Analysis of xx-top500-092-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .325........6...1..............8.2.361..4..........5..4.7....8....3.....8........ initial

Autosolve

position: .325.46.8.8.63..1...68...3....1852636152438..3287..5414579..3862.13.8.548.345.12. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # G2: 7 => CTR => G2: 4,9
* DIS # G3: 9 => CTR => G3: 4,7
* CNT   2 HDP CHAINS /  17 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 # G2: 7 => CTR => G2: 4,9
* DIS G2: 4,9 # G3: 9 => CTR => G3: 4,7
* PRF G2: 4,9 + G3: 4,7 # A1: 7,9 => SOL
* STA G2: 4,9 + G3: 4,7 + A1: 7,9
* CNT   3 HDP CHAINS /   5 HYP OPENED

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

Details

Positions

.325........6...1..............8.2.361..4..........5..4.7....8....3.....8........ initial
.325.46.8.8.63..1...68...3....1852636152438..3287..5414579..3862.13.8.548.345.12. autosolve
732514698589637412146892735974185263615243879328769541457921386261378954893456127 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (20)
C2: 4,9
B3: 4,7
H1: 7,9
I2: 2,5
I3: 2,5
A4: 7,9
B4: 4,7
C4: 4,9
E6: 6,9
F6: 6,9
H5: 7,9
I5: 7,9
B8: 6,9
B9: 6,9
E7: 1,2
F7: 1,2
E8: 6,7
F9: 6,7
G8: 7,9
I9: 7,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,A3: 1.. / A1 = 1  => 22 pairs (_) / A3 = 1  => 19 pairs (_)
E7,F7: 1.. / E7 = 1  => 20 pairs (_) / F7 = 1  => 18 pairs (_)
A1,E1: 1.. / A1 = 1  => 22 pairs (_) / E1 = 1  => 19 pairs (_)
F3,F7: 1.. / F3 = 1  => 20 pairs (_) / F7 = 1  => 18 pairs (_)
I2,I3: 2.. / I2 = 2  => 20 pairs (_) / I3 = 2  => 20 pairs (_)
E7,F7: 2.. / E7 = 2  => 18 pairs (_) / F7 = 2  => 20 pairs (_)
F2,I2: 2.. / F2 = 2  => 20 pairs (_) / I2 = 2  => 20 pairs (_)
E3,E7: 2.. / E3 = 2  => 20 pairs (_) / E7 = 2  => 18 pairs (_)
C2,B3: 4.. / C2 = 4  => 18 pairs (_) / B3 = 4  => 19 pairs (_)
G2,G3: 4.. / G2 = 4  => 19 pairs (_) / G3 = 4  => 18 pairs (_)
B4,C4: 4.. / B4 = 4  => 18 pairs (_) / C4 = 4  => 19 pairs (_)
C2,G2: 4.. / C2 = 4  => 18 pairs (_) / G2 = 4  => 19 pairs (_)
B3,G3: 4.. / B3 = 4  => 19 pairs (_) / G3 = 4  => 18 pairs (_)
B3,B4: 4.. / B3 = 4  => 19 pairs (_) / B4 = 4  => 18 pairs (_)
C2,C4: 4.. / C2 = 4  => 18 pairs (_) / C4 = 4  => 19 pairs (_)
A2,A3: 5.. / A2 = 5  => 20 pairs (_) / A3 = 5  => 20 pairs (_)
I2,I3: 5.. / I2 = 5  => 20 pairs (_) / I3 = 5  => 20 pairs (_)
A2,I2: 5.. / A2 = 5  => 20 pairs (_) / I2 = 5  => 20 pairs (_)
A3,I3: 5.. / A3 = 5  => 20 pairs (_) / I3 = 5  => 20 pairs (_)
E6,F6: 6.. / E6 = 6  =>  0 pairs (*) / F6 = 6  =>  0 pairs (X)
B8,B9: 6.. / B8 = 6  =>  0 pairs (*) / B9 = 6  =>  0 pairs (X)
E8,F9: 6.. / E8 = 6  =>  0 pairs (X) / F9 = 6  =>  0 pairs (_)
B8,E8: 6.. / B8 = 6  =>  0 pairs (*) / E8 = 6  =>  0 pairs (X)
B9,F9: 6.. / B9 = 6  =>  0 pairs (X) / F9 = 6  =>  0 pairs (_)
E6,E8: 6.. / E6 = 6  =>  0 pairs (*) / E8 = 6  =>  0 pairs (X)
F6,F9: 6.. / F6 = 6  =>  0 pairs (X) / F9 = 6  =>  0 pairs (_)
A4,B4: 7.. / A4 = 7  => 18 pairs (_) / B4 = 7  => 19 pairs (_)
H5,I5: 7.. / H5 = 7  =>  0 pairs (*) / I5 = 7  =>  0 pairs (X)
E8,F9: 7.. / E8 = 7  =>  0 pairs (*) / F9 = 7  =>  0 pairs (X)
G8,I9: 7.. / G8 = 7  =>  0 pairs (X) / I9 = 7  =>  0 pairs (_)
E8,G8: 7.. / E8 = 7  =>  0 pairs (*) / G8 = 7  =>  0 pairs (X)
F9,I9: 7.. / F9 = 7  =>  0 pairs (X) / I9 = 7  =>  0 pairs (_)
B3,B4: 7.. / B3 = 7  => 18 pairs (_) / B4 = 7  => 19 pairs (_)
H1,H5: 7.. / H1 = 7  =>  0 pairs (X) / H5 = 7  =>  0 pairs (_)
I5,I9: 7.. / I5 = 7  =>  0 pairs (X) / I9 = 7  =>  0 pairs (_)
A4,C4: 9.. / A4 = 9  => 19 pairs (_) / C4 = 9  => 18 pairs (_)
E6,F6: 9.. / E6 = 9  =>  0 pairs (X) / F6 = 9  =>  0 pairs (_)
H5,I5: 9.. / H5 = 9  =>  0 pairs (X) / I5 = 9  =>  0 pairs (_)
B8,B9: 9.. / B8 = 9  =>  0 pairs (X) / B9 = 9  =>  0 pairs (_)
G8,I9: 9.. / G8 = 9  =>  0 pairs (*) / I9 = 9  =>  0 pairs (X)
B8,G8: 9.. / B8 = 9  =>  0 pairs (X) / G8 = 9  =>  0 pairs (_)
B9,I9: 9.. / B9 = 9  =>  0 pairs (*) / I9 = 9  =>  0 pairs (X)
C2,C4: 9.. / C2 = 9  => 19 pairs (_) / C4 = 9  => 18 pairs (_)
H1,H5: 9.. / H1 = 9  =>  0 pairs (*) / H5 = 9  =>  0 pairs (X)
I5,I9: 9.. / I5 = 9  =>  0 pairs (*) / I9 = 9  =>  0 pairs (X)
* DURATION: 0:01:23.796610  START: 05:55:19.701791  END: 05:56:43.498401 2017-05-04
* CP COUNT: (45)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B3,B4,B8,B9,C2,C4,E6,E7,E8,F6,F7,F9,G8,H1,H5,I2,I3,I5,I9)
* .325.46.8.8.63..1...68...3....1852636152438..3287..5414579..3862.13.8.548.345.12.
* PAIR C2: 4,9 ROW 2
G2: 4,9,7                                # reduction candidate for 4,9
G2: 7 => CTR
* .325.46.8.8463.71..768..43.7491852636152438793287..5414579..3862.1378954893456127
G2: 4,9                                  # 23 pairs
* PAIR B3: 4,7 ROW 3
G3: 4,7,9                                # reduction candidate for 4,7
G3: 9 => CTR
* .325.467878963241..468..93..741852636152438973287..5414579..386291368754863457129
G3: 4,7                                  # 21 pairs
* PAIR H1: 7,9 BLK 3
G2: 7,9,4                                # reduction candidate for 7,9
G2: 7,9                                  # 18 pairs
G3: 7,9,4                                # reduction candidate for 7,9
G3: 7,9                                  # 19 pairs
* PAIR H1: 7,9 ROW 1
A1: 7,9,1                                # reduction candidate for 7,9
A1: 7,9                                  # 19 pairs
E1: 7,9,1                                # reduction candidate for 7,9
E1: 7,9                                  # 22 pairs
* PAIR A4: 7,9 COL A
A1: 7,9,1                                # reduction candidate for 7,9
A1: 7,9                                  # 19 pairs
A2: 7,9,5                                # reduction candidate for 7,9
A2: 7,9                                  # 20 pairs
A3: 7,9,1,5                              # reduction candidate for 7,9
A3: 7,9                                  # 24 pairs
* PAIR E7: 1,2 COL E
E3: 1,2,7,9                              # reduction candidate for 1,2
E3: 1,2                                  # 22 pairs
E3: 7,9                                  # 19 pairs
* PAIR F7: 1,2 COL F
F3: 1,2,7,9                              # reduction candidate for 1,2
F3: 7,9                                  # 20 pairs
F3: 1,2                                  # 20 pairs
* PAIR G8: 7,9 COL G
G2: 7,9,4                                # reduction candidate for 7,9
G2: 7,9                                  # 18 pairs
G3: 7,9,4                                # reduction candidate for 7,9
G3: 7,9                                  # 19 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-092-base-pr-000.dot
* REASONING
* DIS # G2: 7 => CTR => G2: 4,9
* DIS # G3: 9 => CTR => G3: 4,7
* CNT   2 HDP CHAINS /  17 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B3,B4,B8,B9,C2,C4,E6,E7,E8,F6,F7,F9,G8,H1,H5,I2,I3,I5,I9)
* .325.46.8.8.63..1...68...3....1852636152438..3287..5414579..3862.13.8.548.345.12.
* PAIR C2: 4,9 ROW 2
G2: 4,9,7                                # reduction candidate for 4,9
G2: 7 => CTR
* .325.46.8.8463.71..768..43.7491852636152438793287..5414579..3862.1378954893456127
* PAIR RESTART
* PAIR B3: 4,7 ROW 3
G3: 4,7,9                                # reduction candidate for 4,7
G3: 9 => CTR
* .325.4678.8.63.41..468..93..741852636152438973287.95414579..386291368.548.345.12.
* PAIR RESTART
* PAIR H1: 7,9 ROW 1
A1: 7,9,1                                # reduction candidate for 7,9
A1: 7,9 => SOLVED
* 732514698589637412146892735974185263615243879328769541457921386261378954893456127
* DURATION: 0:00:06.401703  START: 05:57:01.679147  END: 05:57:08.080850 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-092-base-pr-001.dot
* REASONING
* DIS # G2: 7 => CTR => G2: 4,9
* DIS G2: 4,9 # G3: 9 => CTR => G3: 4,7
* PRF G2: 4,9 + G3: 4,7 # A1: 7,9 => SOL
* STA G2: 4,9 + G3: 4,7 + A1: 7,9
* CNT   3 HDP CHAINS /   5 HYP OPENED

Header Info

Top 500 Minimum 17 092

solution: 732514698589637412146892735974185263615243879328769541457921386261378954893456127
info: 1567     FNBTWXY  S8.f     18308

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

Solution

position: 732514698589637412146892735974185263615243879328769541457921386261378954893456127 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:

* INC # G2: 4,9 => UNS
* DIS # G2: 7 => CTR => G2: 4,9
* INC # G3: 4,7 => UNS
* DIS # G3: 9 => CTR => G3: 4,7
* INC # G2: 7,9 => UNS
* INC # G3: 7,9 => UNS
* INC # A1: 7,9 => UNS
* INC # E1: 7,9 => UNS
* INC # A1: 7,9 => UNS
* INC # A2: 7,9 => UNS
* INC # A3: 7,9 => UNS
* INC # E3: 1,2 => UNS
* INC # E3: 7,9 => UNS
* INC # F3: 1,2 => UNS
* INC # F3: 7,9 => UNS
* INC # G2: 7,9 => UNS
* INC # G3: 7,9 => UNS
* CNT  17 HDP CHAINS /  17 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G2: 4,9 => UNS
* DIS # G2: 7 => CTR => G2: 4,9
* INC G2: 4,9 # G3: 4,7 => UNS
* DIS G2: 4,9 # G3: 9 => CTR => G3: 4,7
* PRF G2: 4,9 + G3: 4,7 # A1: 7,9 => SOL
* STA G2: 4,9 + G3: 4,7 + A1: 7,9
* CNT   5 HDP CHAINS /   5 HYP OPENED