  => 15 pairs (_) / C6 = 1  =>  0 pairs (X)
B1,I1: 1.. / B1 = 1  => 12 pairs (_) / I1 = 1  =>  0 pairs (X)
C4,H4: 1.. / C4 = 1  => 15 pairs (_) / H4 = 1  =>  0 pairs (X)
E5,H5: 1.. / E5 = 1  => 14 pairs (_) / H5 = 1  => 19 pairs (_)
F2,F6: 1.. / F2 = 1  => 15 pairs (_) / F6 = 1  =>  0 pairs (X)
D2,D3: 5.. / D2 = 5  =>  0 pairs (X) / D3 = 5  => 15 pairs (_)
A5,C6: 5.. / A5 = 5  => 13 pairs (_) / C6 = 5  =>  0 pairs (X)
A8,B8: 5.. / A8 = 5  =>  0 pairs (X) / B8 = 5  => 13 pairs (_)
E9,F9: 5.. / E9 = 5  => 12 pairs (_) / F9 = 5  => 15 pairs (_)
H7,I7: 5.. / H7 = 5  => 14 pairs (_) / I7 = 5  =>  0 pairs (X)
B1,I1: 5.. / B1 = 5  =>  0 pairs (X) / I1 = 5  => 12 pairs (_)
A5,E5: 5.. / A5 = 5  => 13 pairs (_) / E5 = 5  =>  0 pairs (X)
A5,A8: 5.. / A5 = 5  => 13 pairs (_) / A8 = 5  =>  0 pairs (X)
C2,C6: 5.. / C2 = 5  => 13 pairs (_) / C6 = 5  =>  0 pairs (X)
F6,F9: 5.. / F6 = 5  => 12 pairs (_) / F9 = 5  => 15 pairs (_)
H3,H7: 5.. / H3 = 5  =>  0 pairs (X) / H7 = 5  => 14 pairs (_)
B2,B3: 7.. / B2 = 7  => 14 pairs (_) / B3 = 7  =>  0 pairs (*)
I2,I3: 7.. / I2 = 7  =>  0 pairs (*) / I3 = 7  =>  0 pairs (X)
B2,I2: 7.. / B2 = 7  => 14 pairs (_) / I2 = 7  =>  0 pairs (*)
B3,I3: 7.. / B3 = 7  =>  0 pairs (*) / I3 = 7  =>  0 pairs (X)
D4,E6: 8.. / D4 = 8  =>  0 pairs (X) / E6 = 8  => 22 pairs (_)
H4,I6: 8.. / H4 = 8  => 22 pairs (_) / I6 = 8  =>  0 pairs (X)
D2,I2: 8.. / D2 = 8  =>  0 pairs (*) / I2 = 8  =>  0 pairs (X)
D4,H4: 8.. / D4 = 8  =>  0 pairs (X) / H4 = 8  => 22 pairs (_)
E6,I6: 8.. / E6 = 8  => 22 pairs (_) / I6 = 8  =>  0 pairs (X)
E3,E6: 8.. / E3 = 8  =>  0 pairs (X) / E6 = 8  => 22 pairs (_)
H3,H4: 8.. / H3 = 8  =>  0 pairs (X) / H4 = 8  => 22 pairs (_)
A8,B8: 9.. / A8 = 9  => 13 pairs (_) / B8 = 9  =>  0 pairs (X)
E9,F9: 9.. / E9 = 9  => 15 pairs (_) / F9 = 9  => 12 pairs (_)
H7,I7: 9.. / H7 = 9  =>  0 pairs (X) / I7 = 9  => 14 pairs (_)
A5,A8: 9.. / A5 = 9  =>  0 pairs (X) / A8 = 9  => 13 pairs (_)
I6,I7: 9.. / I6 = 9  =>  0 pairs (X) / I7 = 9  => 14 pairs (_)
* DURATION: 0:00:57.760797  START: 03:13:23.359634  END: 03:14:21.120431 2017-05-04
* CP COUNT: (33)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A8,B1,B8,C2,C4,D4,E9,F2,F9,H5,H7,I1,I7)
* 8.672394.4...6.23.3.2..46..63..475.2.876.24.324.3..76.7241368....34781261682..374
* PAIR B1: 1,5 BLK 1
B2: 1,5,7,9                              # reduction candidate for 1,5
B2: 1,5 => CTR
* 8.672394.4.98612373725946..6319475829876524.324.3..76.7241368...934781261682..374
B2: 7,9                                  # 15 pairs
B3: 1,5,7,9                              # reduction candidate for 1,5
B3: 1,5 => CTR
* 8.672394147986123.3.2..46.7631.475.29876524132453197687241368.9593478126168295374
B3: 7,9                                  # 15 pairs
* PAIR C2: 5,9 BLK 1
B2: 5,9,1,7                              # reduction candidate for 5,9
B2: 5,9 => SOLVED
* 816723945495861237372594618631947582587612493249385761724136859953478126168259374
B2: 1,7                                  # 15 pairs
B3: 5,9,1,7                              # reduction candidate for 5,9
B3: 5,9                                  # 14 pairs
* PAIR C2: 5,9 ROW 2
D2: 5,9,8                                # reduction candidate for 5,9
D2: 5,9 => CTR
* 8.672394.47..612383.28946.7631947582.87612493249385761724136859953478126168259374
D2: 8 => SOLVED
* 816723945495861237372594618631947582587612493249385761724136859953478126168259374
* PAIR C2: 5,9 COL C
C6: 5,9,1                                # reduction candidate for 5,9
C6: 1 => CTR
* 8.672394.4.5.6.23.3.25.46..6398475125876124932413..7687241368599534781261682..374
C6: 5,9                                  # 15 pairs
* PAIR F2: 1,9 BLK 2
E3: 1,9,8                                # reduction candidate for 1,9
E3: 8 => CTR
* 8.672394.4...6123.3.2.846..63.8475.2.876.24.324.3..7687241368.9..34781261682..374
E3: 1,9                                  # 22 pairs
* PAIR F2: 1,9 ROW 2
B2: 1,9,5,7                              # reduction candidate for 1,9
B2: 1,9 => SOLVED
* 816723945495861237372594618631947582587612493249385761724136859953478126168259374
B2: 5,7                                  # 15 pairs
* PAIR F2: 1,9 COL F
F6: 1,9,5                                # reduction candidate for 1,9
F6: 1,9                                  # 15 pairs
F6: 5                                    # 12 pairs
* PAIR I1: 1,5 BLK 3
I2: 1,5,7,8                              # reduction candidate for 1,5
I2: 1,5 => CTR
* 8.672394.47.86.23.3.25.46.763.947582.876.24.324.38.76.724136859..34781261682..374
I2: 7,8                                  # 15 pairs
H3: 1,5,8                                # reduction candidate for 1,5
H3: 1,5                                  # 22 pairs
I3: 1,5,7,8                              # reduction candidate for 1,5
I3: 1,5 => CTR
* 8.672394.4...6.237372..468.63.8475.2.876.24.324.3..768724136859..34781261682..374
I3: 7,8                                  # 15 pairs
* PAIR C4: 1,9 BLK 4
C6: 1,9,5                                # reduction candidate for 1,9
C6: 5 => CTR
* 8.672394.4.9.6123.3.298465.631.475.29876524132453..76.7241368..593478126168295374
C6: 1,9                                  # 13 pairs
* PAIR C4: 1,9 ROW 4
H4: 1,9,8                                # reduction candidate for 1,9
H4: 1,9 => CTR
* 8.672394.4...6.23.3.2..468.63.8475.2.876.24.324.3..768724136859..34781261682..374
H4: 8                                    # 22 pairs
* PAIR A5: 5,9 BLK 4
C6: 5,9,1                                # reduction candidate for 5,9
C6: 1 => CTR
* 8.672394.4.5.6.23.3.25.46..6398475125876124932413..7687241368599534781261682..374
C6: 5,9                                  # 15 pairs
* PAIR A5: 5,9 ROW 5
E5: 5,9,1                                # reduction candidate for 5,9
E5: 5,9                                  # 19 pairs
E5: 1                                    # 14 pairs
* PAIR D4: 8,9 BLK 5
E6: 8,9,1,5                              # reduction candidate for 8,9
E6: 1,5 => CTR
* 8.672394.4...6.23.3.2.846..63.8475.2.876.24.324.3..7687241368.9..34781261682..374
E6: 8,9                                  # 17 pairs
* PAIR D4: 8,9 ROW 4
H4: 8,9,1                                # reduction candidate for 8,9
H4: 1 => CTR
* 8.672394.4...6.23.3.2..468.63.847512.876124932413..7687241368599534781261682..374
H4: 8,9                                  # 15 pairs
* PAIR D4: 8,9 COL D
D2: 8,9,5                                # reduction candidate for 8,9
D2: 8,9                                  # 15 pairs
D3: 8,9,5                                # reduction candidate for 8,9
D3: 8,9 => CTR
* 8.672394.4795612383.28946.763..47582.876.24.324538.76.7241368..5934781261682.5374
D3: 5                                    # 15 pairs
* PAIR H5: 1,9 BLK 6
H4: 1,9,8                                # reduction candidate for 1,9
H4: 1,9 => CTR
* 8.672394.4...6.23.3.2..468.63.8475.2.876.24.324.3..768724136859..34781261682..374
H4: 8                                    # 22 pairs
I6: 1,9,8                                # reduction candidate for 1,9
I6: 1,9                                  # 22 pairs
* PAIR H5: 1,9 ROW 5
E5: 1,9,5                                # reduction candidate for 1,9
E5: 5 => CTR
* 8.672394.4.9.6123.3.298465.63..475.2.876524132453..76.7241368..593478126168295374
E5: 1,9                                  # 13 pairs
* PAIR B8: 5,9 COL B
B2: 5,9,1,7                              # reduction candidate for 5,9
B2: 5,9 => SOLVED
* 816723945495861237372594618631947582587612493249385761724136859953478126168259374
B2: 1,7                                  # 15 pairs
B3: 5,9,1,7                              # reduction candidate for 5,9
B3: 5,9                                  # 14 pairs
* PAIR E9: 5,9 COL E
E5: 5,9,1                                # reduction candidate for 5,9
E5: 5,9                                  # 19 pairs
E6: 5,9,1,8                              # reduction candidate for 5,9
E6: 5,9 => CTR
* 8.672394.4...6.23.3.2.846..63.8475.2.8761249324.3..7687241368599534781261682..374
E6: 1,8                                  # 15 pairs
* PAIR F9: 5,9 COL F
F6: 5,9,1                                # reduction candidate for 5,9
F6: 1 => CTR
* 8.672394.4...6923.392.146.7631947582.8765241324.3.176.7241368....34781261682.5374
F6: 5,9                                  # 15 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-019-base-pr-000.dot
* REASONING
* DIS # B2: 1,5 => CTR => B2: 7,9
* DIS # B3: 1,5 => CTR => B3: 7,9
* PRF # B2: 5,9 => SOL
* DIS # D2: 5,9 => CTR => D2: 8
* PRF # D2: 8 => SOL
* DIS # C6: 1 => CTR => C6: 5,9
* DIS # E3: 8 => CTR => E3: 1,9
* PRF # B2: 1,9 => SOL
* DIS # I2: 1,5 => CTR => I2: 7,8
* DIS # I3: 1,5 => CTR => I3: 7,8
* DIS # C6: 5 => CTR => C6: 1,9
* DIS # H4: 1,9 => CTR => H4: 8
* DIS # C6: 1 => CTR => C6: 5,9
* DIS # E6: 1,5 => CTR => E6: 8,9
* DIS # H4: 1 => CTR => H4: 8,9
* DIS # D3: 8,9 => CTR => D3: 5
* DIS # H4: 1,9 => CTR => H4: 8
* DIS # E5: 5 => CTR => E5: 1,9
* PRF # B2: 5,9 => SOL
* DIS # E6: 5,9 => CTR => E6: 1,8
* DIS # F6: 1 => CTR => F6: 5,9
* CNT  21 HDP CHAINS /  50 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A8,B1,B8,C2,C4,D4,E9,F2,F9,H5,H7,I1,I7)
* 8.672394.4...6.23.3.2..46..63..475.2.876.24.324.3..76.7241368....34781261682..374
* PAIR B1: 1,5 BLK 1
B2: 1,5,7,9                              # reduction candidate for 1,5
B2: 1,5 => CTR
* 8.672394.4.98612373725946..6319475829876524.324.3..76.7241368...934781261682..374
B3: 1,5,7,9                              # reduction candidate for 1,5
B3: 1,5 => CTR
* 8.672394147986123.3.2..46.7631.475.29876524132453197687241368.9593478126168295374
* PAIR F2: 1,9 BLK 2
E3: 1,9,8                                # reduction candidate for 1,9
E3: 1,9 => SOLVED
* 816723945495861237372594618631947582587612493249385761724136859953478126168259374
* DURATION: 0:00:04.413853  START: 03:15:08.994780  END: 03:15:13.408633 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-019-base-pr-001.dot
* REASONING
* DIS # B2: 1,5 => CTR => B2: 7,9
* DIS B2: 7,9 # B3: 1,5 => CTR => B3: 7,9
* PRF B2: 7,9 + B3: 7,9 # E3: 1,9 => SOL
* STA B2: 7,9 + B3: 7,9 + E3: 1,9
* CNT   3 HDP CHAINS /   3 HYP OPENED

Header Info

Top 500 Minimum 17 019

solution: 816723945495861237372594618631947582587612493249385761724136859953478126168259374
info: 1311     FNBTWXY  S8.f     38428

http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/

Solution

position: 816723945495861237372594618631947582587612493249385761724136859953478126168259374 solved
Solution

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:

* DIS # B2: 1,5 => CTR => B2: 7,9
* INC # B2: 7,9 => UNS
* DIS # B3: 1,5 => CTR => B3: 7,9
* INC # B3: 7,9 => UNS
* PRF # B2: 5,9 => SOL
* INC # B2: 1,7 => UNS
* INC # B3: 5,9 => UNS
* DIS # D2: 5,9 => CTR => D2: 8
* PRF # D2: 8 => SOL
* INC # C6: 5,9 => UNS
* DIS # C6: 1 => CTR => C6: 5,9
* INC # E3: 1,9 => UNS
* DIS # E3: 8 => CTR => E3: 1,9
* PRF # B2: 1,9 => SOL
* INC # B2: 5,7 => UNS
* INC # F6: 1,9 => UNS
* INC # F6: 5 => UNS
* DIS # I2: 1,5 => CTR => I2: 7,8
* INC # I2: 7,8 => UNS
* INC # H3: 1,5 => UNS
* DIS # I3: 1,5 => CTR => I3: 7,8
* INC # I3: 7,8 => UNS
* INC # C6: 1,9 => UNS
* DIS # C6: 5 => CTR => C6: 1,9
* DIS # H4: 1,9 => CTR => H4: 8
* INC # H4: 8 => UNS
* INC # C6: 5,9 => UNS
* DIS # C6: 1 => CTR => C6: 5,9
* INC # E5: 5,9 => UNS
* INC # E5: 1 => UNS
* INC # E6: 8,9 => UNS
* DIS # E6: 1,5 => CTR => E6: 8,9
* INC # H4: 8,9 => UNS
* DIS # H4: 1 => CTR => H4: 8,9
* INC # D2: 8,9 => UNS
* DIS # D3: 8,9 => CTR => D3: 5
* INC # D3: 5 => UNS
* DIS # H4: 1,9 => CTR => H4: 8
* INC # H4: 8 => UNS
* INC # I6: 1,9 => UNS
* INC # E5: 1,9 => UNS
* DIS # E5: 5 => CTR => E5: 1,9
* PRF # B2: 5,9 => SOL
* INC # B2: 1,7 => UNS
* INC # B3: 5,9 => UNS
* INC # E5: 5,9 => UNS
* DIS # E6: 5,9 => CTR => E6: 1,8
* INC # E6: 1,8 => UNS
* INC # F6: 5,9 => UNS
* DIS # F6: 1 => CTR => F6: 5,9
* CNT  50 HDP CHAINS /  50 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B2: 1,5 => CTR => B2: 7,9
* DIS B2: 7,9 # B3: 1,5 => CTR => B3: 7,9
* PRF B2: 7,9 + B3: 7,9 # E3: 1,9 => SOL
* STA B2: 7,9 + B3: 7,9 + E3: 1,9
* CNT   3 HDP CHAINS /   3 HYP OPENED