Analysis of zz-menneske-no-06903973-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ...1.4.6.8........3....6..5.45..2.....2...57.....3...9....7.......9....8..6....2. initial

Autosolve

position: ...1.4.6.86.......3....6..5.45..2....32...57.....3.2.9....7.......9....8..6....2. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # D6: 6,7 => CTR => D6: 4,5
* PRF # A4: 6,7 => SOL
* DIS # H7: 1,4 => CTR => H7: 3,5,9
* DIS # H8: 1,4 => CTR => H8: 3,5
* CNT   4 HDP CHAINS /  18 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 # D6: 6,7 => CTR => D6: 4,5
* DIS D6: 4,5 # I5: 1,4 => CTR => I5: 6
* DIS D6: 4,5 + I5: 6 # B1: 7,9 => CTR => B1: 2,5
* DIS D6: 4,5 + I5: 6 + B1: 2,5 # G1: 7,9 => CTR => G1: 3,8
* PRF D6: 4,5 + I5: 6 + B1: 2,5 + G1: 3,8 # I9: 1 => SOL
* STA D6: 4,5 + I5: 6 + B1: 2,5 + G1: 3,8 + I9: 1
* CNT   5 HDP CHAINS /  22 HYP OPENED

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

Details

Positions

...1.4.6.8........3....6..5.45..2.....2...57.....3...9....7.......9....8..6....2. initial
...1.4.6.86.......3....6..5.45..2....32...57.....3.2.9....7.......9....8..6....2. autosolve
259184367867359412314726895745692183932418576681537249198275634423961758576843921 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (5)
C1: 7,9
D4: 6,7
H6: 1,4
D7: 2,6
E8: 2,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
I1,I2: 2.. / I1 = 2  =>  0 pairs (X) / I2 = 2  =>  7 pairs (_)
D7,E8: 2.. / D7 = 2  =>  5 pairs (_) / E8 = 2  =>  0 pairs (X)
D2,F2: 3.. / D2 = 3  =>  5 pairs (_) / F2 = 3  =>  0 pairs (X)
G1,I1: 3.. / G1 = 3  =>  8 pairs (_) / I1 = 3  => 11 pairs (_)
C7,C8: 3.. / C7 = 3  =>  9 pairs (_) / C8 = 3  =>  6 pairs (_)
D2,D9: 3.. / D2 = 3  =>  5 pairs (_) / D9 = 3  =>  0 pairs (X)
C2,C3: 4.. / C2 = 4  =>  6 pairs (_) / C3 = 4  =>  5 pairs (_)
I5,H6: 4.. / I5 = 4  =>  0 pairs (X) / H6 = 4  =>  6 pairs (_)
A7,A8: 4.. / A7 = 4  =>  5 pairs (_) / A8 = 4  =>  5 pairs (_)
D9,E9: 4.. / D9 = 4  =>  9 pairs (_) / E9 = 4  =>  7 pairs (_)
D6,H6: 4.. / D6 = 4  =>  0 pairs (X) / H6 = 4  =>  6 pairs (_)
E5,E9: 4.. / E5 = 4  =>  9 pairs (_) / E9 = 4  =>  7 pairs (_)
A1,B1: 5.. / A1 = 5  =>  8 pairs (_) / B1 = 5  =>  6 pairs (_)
D6,F6: 5.. / D6 = 5  =>  8 pairs (_) / F6 = 5  => 12 pairs (_)
H7,H8: 5.. / H7 = 5  =>  5 pairs (_) / H8 = 5  =>  6 pairs (_)
E2,E9: 5.. / E2 = 5  =>  5 pairs (_) / E9 = 5  =>  0 pairs (X)
D7,E8: 6.. / D7 = 6  =>  0 pairs (X) / E8 = 6  =>  5 pairs (_)
A6,D6: 6.. / A6 = 6  =>  6 pairs (_) / D6 = 6  =>  0 pairs (X)
E8,G8: 6.. / E8 = 6  =>  5 pairs (_) / G8 = 6  =>  0 pairs (X)
A4,D4: 7.. / A4 = 7  =>  0 pairs (*) / D4 = 7  =>  0 pairs (X)
F2,F6: 7.. / F2 = 7  => 11 pairs (_) / F6 = 7  =>  0 pairs (*)
B6,C6: 8.. / B6 = 8  =>  7 pairs (_) / C6 = 8  =>  6 pairs (_)
G4,H4: 8.. / G4 = 8  =>  8 pairs (_) / H4 = 8  =>  9 pairs (_)
E1,G1: 8.. / E1 = 8  =>  7 pairs (_) / G1 = 8  => 14 pairs (_)
C6,C7: 8.. / C6 = 8  =>  6 pairs (_) / C7 = 8  =>  7 pairs (_)
H3,H4: 8.. / H3 = 8  =>  8 pairs (_) / H4 = 8  =>  9 pairs (_)
A4,A5: 9.. / A4 = 9  => 11 pairs (_) / A5 = 9  =>  0 pairs (*)
A4,E4: 9.. / A4 = 9  => 11 pairs (_) / E4 = 9  =>  0 pairs (*)
B9,G9: 9.. / B9 = 9  =>  5 pairs (_) / G9 = 9  =>  5 pairs (_)
F2,F5: 9.. / F2 = 9  =>  0 pairs (*) / F5 = 9  =>  0 pairs (X)
* DURATION: 0:00:42.927739  START: 06:40:06.875162  END: 06:40:49.802901 2017-05-01
* CP COUNT: (30)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C1,D4,D7,E8,H6)
* ...1.4.6.86.......3....6..5.45..2....32...57.....3.2.9....7.......9....8..6....2.
* PAIR C1: 7,9 BLK 1
B1: 7,9,2,5                              # reduction candidate for 7,9
B1: 7,9                                  # 18 pairs
C2: 7,9,1,4                              # reduction candidate for 7,9
C2: 7,9                                  # 19 pairs
B3: 7,9,1,2                              # reduction candidate for 7,9
B3: 7,9                                  # 15 pairs
C3: 7,9,1,4                              # reduction candidate for 7,9
C3: 7,9                                  # 15 pairs
* PAIR C1: 7,9 ROW 1
G1: 7,9,3,8                              # reduction candidate for 7,9
G1: 7,9                                  # 16 pairs
G1: 3,8                                  #  6 pairs
* PAIR D4: 6,7 BLK 5
D6: 6,7,4,5                              # reduction candidate for 6,7
D6: 6,7 => CTR
* 25.1.4.6.86.357..23..826..5945712.8.632489571...6352495..27.634423961758..654..2.
D6: 4,5                                  #  7 pairs
* PAIR D4: 6,7 ROW 4
A4: 6,7,1,9                              # reduction candidate for 6,7
A4: 6,7 => SOLVED
* 259184367867359412314726895745692183932418576681537249198275634423961758576843921
A4: 1,9                                  # 11 pairs
* PAIR H6: 1,4 BLK 6
I5: 1,4,6                                # reduction candidate for 1,4
I5: 6                                    # 17 pairs
I5: 1,4                                  # 15 pairs
* PAIR H6: 1,4 COL H
H2: 1,4,9                                # reduction candidate for 1,4
H2: 1,4                                  #  9 pairs
H3: 1,4,8,9                              # reduction candidate for 1,4
H3: 1,4                                  # 20 pairs
H7: 1,4,3,5,9                            # reduction candidate for 1,4
H7: 1,4 => CTR
* 7..184.6.86.357.923..296.859457.283.1328.957.6...3.2.9...67....4..92.658..6....2.
H7: 3,5,9                                #  5 pairs
H8: 1,4,3,5                              # reduction candidate for 1,4
H8: 1,4 => CTR
* .59184.6.86.357.923..296.859457628311328495766..531249.2167895....92.6.85.641..2.
H8: 3,5                                  #  6 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-menneske-no-06903973-base-pr-000.dot
* REASONING
* DIS # D6: 6,7 => CTR => D6: 4,5
* PRF # A4: 6,7 => SOL
* DIS # H7: 1,4 => CTR => H7: 3,5,9
* DIS # H8: 1,4 => CTR => H8: 3,5
* CNT   4 HDP CHAINS /  18 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C1,D4,D7,E8,H6)
* ...1.4.6.86.......3....6..5.45..2....32...57.....3.2.9....7.......9....8..6....2.
* PAIR C1: 7,9 BLK 1
B1: 7,9,2,5                              # reduction candidate for 7,9
B1: 7,9                                  # 18 pairs
C2: 7,9,1,4                              # reduction candidate for 7,9
C2: 7,9                                  # 19 pairs
B3: 7,9,1,2                              # reduction candidate for 7,9
B3: 7,9                                  # 15 pairs
C3: 7,9,1,4                              # reduction candidate for 7,9
C3: 7,9                                  # 15 pairs
* PAIR C1: 7,9 ROW 1
G1: 7,9,3,8                              # reduction candidate for 7,9
G1: 7,9                                  # 16 pairs
G1: 3,8                                  #  6 pairs
* PAIR D4: 6,7 BLK 5
D6: 6,7,4,5                              # reduction candidate for 6,7
D6: 6,7 => CTR
* 25.1.4.6.86.357..23..826..5945712.8.632489571...6352495..27.634423961758..654..2.
* PAIR H6: 1,4 BLK 6
I5: 1,4,6                                # reduction candidate for 1,4
I5: 1,4 => CTR
* ..91.436786.357..23...96..5945712...132..95746..435219....7.......96.7.87.654..2.

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A4,A5,C1,D3,D4,D5,D7,D9,E4,E5,E8,E9,F2,F6,H2,I1,I4)
* ...1.4.6.86.35...23....6..5.45..2....32...5766..53.249....7...44..9....8..6....2.
* PAIR C1: 7,9 BLK 1
B1: 7,9,2,5                              # reduction candidate for 7,9
B1: 7,9 => CTR
* 5..12486386.35...232.786..5745692.81932...5766..5372492...7...44..9....8..6....2.
C2: 7,9,1,4                              # reduction candidate for 7,9
C2: 7,9                                  # 28 pairs
B3: 7,9,1,2                              # reduction candidate for 7,9
B3: 7,9                                  # 25 pairs
C3: 7,9,1,4                              # reduction candidate for 7,9
C3: 7,9                                  # 27 pairs
* PAIR C1: 7,9 ROW 1
G1: 7,9,3,8                              # reduction candidate for 7,9
G1: 7,9 => CTR
* 25918476386.359.1237...6..5745692..1932...5766..537249...27.6.442796...8..6....27
* PAIR RESTART
* PAIR C1: 7,9 BLK 1
C2: 7,9,1,4                              # reduction candidate for 7,9
C2: 7,9                                  # 30 pairs
B3: 7,9,1,2                              # reduction candidate for 7,9
B3: 7,9                                  # 26 pairs
C3: 7,9,1,4                              # reduction candidate for 7,9
C3: 7,9                                  # 28 pairs
* PAIR F2: 7,9 ROW 2
C2: 7,9,1,4                              # reduction candidate for 7,9
C2: 7,9                                  # 30 pairs
G2: 7,9,1,4                              # reduction candidate for 7,9
G2: 7,9                                  # 22 pairs
* PAIR D3: 2,7 ROW 3
B3: 2,7,1,9                              # reduction candidate for 2,7
B3: 2,7                                  # 26 pairs
B3: 1,9                                  # 26 pairs
* PAIR I1: 3,7 COL I
I9: 3,7,1                                # reduction candidate for 3,7
I9: 1 => SOLVED
* 259184367867359412314726895745692183932418576681537249198275634423961758576843921
* DURATION: 0:00:25.664267  START: 06:41:05.464669  END: 06:41:31.128936 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-menneske-no-06903973-base-pr-001.dot
* REASONING
* DIS # D6: 6,7 => CTR => D6: 4,5
* DIS D6: 4,5 # I5: 1,4 => CTR => I5: 6
* DIS D6: 4,5 + I5: 6 # B1: 7,9 => CTR => B1: 2,5
* DIS D6: 4,5 + I5: 6 + B1: 2,5 # G1: 7,9 => CTR => G1: 3,8
* PRF D6: 4,5 + I5: 6 + B1: 2,5 + G1: 3,8 # I9: 1 => SOL
* STA D6: 4,5 + I5: 6 + B1: 2,5 + G1: 3,8 + I9: 1
* CNT   5 HDP CHAINS /  22 HYP OPENED

Header Info

http://www.menneske.no/sudoku/utskrift.html?number=6903973
umulig

--------------------------------------------------
level: medium

* PAIR REDUCTION ..
* ROUND 1: ...1.4.6.86.......3....6..5.45..2....32...57.....3.2.9....7.......9....8..6....2.
C1: 7,9
B1: 2,5,7,9                              # reduction candidate for 7,9
C2: 1,4,7,9                              # reduction candidate for 7,9
B3: 1,2,7,9                              # reduction candidate for 7,9
C3: 1,4,7,9                              # reduction candidate for 7,9
G1: 3,7,8,9                              # reduction candidate for 7,9
D4: 6,7
D6: 4,5,6,7                              # reduction candidate for 6,7
D6: 6,7 => CTR
* 25.1.4.6.86.357..23..826..5945712.8.632489571...6352495..27.634423961758..654..2.
H6: 1,4
I5: 1,4,6                                # reduction candidate for 1,4
I5: 1,4 => CTR
* ..91.436786.357..23...96..5945712...132..95746..435219....7.......96.7.87.654..2.
D7: 2,6
E8: 2,6
* ROUND 2: ...1.4.6.86.35...23....6..5.45..2....32...5766..53.249....7...44..9....8..6....2.
C1: 7,9
B1: 2,5,7,9                              # reduction candidate for 7,9
B1: 7,9 => CTR
* 5..12486386.35...232.786..5745692.81932...5766..5372492...7...44..9....8..6....2.
C2: 1,4,7,9                              # reduction candidate for 7,9
B3: 1,2,7,9                              # reduction candidate for 7,9
C3: 1,4,7,9                              # reduction candidate for 7,9
G1: 3,7,8,9                              # reduction candidate for 7,9
G1: 7,9 => CTR
* 25918476386.359.1237...6..5745692..1932...5766..537249...27.6.442796...8..6....27
F2: 7,9
C2: 1,4,7,9                              # reduction candidate for 7,9
G2: 1,4,7,9                              # reduction candidate for 7,9
D3: 2,7
B3: 1,2,7,9                              # reduction candidate for 2,7
I1: 3,7
I9: 1,3,7                                # reduction candidate for 3,7
I9: 1 => SOLVED
* 259184367867359412314726895745692183932418576681537249198275634423961758576843921
* SOLVED!

Solution

position: 259184367867359412314726895745692183932418576681537249198275634423961758576843921 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 # B1: 7,9 => UNS
* INC # C2: 7,9 => UNS
* INC # B3: 7,9 => UNS
* INC # C3: 7,9 => UNS
* INC # G1: 7,9 => UNS
* INC # G1: 3,8 => UNS
* DIS # D6: 6,7 => CTR => D6: 4,5
* INC # D6: 4,5 => UNS
* PRF # A4: 6,7 => SOL
* INC # A4: 1,9 => UNS
* INC # I5: 1,4 => UNS
* INC # I5: 6 => UNS
* INC # H2: 1,4 => UNS
* INC # H3: 1,4 => UNS
* DIS # H7: 1,4 => CTR => H7: 3,5,9
* INC # H7: 3,5,9 => UNS
* DIS # H8: 1,4 => CTR => H8: 3,5
* INC # H8: 3,5 => UNS
* CNT  18 HDP CHAINS /  18 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B1: 7,9 => UNS
* INC # C2: 7,9 => UNS
* INC # B3: 7,9 => UNS
* INC # C3: 7,9 => UNS
* INC # G1: 7,9 => UNS
* INC # G1: 3,8 => UNS
* DIS # D6: 6,7 => CTR => D6: 4,5
* DIS D6: 4,5 # I5: 1,4 => CTR => I5: 6
* DIS D6: 4,5 + I5: 6 # B1: 7,9 => CTR => B1: 2,5
* INC D6: 4,5 + I5: 6 + B1: 2,5 # C2: 7,9 => UNS
* INC D6: 4,5 + I5: 6 + B1: 2,5 # B3: 7,9 => UNS
* INC D6: 4,5 + I5: 6 + B1: 2,5 # C3: 7,9 => UNS
* DIS D6: 4,5 + I5: 6 + B1: 2,5 # G1: 7,9 => CTR => G1: 3,8
* INC D6: 4,5 + I5: 6 + B1: 2,5 + G1: 3,8 # C2: 7,9 => UNS
* INC D6: 4,5 + I5: 6 + B1: 2,5 + G1: 3,8 # B3: 7,9 => UNS
* INC D6: 4,5 + I5: 6 + B1: 2,5 + G1: 3,8 # C3: 7,9 => UNS
* INC D6: 4,5 + I5: 6 + B1: 2,5 + G1: 3,8 # C2: 7,9 => UNS
* INC D6: 4,5 + I5: 6 + B1: 2,5 + G1: 3,8 # G2: 7,9 => UNS
* INC D6: 4,5 + I5: 6 + B1: 2,5 + G1: 3,8 # B3: 2,7 => UNS
* INC D6: 4,5 + I5: 6 + B1: 2,5 + G1: 3,8 # B3: 1,9 => UNS
* INC D6: 4,5 + I5: 6 + B1: 2,5 + G1: 3,8 # I9: 3,7 => UNS
* PRF D6: 4,5 + I5: 6 + B1: 2,5 + G1: 3,8 # I9: 1 => SOL
* STA D6: 4,5 + I5: 6 + B1: 2,5 + G1: 3,8 + I9: 1
* CNT  22 HDP CHAINS /  22 HYP OPENED