Analysis of zz-menneske-no-06912919-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 9.....2...5..7.......4...6..2.8....7.9....14.4....9....18.52.........65...71..... initial

Autosolve

position: 9.....2...5..7.......4...6..2.8....7.9....14.4....9....18.52...2.9...6515.71..... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # H2: 3,9 => CTR => H2: 1,8
* DIS # H9: 3,9 => CTR => H9: 2,8
* DIS # B9: 4 => CTR => B9: 3,6
* DIS # D7: 9 => CTR => D7: 3,6
* DIS # B9: 3,4 => CTR => B9: 6
* DIS # D5: 3,7 => CTR => D5: 2,5,6
* CNT   6 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 # H2: 3,9 => CTR => H2: 1,8
* DIS H2: 1,8 # H9: 3,9 => CTR => H9: 2,8
* DIS H2: 1,8 + H9: 2,8 # H7: 7 => CTR => H7: 3,9
* DIS H2: 1,8 + H9: 2,8 + H7: 3,9 # G4: 5 => CTR => G4: 3,9
* DIS H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 # B9: 4 => CTR => B9: 3,6
* DIS H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 # A2: 8 => CTR => A2: 3,6
* DIS H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 + A2: 3,6 # B3: 7 => CTR => B3: 3,8
* DIS H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 + A2: 3,6 + B3: 3,8 # I1: 3,8 => CTR => I1: 5
* PRF H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 + A2: 3,6 + B3: 3,8 + I1: 5 => SOL
* STA H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 + A2: 3,6 + B3: 3,8 + I1: 5
* CNT   9 HDP CHAINS /  20 HYP OPENED

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

Details

Positions

9.....2...5..7.......4...6..2.8....7.9....14.4....9....18.52.........65...71..... initial
9.....2...5..7.......4...6..2.8....7.9....14.4....9....18.52...2.9...6515.71..... autosolve
984361275652978413731425869125846937896537142473219586318652794249783651567194328 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
D2: 2,9
E3: 2,9
A5: 7,8
B6: 7,8
H4: 3,9
A7: 3,6
B8: 3,4
D8: 3,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H1,H2: 1.. / H1 = 1  =>  0 pairs (X) / H2 = 1  =>  8 pairs (_)
C6,E6: 1.. / C6 = 1  => 14 pairs (_) / E6 = 1  =>  8 pairs (_)
C2,C3: 2.. / C2 = 2  => 15 pairs (_) / C3 = 2  =>  0 pairs (X)
D2,E3: 2.. / D2 = 2  =>  0 pairs (X) / E3 = 2  => 15 pairs (_)
H9,I9: 2.. / H9 = 2  =>  0 pairs (*) / I9 = 2  =>  0 pairs (X)
C2,D2: 2.. / C2 = 2  => 15 pairs (_) / D2 = 2  =>  0 pairs (X)
C3,E3: 2.. / C3 = 2  =>  0 pairs (X) / E3 = 2  => 15 pairs (_)
H6,H9: 2.. / H6 = 2  =>  8 pairs (_) / H9 = 2  =>  0 pairs (*)
C1,C2: 4.. / C1 = 4  =>  8 pairs (_) / C2 = 4  =>  0 pairs (X)
E4,F4: 4.. / E4 = 4  =>  9 pairs (_) / F4 = 4  =>  9 pairs (_)
B8,B9: 4.. / B8 = 4  => 11 pairs (_) / B9 = 4  =>  0 pairs (X)
G7,I7: 4.. / G7 = 4  =>  0 pairs (X) / I7 = 4  =>  8 pairs (_)
C1,I1: 4.. / C1 = 4  =>  8 pairs (_) / I1 = 4  =>  0 pairs (X)
G2,G7: 4.. / G2 = 4  =>  8 pairs (_) / G7 = 4  =>  0 pairs (X)
I5,I6: 6.. / I5 = 6  =>  0 pairs (X) / I6 = 6  =>  8 pairs (_)
A7,B9: 6.. / A7 = 6  =>  0 pairs (X) / B9 = 6  => 11 pairs (_)
A7,D7: 6.. / A7 = 6  =>  0 pairs (X) / D7 = 6  => 11 pairs (_)
B1,B9: 6.. / B1 = 6  =>  0 pairs (X) / B9 = 6  => 11 pairs (_)
H1,G3: 7.. / H1 = 7  => 11 pairs (_) / G3 = 7  =>  0 pairs (X)
A5,B6: 7.. / A5 = 7  => 11 pairs (_) / B6 = 7  => 16 pairs (_)
D8,F8: 7.. / D8 = 7  => 15 pairs (_) / F8 = 7  => 10 pairs (_)
G7,H7: 7.. / G7 = 7  => 11 pairs (_) / H7 = 7  =>  0 pairs (X)
B1,H1: 7.. / B1 = 7  =>  0 pairs (X) / H1 = 7  => 11 pairs (_)
B6,D6: 7.. / B6 = 7  => 16 pairs (_) / D6 = 7  => 11 pairs (_)
A3,A5: 7.. / A3 = 7  => 16 pairs (_) / A5 = 7  => 11 pairs (_)
F5,F8: 7.. / F5 = 7  => 15 pairs (_) / F8 = 7  => 10 pairs (_)
G3,G7: 7.. / G3 = 7  =>  0 pairs (X) / G7 = 7  => 11 pairs (_)
H1,H7: 7.. / H1 = 7  => 11 pairs (_) / H7 = 7  =>  0 pairs (X)
A5,B6: 8.. / A5 = 8  => 16 pairs (_) / B6 = 8  => 11 pairs (_)
E8,F8: 8.. / E8 = 8  =>  8 pairs (_) / F8 = 8  => 22 pairs (_)
A5,I5: 8.. / A5 = 8  => 16 pairs (_) / I5 = 8  => 11 pairs (_)
E1,E8: 8.. / E1 = 8  => 22 pairs (_) / E8 = 8  =>  8 pairs (_)
D2,E3: 9.. / D2 = 9  => 15 pairs (_) / E3 = 9  =>  0 pairs (X)
G4,H4: 9.. / G4 = 9  => 13 pairs (_) / H4 = 9  =>  9 pairs (_)
D7,E9: 9.. / D7 = 9  =>  0 pairs (X) / E9 = 9  => 15 pairs (_)
D2,D7: 9.. / D2 = 9  => 15 pairs (_) / D7 = 9  =>  0 pairs (X)
E3,E9: 9.. / E3 = 9  =>  0 pairs (X) / E9 = 9  => 15 pairs (_)
* DURATION: 0:00:55.239364  START: 07:03:29.372930  END: 07:04:24.612294 2017-05-01
* CP COUNT: (37)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A7,B6,B8,D2,D8,E3,H4)
* 9.....2...5..7.......4...6..2.8....7.9....14.4....9....18.52...2.9...6515.71.....
* PAIR A5: 7,8 COL A
A3: 7,8,1,3                              # reduction candidate for 7,8
A3: 1,3                                  # 15 pairs
A3: 7,8                                  #  9 pairs
* PAIR B6: 7,8 COL B
B1: 7,8,3,6                              # reduction candidate for 7,8
B1: 7,8                                  # 13 pairs
B3: 7,8,3                                # reduction candidate for 7,8
B3: 7,8                                  # 13 pairs
* PAIR H4: 3,9 BLK 6
G4: 3,9,5                                # reduction candidate for 3,9
G4: 3,9                                  # 13 pairs
G4: 5                                    #  9 pairs
* PAIR H4: 3,9 COL H
H2: 3,9,1,8                              # reduction candidate for 3,9
H2: 3,9 => CTR
* 97....21..5..7.8..83.4..76..2.8....779....14848.7.9.26318652479249387651567194382
H2: 1,8                                  #  9 pairs
H7: 3,9,7                                # reduction candidate for 3,9
H7: 3,9                                  # 11 pairs
H9: 3,9,2,8                              # reduction candidate for 3,9
H9: 3,9 => CTR
* 97.5..2...5.97.....3.42.76..2.84..9779....14848.7.9.26318652.7.249387651567194832
H9: 2,8                                  #  9 pairs
* PAIR A7: 3,6 BLK 7
B9: 3,6,4                                # reduction candidate for 3,6
B9: 4 => CTR
* 964...27..5.27641978.49..6..268....7.9...714.47...9...6189527342397..651547163...
B9: 3,6                                  # 11 pairs
* PAIR A7: 3,6 ROW 7
D7: 3,6,9                                # reduction candidate for 3,6
D7: 9 => CTR
* 964...27..5327641917249..6.3268...97795..3148481729...6189527342.9...6515.716....
D7: 3,6                                  # 15 pairs
* PAIR A7: 3,6 COL A
A2: 3,6,1,8                              # reduction candidate for 3,6
A2: 3,6                                  # 12 pairs
A4: 3,6,1                                # reduction candidate for 3,6
A4: 3,6                                  # 11 pairs
* PAIR B8: 3,4 BLK 7
B9: 3,4,6                                # reduction candidate for 3,4
B9: 3,4 => CTR
* 964...27.85327641917249..6.3268..597795..314.4.1..9...6189527342.9...6515.716.9..
B9: 6                                    # 11 pairs
* PAIR B8: 3,4 ROW 8
E8: 3,4,8                                # reduction candidate for 3,4
E8: 3,4                                  # 22 pairs
F8: 3,4,7,8                              # reduction candidate for 3,4
F8: 3,4                                  # 17 pairs
* PAIR D8: 3,7 BLK 8
F8: 3,7,4,8                              # reduction candidate for 3,7
F8: 4,8                                  # 18 pairs
F8: 3,7                                  # 11 pairs
* PAIR D8: 3,7 COL D
D5: 3,7,2,5,6                            # reduction candidate for 3,7
D5: 3,7 => CTR
* 9.45.127..5297.41.7.142..6.12.8....789....14247.219..6.18.527.42.9...6515.719..2.
D5: 2,5,6                                #  8 pairs
D6: 3,7,2,5,6                            # reduction candidate for 3,7
D6: 3,7                                  # 11 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-menneske-no-06912919-base-pr-000.dot
* REASONING
* DIS # H2: 3,9 => CTR => H2: 1,8
* DIS # H9: 3,9 => CTR => H9: 2,8
* DIS # B9: 4 => CTR => B9: 3,6
* DIS # D7: 9 => CTR => D7: 3,6
* DIS # B9: 3,4 => CTR => B9: 6
* DIS # D5: 3,7 => CTR => D5: 2,5,6
* CNT   6 HDP CHAINS /  26 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A7,B6,B8,D2,D8,E3,H4)
* 9.....2...5..7.......4...6..2.8....7.9....14.4....9....18.52...2.9...6515.71.....
* PAIR A5: 7,8 COL A
A3: 7,8,1,3                              # reduction candidate for 7,8
A3: 1,3                                  # 15 pairs
A3: 7,8                                  #  9 pairs
* PAIR B6: 7,8 COL B
B1: 7,8,3,6                              # reduction candidate for 7,8
B1: 7,8                                  # 13 pairs
B3: 7,8,3                                # reduction candidate for 7,8
B3: 7,8                                  # 13 pairs
* PAIR H4: 3,9 BLK 6
G4: 3,9,5                                # reduction candidate for 3,9
G4: 3,9                                  # 13 pairs
G4: 5                                    #  9 pairs
* PAIR H4: 3,9 COL H
H2: 3,9,1,8                              # reduction candidate for 3,9
H2: 3,9 => CTR
* 97....21..5..7.8..83.4..76..2.8....779....14848.7.9.26318652479249387651567194382
H7: 3,9,7                                # reduction candidate for 3,9
H7: 3,9                                  # 11 pairs
H9: 3,9,2,8                              # reduction candidate for 3,9
H9: 3,9 => CTR
* 97.5..2...5.97.....3.42.76..2.84..9779....14848.7.9.26318652.7.249387651567194832
* RESTART
* PAIR H4: 3,9 COL H
H7: 3,9,7                                # reduction candidate for 3,9
H7: 7 => CTR
* 97....2...5..7.....3.4..76..2.84..9779....14848.7.9.26318652.7.249387651567194382
* PAIR RESTART
* PAIR H4: 3,9 BLK 6
G4: 3,9,5                                # reduction candidate for 3,9
G4: 5 => CTR
* 964...27..5327641917249..6.32.8..59779....14848.7.93266189527342.93.7651537164982
* PAIR A7: 3,6 BLK 7
B9: 3,6,4                                # reduction candidate for 3,6
B9: 4 => CTR
* 964...27..5297641...142..6..2.8....7.9....14.4....9....18.527.42.9...6515.71.....
* PAIR A7: 3,6 COL A
A2: 3,6,8                                # reduction candidate for 3,6
A2: 8 => CTR
* 9.4.1827.85..7.41.17249.86.625841..7793.2.148481739526318.527.42493876515.71.4.82
* PAIR RESTART

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A3,A5,B1,B6,C4,C5,D1,D8,F2,F4,F8,G6,G9,H6,H9,I2)
* 9.4.6127.65297.41...142..6912.84.937.9..3.14.4.3.19..6318652794249.8.651567194...
* PAIR B1: 3,8 BLK 1
B3: 3,8,7                                # reduction candidate for 3,8
B3: 7 => CTR
* 93456127865297841387142356912.84.93779.23.145483.19..6318652794249.8.651567194...
* PAIR B1: 3,8 ROW 1
I1: 3,8,5                                # reduction candidate for 3,8
I1: 3,8 => CTR
* 9.456127.65297.41.7.142.56912.84.93789..3.1454732198.6318652794249.8.651567194...
I1: 5 => SOLVED
* 984361275652978413731425869125846937896537142473219586318652794249783651567194328
* DURATION: 0:00:22.498545  START: 07:04:45.316003  END: 07:05:07.814548 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-menneske-no-06912919-base-pr-001.dot
* REASONING
* DIS # H2: 3,9 => CTR => H2: 1,8
* DIS H2: 1,8 # H9: 3,9 => CTR => H9: 2,8
* DIS H2: 1,8 + H9: 2,8 # H7: 7 => CTR => H7: 3,9
* DIS H2: 1,8 + H9: 2,8 + H7: 3,9 # G4: 5 => CTR => G4: 3,9
* DIS H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 # B9: 4 => CTR => B9: 3,6
* DIS H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 # A2: 8 => CTR => A2: 3,6
* DIS H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 + A2: 3,6 # B3: 7 => CTR => B3: 3,8
* DIS H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 + A2: 3,6 + B3: 3,8 # I1: 3,8 => CTR => I1: 5
* PRF H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 + A2: 3,6 + B3: 3,8 + I1: 5 => SOL
* STA H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 + A2: 3,6 + B3: 3,8 + I1: 5
* CNT   9 HDP CHAINS /  20 HYP OPENED

Header Info

http://www.menneske.no/sudoku/utskrift.html?number=6912919
umulig

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

* PAIR REDUCTION ..
* ROUND 1: 9.....2...5..7.......4...6..2.8....7.9....14.4....9....18.52...2.9...6515.71.....
D2: 2,9
E3: 2,9
A5: 7,8
A3: 1,3,7,8                              # reduction candidate for 7,8
B6: 7,8
B1: 3,6,7,8                              # reduction candidate for 7,8
B3: 3,7,8                                # reduction candidate for 7,8
H4: 3,9
G4: 3,5,9                                # reduction candidate for 3,9
H2: 1,3,8,9                              # reduction candidate for 3,9
H2: 3,9 => CTR
* 97....21..5..7.8..83.4..76..2.8....779....14848.7.9.26318652479249387651567194382
H7: 3,7,9                                # reduction candidate for 3,9
H7: 7 => CTR
* 97.5..2...5.97.....3.42.76..2.84...779....14848.7.9.26318652.7.249387651567194..2
A7: 3,6
B9: 3,4,6                                # reduction candidate for 3,6
B9: 4 => CTR
* 964...27..5.27641978.49..6..268....7.9...714.47...9...6189527342397..651547163...
A2: 3,6,8                                # reduction candidate for 3,6
A2: 8 => CTR
* 9.4.1827.85..7.41.17.4..86..25841..7793...1484817395263186527942493876515671.4.82
D8: 3,7
* ROUND 2: 9.4.6127.65297.41...142..6912.84.937.9..3.14.4.3.19..6318652794249.8.651567194...
B1: 3,8
B3: 3,7,8                                # reduction candidate for 3,8
B3: 7 => CTR
* 93456127865297841387142356912.84.93779.23.145483.19..6318652794249.8.651567194...
I1: 3,5,8                                # reduction candidate for 3,8
I1: 3,8 => CTR
* 9.456127.65297.41.7.142.56912.84.93789..3.1454732198.6318652794249.8.651567194...
I1: 5 => SOLVED
* 984361275652978413731425869125846937896537142473219586318652794249783651567194328
* SOLVED!

Solution

position: 984361275652978413731425869125846937896537142473219586318652794249783651567194328 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 # A3: 7,8 => UNS
* INC # A3: 1,3 => UNS
* INC # B1: 7,8 => UNS
* INC # B3: 7,8 => UNS
* INC # G4: 3,9 => UNS
* INC # G4: 5 => UNS
* DIS # H2: 3,9 => CTR => H2: 1,8
* INC # H2: 1,8 => UNS
* INC # H7: 3,9 => UNS
* DIS # H9: 3,9 => CTR => H9: 2,8
* INC # H9: 2,8 => UNS
* INC # B9: 3,6 => UNS
* DIS # B9: 4 => CTR => B9: 3,6
* INC # D7: 3,6 => UNS
* DIS # D7: 9 => CTR => D7: 3,6
* INC # A2: 3,6 => UNS
* INC # A4: 3,6 => UNS
* DIS # B9: 3,4 => CTR => B9: 6
* INC # B9: 6 => UNS
* INC # E8: 3,4 => UNS
* INC # F8: 3,4 => UNS
* INC # F8: 3,7 => UNS
* INC # F8: 4,8 => UNS
* DIS # D5: 3,7 => CTR => D5: 2,5,6
* INC # D5: 2,5,6 => UNS
* INC # D6: 3,7 => UNS
* CNT  26 HDP CHAINS /  26 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A3: 7,8 => UNS
* INC # A3: 1,3 => UNS
* INC # B1: 7,8 => UNS
* INC # B3: 7,8 => UNS
* INC # G4: 3,9 => UNS
* INC # G4: 5 => UNS
* DIS # H2: 3,9 => CTR => H2: 1,8
* INC H2: 1,8 # H7: 3,9 => UNS
* DIS H2: 1,8 # H9: 3,9 => CTR => H9: 2,8
* INC H2: 1,8 + H9: 2,8 # H7: 3,9 => UNS
* DIS H2: 1,8 + H9: 2,8 # H7: 7 => CTR => H7: 3,9
* INC H2: 1,8 + H9: 2,8 + H7: 3,9 # G4: 3,9 => UNS
* DIS H2: 1,8 + H9: 2,8 + H7: 3,9 # G4: 5 => CTR => G4: 3,9
* INC H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 # B9: 3,6 => UNS
* DIS H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 # B9: 4 => CTR => B9: 3,6
* INC H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 # A2: 3,6 => UNS
* DIS H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 # A2: 8 => CTR => A2: 3,6
* INC H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 + A2: 3,6 # B3: 3,8 => UNS
* DIS H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 + A2: 3,6 # B3: 7 => CTR => B3: 3,8
* DIS H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 + A2: 3,6 + B3: 3,8 # I1: 3,8 => CTR => I1: 5
* PRF H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 + A2: 3,6 + B3: 3,8 + I1: 5 => SOL
* STA H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 + A2: 3,6 + B3: 3,8 + I1: 5
* CNT  21 HDP CHAINS /  20 HYP OPENED