Analysis of zz-menneske-no-06913216-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 7.8....4.....7.3...46..5.....21.....3..8....1.....67........29..8..9..5..1......8 initial

Autosolve

position: 738....4..2..7.3...46..5.....21.....3..8....1.....67........29..8..9.15..1......8 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # G1: 6,9 => CTR => G1: 5
* DIS # I1: 6,9 => CTR => I1: 2,5
* DIS # D2: 6,9 => CTR => D2: 4
* DIS # I4: 6,9 => CTR => I4: 3,4,5
* DIS # G4: 4,5,6 => CTR => G4: 8,9
* DIS # A9: 4,6 => CTR => A9: 2,5,9
* DIS # D9: 4,6 => CTR => D9: 2,3,5,7
* DIS # G4: 4,6 => CTR => G4: 5,8,9
* CNT   8 HDP CHAINS /  26 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 # G1: 6,9 => CTR => G1: 5
* DIS G1: 5 # I1: 6,9 => CTR => I1: 2
* PRF G1: 5 + I1: 2 => SOL
* STA G1: 5 + I1: 2
* CNT   3 HDP CHAINS /   4 HYP OPENED

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

Details

Positions

7.8....4.....7.3...46..5.....21.....3..8....1.....67........29..8..9..5..1......8 initial
738....4..2..7.3...46..5.....21.....3..8....1.....67........29..8..9.15..1......8 autosolve
738619542125478369946235817672143985394857621851926734467581293283794156519362478 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
A3: 1,9
I2: 6,9
G3: 8,9
B6: 5,9
H5: 2,6
E7: 1,8
F7: 1,8
G9: 4,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E1,F1: 1.. / E1 = 1  =>  0 pairs (*) / F1 = 1  =>  0 pairs (X)
H2,H3: 1.. / H2 = 1  =>  0 pairs (X) / H3 = 1  =>  0 pairs (_)
A6,C6: 1.. / A6 = 1  =>  0 pairs (X) / C6 = 1  =>  9 pairs (_)
E7,F7: 1.. / E7 = 1  =>  0 pairs (X) / F7 = 1  =>  0 pairs (_)
A3,H3: 1.. / A3 = 1  =>  0 pairs (X) / H3 = 1  =>  0 pairs (_)
C2,C6: 1.. / C2 = 1  =>  0 pairs (X) / C6 = 1  =>  9 pairs (_)
E1,E7: 1.. / E1 = 1  =>  0 pairs (*) / E7 = 1  =>  0 pairs (X)
F1,F7: 1.. / F1 = 1  =>  0 pairs (X) / F7 = 1  =>  0 pairs (_)
A8,A9: 2.. / A8 = 2  =>  9 pairs (_) / A9 = 2  => 11 pairs (_)
D3,E3: 3.. / D3 = 3  =>  9 pairs (_) / E3 = 3  =>  0 pairs (*)
D2,F2: 4.. / D2 = 4  => 10 pairs (_) / F2 = 4  =>  0 pairs (X)
A2,C2: 5.. / A2 = 5  => 10 pairs (_) / C2 = 5  => 10 pairs (_)
G1,I1: 5.. / G1 = 5  =>  8 pairs (_) / I1 = 5  =>  0 pairs (X)
E1,E9: 6.. / E1 = 6  =>  0 pairs (X) / E9 = 6  =>  0 pairs (_)
H3,I3: 7.. / H3 = 7  =>  0 pairs (X) / I3 = 7  =>  8 pairs (_)
F4,F5: 7.. / F4 = 7  =>  8 pairs (_) / F5 = 7  => 10 pairs (_)
B4,F4: 7.. / B4 = 7  => 10 pairs (_) / F4 = 7  =>  8 pairs (_)
H3,H9: 7.. / H3 = 7  =>  0 pairs (X) / H9 = 7  =>  8 pairs (_)
F2,E3: 8.. / F2 = 8  =>  0 pairs (*) / E3 = 8  =>  0 pairs (X)
A4,A6: 8.. / A4 = 8  =>  0 pairs (X) / A6 = 8  => 10 pairs (_)
E7,F7: 8.. / E7 = 8  =>  0 pairs (*) / F7 = 8  =>  0 pairs (X)
F2,H2: 8.. / F2 = 8  =>  0 pairs (*) / H2 = 8  =>  0 pairs (X)
A6,H6: 8.. / A6 = 8  => 10 pairs (_) / H6 = 8  =>  0 pairs (X)
E3,E7: 8.. / E3 = 8  =>  0 pairs (X) / E7 = 8  =>  0 pairs (_)
F2,F7: 8.. / F2 = 8  =>  0 pairs (*) / F7 = 8  =>  0 pairs (X)
G3,G4: 8.. / G3 = 8  =>  0 pairs (*) / G4 = 8  =>  0 pairs (X)
A9,C9: 9.. / A9 = 9  =>  0 pairs (X) / C9 = 9  =>  9 pairs (_)
C2,C9: 9.. / C2 = 9  =>  0 pairs (X) / C9 = 9  =>  9 pairs (_)
* DURATION: 0:00:41.563603  START: 07:07:01.867568  END: 07:07:43.431171 2017-05-01
* CP COUNT: (28)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B6,E7,F7,G3,G9,H5,I2)
* 738....4..2..7.3...46..5.....21.....3..8....1.....67........29..8..9.15..1......8
* PAIR A3: 1,9 BLK 1
A2: 1,9,5                                # reduction candidate for 1,9
A2: 1,9                                  # 10 pairs
C2: 1,9,5                                # reduction candidate for 1,9
C2: 1,9                                  # 10 pairs
* PAIR I2: 6,9 BLK 3
G1: 6,9,5                                # reduction candidate for 6,9
G1: 6,9 => CTR
* 738.12945.2.4783161469358....21.....3..8....1..1..67......8129..8..9.15..1..6.4.8
G1: 5                                    #  8 pairs
I1: 6,9,2,5                              # reduction candidate for 6,9
I1: 6,9 => CTR
* 738.12549.2.4783161469358....21.....3..8....1.91..67......8129..8..9.15..1..6.4.8
I1: 2,5                                  #  9 pairs
* PAIR I2: 6,9 ROW 2
D2: 6,9,4                                # reduction candidate for 6,9
D2: 6,9 => CTR
* 738....4..2..7438..46.8591...21.....3..8....1.....67........29..8..9.15..1......8
D2: 4                                    # 10 pairs
* PAIR I2: 6,9 COL I
I4: 6,9,3,4,5                            # reduction candidate for 6,9
I4: 6,9 => CTR
* 738.61.4..2..7.386.46.8591...21.....3..8....1.....67......1829..8..9.15..1......8
I4: 3,4,5                                #  8 pairs
* PAIR G3: 8,9 COL G
G4: 8,9,4,5,6                            # reduction candidate for 8,9
G4: 4,5,6 => CTR
* 738619542.2.478369946235817.921.....3..8..921...9267......8129..8..9415..19.6.478
G4: 8,9                                  # 10 pairs
* PAIR B6: 5,9 BLK 4
B4: 5,9,6,7                              # reduction candidate for 5,9
B4: 5,9                                  # 13 pairs
B5: 5,9,6,7                              # reduction candidate for 5,9
B5: 5,9                                  # 14 pairs
* PAIR B6: 5,9 ROW 6
D6: 5,9,2,3,4                            # reduction candidate for 5,9
D6: 5,9                                  # 10 pairs
I6: 5,9,2,3,4                            # reduction candidate for 5,9
I6: 5,9                                  # 14 pairs
* PAIR G9: 4,6 BLK 9
I7: 4,6,3,7                              # reduction candidate for 4,6
I7: 4,6                                  # 11 pairs
I8: 4,6,3,7                              # reduction candidate for 4,6
I8: 4,6                                  # 11 pairs
* PAIR G9: 4,6 ROW 9
A9: 4,6,2,5,9                            # reduction candidate for 4,6
A9: 4,6 => CTR
* 738.61.4..2..7.386.46.8591...21.....3..8....1.....67......1829.28..9.15..19.....8
A9: 2,5,9                                #  8 pairs
D9: 4,6,2,3,5,7                          # reduction candidate for 4,6
D9: 4,6 => CTR
* 738.61.4..2..7.386.46.8591...21.....3..8....1.....67......1829..8..9.15..1......8
D9: 2,3,5,7                              #  8 pairs
E9: 4,6,2,3,5                            # reduction candidate for 4,6
E9: 4,6                                  # 11 pairs
* PAIR G9: 4,6 COL G
G4: 4,6,5,8,9                            # reduction candidate for 4,6
G4: 4,6 => CTR
* 738619542.2.478369946235817.921..6..36.8..921...9267......8129..8..9415..19.6.478
G4: 5,8,9                                #  8 pairs
G5: 4,6,5,9                              # reduction candidate for 4,6
G5: 4,6                                  # 10 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-menneske-no-06913216-base-pr-000.dot
* REASONING
* DIS # G1: 6,9 => CTR => G1: 5
* DIS # I1: 6,9 => CTR => I1: 2,5
* DIS # D2: 6,9 => CTR => D2: 4
* DIS # I4: 6,9 => CTR => I4: 3,4,5
* DIS # G4: 4,5,6 => CTR => G4: 8,9
* DIS # A9: 4,6 => CTR => A9: 2,5,9
* DIS # D9: 4,6 => CTR => D9: 2,3,5,7
* DIS # G4: 4,6 => CTR => G4: 5,8,9
* CNT   8 HDP CHAINS /  26 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B6,E7,F7,G3,G9,H5,I2)
* 738....4..2..7.3...46..5.....21.....3..8....1.....67........29..8..9.15..1......8
* PAIR A3: 1,9 BLK 1
A2: 1,9,5                                # reduction candidate for 1,9
A2: 1,9                                  # 10 pairs
C2: 1,9,5                                # reduction candidate for 1,9
C2: 1,9                                  # 10 pairs
* PAIR I2: 6,9 BLK 3
G1: 6,9,5                                # reduction candidate for 6,9
G1: 6,9 => CTR
* 738.12945.2.4783161469358....21.....3..8....1..1..67......8129..8..9.15..1..6.4.8
I1: 6,9,2                                # reduction candidate for 6,9
I1: 6,9 => CTR
* 738.12549.2.4783161469358....21.....3..8....1.91..67......8129..8..9.15..1..6.4.8
I1: 2 => SOLVED
* 738619542125478369946235817672143985394857621851926734467581293283794156519362478
* DURATION: 0:00:04.273441  START: 07:08:01.728170  END: 07:08:06.001611 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-menneske-no-06913216-base-pr-001.dot
* REASONING
* DIS # G1: 6,9 => CTR => G1: 5
* DIS G1: 5 # I1: 6,9 => CTR => I1: 2
* PRF G1: 5 + I1: 2 => SOL
* STA G1: 5 + I1: 2
* CNT   3 HDP CHAINS /   4 HYP OPENED

Header Info

http://www.menneske.no/sudoku/utskrift.html?number=6913216
umulig

* PAIR REDUCTION ..
* ROUND 1: 738....4..2..7.3...46..5.....21.....3..8....1.....67........29..8..9.15..1......8
A3: 1,9
A2: 1,5,9                                # reduction candidate for 1,9
C2: 1,5,9                                # reduction candidate for 1,9
A2: 1,5,9                                # reduction candidate for 1,9
I2: 6,9
G1: 5,6,9                                # reduction candidate for 6,9
G1: 6,9 => CTR
* 738.12945.2.4783161469358....21.....3..8....1..1..67......8129..8..9.15..1..6.4.8
I1: 2,6,9                                # reduction candidate for 6,9
I1: 6,9 => CTR
* 738.12549.2.4783161469358....21.....3..8....1.91..67......8129..8..9.15..1..6.4.8
I1: 2 => SOLVED
* 738619542125478369946235817672143985394857621851926734467581293283794156519362478
* SOLVED!

|:step:| 00
--------------------------------------------------

G4: 8,9
I1: 2,5
G5: 4,6

|:step:| 01
--------------------------------------------------

Solution

position: 738619542125478369946235817672143985394857621851926734467581293283794156519362478 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 # A2: 1,9 => UNS
* INC # C2: 1,9 => UNS
* DIS # G1: 6,9 => CTR => G1: 5
* INC # G1: 5 => UNS
* DIS # I1: 6,9 => CTR => I1: 2,5
* INC # I1: 2,5 => UNS
* DIS # D2: 6,9 => CTR => D2: 4
* INC # D2: 4 => UNS
* DIS # I4: 6,9 => CTR => I4: 3,4,5
* INC # I4: 3,4,5 => UNS
* INC # G4: 8,9 => UNS
* DIS # G4: 4,5,6 => CTR => G4: 8,9
* INC # B4: 5,9 => UNS
* INC # B5: 5,9 => UNS
* INC # D6: 5,9 => UNS
* INC # I6: 5,9 => UNS
* INC # I7: 4,6 => UNS
* INC # I8: 4,6 => UNS
* DIS # A9: 4,6 => CTR => A9: 2,5,9
* INC # A9: 2,5,9 => UNS
* DIS # D9: 4,6 => CTR => D9: 2,3,5,7
* INC # D9: 2,3,5,7 => UNS
* INC # E9: 4,6 => UNS
* DIS # G4: 4,6 => CTR => G4: 5,8,9
* INC # G4: 5,8,9 => UNS
* INC # G5: 4,6 => UNS
* CNT  26 HDP CHAINS /  26 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A2: 1,9 => UNS
* INC # C2: 1,9 => UNS
* DIS # G1: 6,9 => CTR => G1: 5
* DIS G1: 5 # I1: 6,9 => CTR => I1: 2
* PRF G1: 5 + I1: 2 => SOL
* STA G1: 5 + I1: 2
* CNT   5 HDP CHAINS /   4 HYP OPENED