Analysis of xx-top500-100-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ...2..8.4...9..3..1........5....6.1.....4.........8....84.3.......7...5..2....... initial

Autosolve

position: ...2..8.4...9..3.11........5..3.6.1.....4.........8....846351.....7...5..25...... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # F3: 4,7 => SOL
* DIS # B2: 4,7 => CTR => B2: 5,6
* DIS # C4: 2,8 => CTR => C4: 7,9
* PRF # C4: 7,9 => SOL
* DIS # C5: 2,8 => CTR => C5: 1,3,6,7,9
* DIS # I5: 2,8 => CTR => I5: 3,5,6,7,9
* DIS # A2: 2,8 => CTR => A2: 4
* PRF # A2: 4 => SOL
* DIS # G6: 2,4 => CTR => G6: 5,6,7,9
* PRF # A2: 2,4 => SOL
* DIS # A2: 8 => CTR => A2: 2,4
* DIS # I5: 3,8 => CTR => I5: 2,5,6,7,9
* DIS # C5: 3,8 => CTR => C5: 1,2,6,7,9
* PRF # H9: 3,8 => SOL
* DIS # H9: 4 => CTR => H9: 3,8
* DIS # B6: 3,4 => CTR => B6: 1,6,7,9
* DIS # H9: 3,4 => CTR => H9: 8
* PRF # H9: 8 => SOL
* DIS # H9: 3 => CTR => H9: 4,8
* CNT  19 HDP CHAINS /  32 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* PRF # F3: 4,7 => SOL
* STA F3: 4,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

...2..8.4...9..3..1........5....6.1.....4.........8....84.3.......7...5..2....... initial
...2..8.4...9..3.11........5..3.6.1.....4.........8....846351.....7...5..25...... autosolve
957213864468957321132864579549326718876149235213578946784635192691782453325491687 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (10)
F2: 4,7
D3: 4,8
A5: 2,8
A6: 2,4
D5: 1,5
D6: 1,5
H5: 3,8
H6: 3,4
A7: 7,9
D9: 4,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E1,F1: 1.. / E1 = 1  =>  0 pairs (*) / F1 = 1  =>  0 pairs (X)
D5,D6: 1.. / D5 = 1  =>  8 pairs (_) / D6 = 1  =>  8 pairs (_)
B8,C8: 1.. / B8 = 1  => 10 pairs (_) / C8 = 1  => 10 pairs (_)
E9,F9: 1.. / E9 = 1  => 11 pairs (_) / F9 = 1  =>  0 pairs (*)
E1,E9: 1.. / E1 = 1  =>  0 pairs (*) / E9 = 1  =>  0 pairs (X)
F1,F9: 1.. / F1 = 1  => 11 pairs (_) / F9 = 1  =>  0 pairs (*)
E8,F8: 2.. / E8 = 2  =>  0 pairs (X) / F8 = 2  =>  0 pairs (_)
H7,I7: 2.. / H7 = 2  => 14 pairs (_) / I7 = 2  => 11 pairs (_)
F5,F8: 2.. / F5 = 2  =>  0 pairs (X) / F8 = 2  =>  0 pairs (_)
F1,F3: 3.. / F1 = 3  =>  0 pairs (*) / F3 = 3  =>  0 pairs (X)
B4,G4: 4.. / B4 = 4  =>  0 pairs (*) / G4 = 4  =>  0 pairs (X)
F8,G8: 4.. / F8 = 4  =>  0 pairs (X) / G8 = 4  =>  0 pairs (_)
A2,A6: 4.. / A2 = 4  =>  0 pairs (*) / A6 = 4  =>  0 pairs (X)
D3,D9: 4.. / D3 = 4  =>  0 pairs (X) / D9 = 4  =>  0 pairs (_)
H6,H9: 4.. / H6 = 4  =>  0 pairs (*) / H9 = 4  =>  0 pairs (X)
B1,B2: 5.. / B1 = 5  => 10 pairs (_) / B2 = 5  => 11 pairs (_)
E1,E2: 5.. / E1 = 5  => 11 pairs (_) / E2 = 5  => 10 pairs (_)
G3,I3: 5.. / G3 = 5  => 10 pairs (_) / I3 = 5  => 10 pairs (_)
D5,D6: 5.. / D5 = 5  =>  8 pairs (_) / D6 = 5  =>  8 pairs (_)
B1,E1: 5.. / B1 = 5  => 10 pairs (_) / E1 = 5  => 11 pairs (_)
B2,E2: 5.. / B2 = 5  => 11 pairs (_) / E2 = 5  => 10 pairs (_)
A7,A9: 7.. / A7 = 7  => 12 pairs (_) / A9 = 7  => 15 pairs (_)
C4,I4: 8.. / C4 = 8  =>  0 pairs (X) / I4 = 8  =>  0 pairs (_)
E8,I8: 8.. / E8 = 8  =>  0 pairs (*) / I8 = 8  =>  0 pairs (X)
A2,A5: 8.. / A2 = 8  =>  0 pairs (X) / A5 = 8  =>  0 pairs (_)
D3,D9: 8.. / D3 = 8  =>  0 pairs (*) / D9 = 8  =>  0 pairs (X)
H5,H9: 8.. / H5 = 8  =>  0 pairs (X) / H9 = 8  =>  0 pairs (_)
* DURATION: 0:00:48.905109  START: 06:10:59.998366  END: 06:11:48.903475 2017-05-04
* CP COUNT: (27)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,A7,D3,D5,D6,D9,F2,H5,H6)
* ...2..8.4...9..3.11........5..3.6.1.....4.........8....846351.....7...5..25......
* PAIR F2: 4,7 BLK 2
F3: 4,7,3                                # reduction candidate for 4,7
F3: 4,7 => SOLVED
* 957213864468957321132864579549326718876149235213578946784635192691782453325491687
F3: 3                                    # 11 pairs
* PAIR F2: 4,7 ROW 2
B2: 4,7,5,6                              # reduction candidate for 4,7
B2: 4,7 => CTR
* .5.2618.484.9573.11..483...5.83.641.2...49.8.4....8.3..846351.....7.4.58.258...43
B2: 5,6                                  # 11 pairs
* PAIR A5: 2,8 BLK 4
C4: 2,8,7,9                              # reduction candidate for 2,8
C4: 2,8 => CTR
* ...2..8.484.9573.11..483...5.83.641.2...49.8.4....8.3..846351.....724.58.25891.4.
C4: 7,9 => SOLVED
* 957213864468957321132864579549326718876149235213578946784635192691782453325491687
C5: 2,8,1,3,6,7,9                        # reduction candidate for 2,8
C5: 2,8 => CTR
* ...2..8.4...9..3.11........5..3.6.18....4..3.4....8....846351.....7...5..25......
C5: 1,3,6,7,9                            # 10 pairs
* PAIR A5: 2,8 ROW 5
I5: 2,8,3,5,6,7,9                        # reduction candidate for 2,8
I5: 2,8 => CTR
* ...2..8.44..9.73.11..864...54.3.6.1.8...49.322...78.4..8463512....78245..25491.8.
I5: 3,5,6,7,9                            # 10 pairs
* PAIR A5: 2,8 COL A
A2: 2,8,4                                # reduction candidate for 2,8
A2: 2,8 => CTR
* ...2..8.484.9573.11..483...5.83.641.2...49.8.4....8.3..846351.....724.58.25891.4.
A2: 4 => SOLVED
* 957213864468957321132864579549326718876149235213578946784635192691782453325491687
* PAIR A6: 2,4 ROW 6
G6: 2,4,5,6,7,9                          # reduction candidate for 2,4
G6: 2,4 => CTR
* ...2..8.484.9573.11..483...5.83.641.2...49.8.4...7823..846351.....724.5..258...4.
G6: 5,6,7,9                              # 10 pairs
* PAIR A6: 2,4 COL A
A2: 2,4,8                                # reduction candidate for 2,4
A2: 2,4 => SOLVED
* 957213864468957321132864579549326718876149235213578946784635192691782453325491687
A2: 8 => CTR
* ...2..8.48..9..3.11........5..3.6.1.2...4....4....8.3..846351.....7.245..25....8.
* PAIR H5: 3,8 BLK 6
I5: 3,8,2,5,6,7,9                        # reduction candidate for 3,8
I5: 3,8 => CTR
* ...2..8.48..9..3.11........5.83.6.1.2...4....4....8....846351.....7...5..25......
I5: 2,5,6,7,9                            # 10 pairs
* PAIR H5: 3,8 ROW 5
C5: 3,8,1,2,6,7,9                        # reduction candidate for 3,8
C5: 3,8 => CTR
* ...2..8.48..9..3.11........5..3.6.1.2...4....4....8.3..846351.....7.245..25....8.
C5: 1,2,6,7,9                            # 10 pairs
* PAIR H5: 3,8 COL H
H9: 3,8,4                                # reduction candidate for 3,8
H9: 3,8 => SOLVED
* 957213864468957321132864579549326718876149235213578946784635192691782453325491687
H9: 4 => CTR
* ...2..8.48..9..3.11..48....5.83.6.1.2...4..8.4....8.3..846351.....7...5..25....4.
* PAIR H6: 3,4 ROW 6
B6: 3,4,1,6,7,9                          # reduction candidate for 3,4
B6: 3,4 => CTR
* ...2.38.44.89573211..864...54.3.6.188...4..3.23...8.4..846351.....78245..254...8.
B6: 1,6,7,9                              # 10 pairs
* PAIR H6: 3,4 COL H
H9: 3,4,8                                # reduction candidate for 3,4
H9: 3,4 => CTR
* ...2..8.48..9..3.11........5.83.6.1.2...4..8.4....8.3..846351.....7.245..25......
H9: 8 => SOLVED
* 957213864468957321132864579549326718876149235213578946784635192691782453325491687
* PAIR A7: 7,9 BLK 7
A9: 7,9,3,6                              # reduction candidate for 7,9
A9: 3,6                                  # 17 pairs
A9: 7,9                                  # 15 pairs
* PAIR A7: 7,9 ROW 7
H7: 7,9,2                                # reduction candidate for 7,9
H7: 7,9                                  # 11 pairs
I7: 7,9,2                                # reduction candidate for 7,9
I7: 7,9                                  # 14 pairs
* PAIR D9: 4,8 ROW 9
H9: 4,8,3                                # reduction candidate for 4,8
H9: 3 => CTR
* ...2..8.4...9..3.11........5..3.6.1.....4..8......8.4..846351.....7...5..25....3.
H9: 4,8                                  # 16 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-100-base-pr-000.dot
* REASONING
* PRF # F3: 4,7 => SOL
* DIS # B2: 4,7 => CTR => B2: 5,6
* DIS # C4: 2,8 => CTR => C4: 7,9
* PRF # C4: 7,9 => SOL
* DIS # C5: 2,8 => CTR => C5: 1,3,6,7,9
* DIS # I5: 2,8 => CTR => I5: 3,5,6,7,9
* DIS # A2: 2,8 => CTR => A2: 4
* PRF # A2: 4 => SOL
* DIS # G6: 2,4 => CTR => G6: 5,6,7,9
* PRF # A2: 2,4 => SOL
* DIS # A2: 8 => CTR => A2: 2,4
* DIS # I5: 3,8 => CTR => I5: 2,5,6,7,9
* DIS # C5: 3,8 => CTR => C5: 1,2,6,7,9
* PRF # H9: 3,8 => SOL
* DIS # H9: 4 => CTR => H9: 3,8
* DIS # B6: 3,4 => CTR => B6: 1,6,7,9
* DIS # H9: 3,4 => CTR => H9: 8
* PRF # H9: 8 => SOL
* DIS # H9: 3 => CTR => H9: 4,8
* CNT  19 HDP CHAINS /  32 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,A7,D3,D5,D6,D9,F2,H5,H6)
* ...2..8.4...9..3.11........5..3.6.1.....4.........8....846351.....7...5..25......
* PAIR F2: 4,7 BLK 2
F3: 4,7,3                                # reduction candidate for 4,7
F3: 4,7 => SOLVED
* 957213864468957321132864579549326718876149235213578946784635192691782453325491687
* DURATION: 0:00:02.738315  START: 06:12:21.173026  END: 06:12:23.911341 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-100-base-pr-001.dot
* REASONING
* PRF # F3: 4,7 => SOL
* STA F3: 4,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 100

solution: 957213864468957321132864579549326718876149235213578946784635192691782453325491687
info: 1579     FNBTHXY  S8.f     7762

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

Solution

position: 957213864468957321132864579549326718876149235213578946784635192691782453325491687 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:

* PRF # F3: 4,7 => SOL
* INC # F3: 3 => UNS
* DIS # B2: 4,7 => CTR => B2: 5,6
* INC # B2: 5,6 => UNS
* DIS # C4: 2,8 => CTR => C4: 7,9
* PRF # C4: 7,9 => SOL
* DIS # C5: 2,8 => CTR => C5: 1,3,6,7,9
* INC # C5: 1,3,6,7,9 => UNS
* DIS # I5: 2,8 => CTR => I5: 3,5,6,7,9
* INC # I5: 3,5,6,7,9 => UNS
* DIS # A2: 2,8 => CTR => A2: 4
* PRF # A2: 4 => SOL
* DIS # G6: 2,4 => CTR => G6: 5,6,7,9
* INC # G6: 5,6,7,9 => UNS
* PRF # A2: 2,4 => SOL
* DIS # A2: 8 => CTR => A2: 2,4
* DIS # I5: 3,8 => CTR => I5: 2,5,6,7,9
* INC # I5: 2,5,6,7,9 => UNS
* DIS # C5: 3,8 => CTR => C5: 1,2,6,7,9
* INC # C5: 1,2,6,7,9 => UNS
* PRF # H9: 3,8 => SOL
* DIS # H9: 4 => CTR => H9: 3,8
* DIS # B6: 3,4 => CTR => B6: 1,6,7,9
* INC # B6: 1,6,7,9 => UNS
* DIS # H9: 3,4 => CTR => H9: 8
* PRF # H9: 8 => SOL
* INC # A9: 7,9 => UNS
* INC # A9: 3,6 => UNS
* INC # H7: 7,9 => UNS
* INC # I7: 7,9 => UNS
* INC # H9: 4,8 => UNS
* DIS # H9: 3 => CTR => H9: 4,8
* CNT  32 HDP CHAINS /  32 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # F3: 4,7 => SOL
* STA F3: 4,7
* CNT   1 HDP CHAINS /   1 HYP OPENED