Analysis of zz-menneske-no-06912222-base.sdk

Contents

Sudoku from http://www.menneske.no/sudoku/utskrift.html?number=6912222

level: medium

Sudoku from http://www.menneske.no/sudoku/utskrift.html?number=6912222

position: .9..8......4...2.....4.2..7..81...69.........91...73..7..5.....13........2..9..1. initial

Autosolve

position: 29..8......4...2.....4.2..7..812..69.........912..73..7..5.....13.2......2..9..1. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C1: 1,3 => CTR => C1: 7
* DIS # C1: 1 => CTR => C1: 3,7
* PRF # D9: 6,8 => SOL
* DIS # H7: 4,8 => CTR => H7: 2,3,9
* DIS # G9: 4,8 => CTR => G9: 5,6,7
* DIS # G9: 5,6 => CTR => G9: 4,7,8
* 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 # C1: 1,3 => CTR => C1: 7
* PRF C1: 7 # D9: 6,8 => SOL
* STA C1: 7 + D9: 6,8
* CNT   2 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

.9..8......4...2.....4.2..7..81...69.........91...73..7..5.....13........2..9..1. initial
29..8......4...2.....4.2..7..812..69.........912..73..7..5.....13.2......2..9..1. autosolve
297385641864719235351462897578123469643958172912647358786531924139274586425896713 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
C3: 1,3
C5: 3,7
D6: 6,8
B7: 4,8
C7: 6,9
A9: 4,8
C9: 5,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C1,C3: 1.. / C1 = 1  =>  0 pairs (X) / C3 = 1  =>  7 pairs (_)
G5,I5: 1.. / G5 = 1  =>  7 pairs (_) / I5 = 1  =>  0 pairs (X)
E7,F7: 1.. / E7 = 1  =>  7 pairs (_) / F7 = 1  =>  7 pairs (_)
H5,I5: 2.. / H5 = 2  =>  0 pairs (X) / I5 = 2  =>  7 pairs (_)
H7,I7: 2.. / H7 = 2  =>  7 pairs (_) / I7 = 2  =>  0 pairs (X)
H5,H7: 2.. / H5 = 2  =>  0 pairs (X) / H7 = 2  =>  7 pairs (_)
I5,I7: 2.. / I5 = 2  =>  7 pairs (_) / I7 = 2  =>  0 pairs (X)
A4,F4: 3.. / A4 = 3  =>  0 pairs (X) / F4 = 3  => 10 pairs (_)
B7,A9: 4.. / B7 = 4  =>  6 pairs (_) / A9 = 4  =>  7 pairs (_)
C8,C9: 5.. / C8 = 5  =>  5 pairs (_) / C9 = 5  =>  7 pairs (_)
A5,B5: 6.. / A5 = 6  =>  7 pairs (_) / B5 = 6  =>  8 pairs (_)
D6,E6: 6.. / D6 = 6  => 10 pairs (_) / E6 = 6  =>  0 pairs (X)
C1,B2: 7.. / C1 = 7  =>  9 pairs (_) / B2 = 7  =>  0 pairs (X)
E8,D9: 7.. / E8 = 7  =>  0 pairs (*) / D9 = 7  =>  0 pairs (X)
C1,D1: 7.. / C1 = 7  =>  9 pairs (_) / D1 = 7  =>  0 pairs (X)
B4,G4: 7.. / B4 = 7  =>  0 pairs (*) / G4 = 7  =>  0 pairs (X)
D9,G9: 7.. / D9 = 7  =>  0 pairs (X) / G9 = 7  =>  0 pairs (_)
C1,C5: 7.. / C1 = 7  =>  9 pairs (_) / C5 = 7  =>  0 pairs (X)
E2,E8: 7.. / E2 = 7  =>  0 pairs (X) / E8 = 7  =>  0 pairs (_)
H5,H8: 7.. / H5 = 7  =>  0 pairs (*) / H8 = 7  =>  0 pairs (X)
B7,A9: 8.. / B7 = 8  =>  7 pairs (_) / A9 = 8  =>  6 pairs (_)
D2,F2: 9.. / D2 = 9  =>  8 pairs (_) / F2 = 9  =>  7 pairs (_)
G3,H3: 9.. / G3 = 9  => 10 pairs (_) / H3 = 9  =>  7 pairs (_)
D5,F5: 9.. / D5 = 9  =>  7 pairs (_) / F5 = 9  =>  8 pairs (_)
C7,C8: 9.. / C7 = 9  =>  7 pairs (_) / C8 = 9  =>  5 pairs (_)
D2,D5: 9.. / D2 = 9  =>  8 pairs (_) / D5 = 9  =>  7 pairs (_)
F2,F5: 9.. / F2 = 9  =>  7 pairs (_) / F5 = 9  =>  8 pairs (_)
* DURATION: 0:00:36.579537  START: 06:55:42.729737  END: 06:56:19.309274 2017-05-01
* CP COUNT: (27)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B7,C3,C5,C7,C9,D6)
* 29..8......4...2.....4.2..7..812..69.........912..73..7..5.....13.2......2..9..1.
* PAIR C3: 1,3 BLK 1
C1: 1,3,7                                # reduction candidate for 1,3
C1: 1,3 => CTR
* 29.78.....74...2.....4.2..7..812.769..7......912..73..7..5.....13.27.....2..9..1.
C1: 7                                    #  9 pairs
* PAIR C3: 1,3 ROW 3
E3: 1,3,5,6                              # reduction candidate for 1,3
E3: 5,6                                  #  8 pairs
E3: 1,3                                  #  8 pairs
* PAIR C5: 3,7 COL C
C1: 3,7,1                                # reduction candidate for 3,7
C1: 1 => CTR
* 29178.....74...2....34.2..7..812.769..7......912..73..7..5.....13.27.....2..9..1.
C1: 3,7                                  #  7 pairs
* PAIR D6: 6,8 COL D
D9: 6,8,3,7                              # reduction candidate for 6,8
D9: 6,8 => SOLVED
* 297385641864719235351462897578123469643958172912647358786531924139274586425896713
D9: 3,7                                  #  8 pairs
* PAIR B7: 4,8 ROW 7
F7: 4,8,1,3,6                            # reduction candidate for 4,8
F7: 4,8                                  # 11 pairs
G7: 4,8,6,9                              # reduction candidate for 4,8
G7: 4,8                                  #  8 pairs
H7: 4,8,2,3,9                            # reduction candidate for 4,8
H7: 4,8 => CTR
* 297.8......4.7.2....14.2.97..812..69..3....2.912..73..7..513..213.2...7..2.79..13
H7: 2,3,9                                #  7 pairs
I7: 4,8,2,3,6                            # reduction candidate for 4,8
I7: 4,8                                  # 11 pairs
* PAIR C7: 6,9 BLK 7
C8: 6,9,5                                # reduction candidate for 6,9
C8: 6,9                                  #  7 pairs
C8: 5                                    #  5 pairs
* PAIR C7: 6,9 ROW 7
G7: 6,9,4,8                              # reduction candidate for 6,9
G7: 6,9                                  #  8 pairs
G7: 4,8                                  #  8 pairs
* PAIR A9: 4,8 ROW 9
F9: 4,8,3,6                              # reduction candidate for 4,8
F9: 4,8                                  #  8 pairs
G9: 4,8,5,6,7                            # reduction candidate for 4,8
G9: 4,8 => CTR
* 297.8......4.7.2....1432..7..8123.69..3......912..73..7..51....13.2......2.79..13
G9: 5,6,7                                #  7 pairs
I9: 4,8,3,5,6                            # reduction candidate for 4,8
I9: 4,8                                  # 11 pairs
* PAIR C9: 5,6 BLK 7
C8: 5,6,9                                # reduction candidate for 5,6
C8: 5,6                                  #  7 pairs
C8: 9                                    #  5 pairs
* PAIR C9: 5,6 ROW 9
G9: 5,6,4,7,8                            # reduction candidate for 5,6
G9: 5,6 => CTR
* 297.8......4.7.2....1432..7..8123.69..3......912..73..7..51....13.2......2.79..13
G9: 4,7,8                                #  7 pairs
I9: 5,6,3,4,8                            # reduction candidate for 5,6
I9: 5,6                                  # 10 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-menneske-no-06912222-base-pr-000.dot
* REASONING
* DIS # C1: 1,3 => CTR => C1: 7
* DIS # C1: 1 => CTR => C1: 3,7
* PRF # D9: 6,8 => SOL
* DIS # H7: 4,8 => CTR => H7: 2,3,9
* DIS # G9: 4,8 => CTR => G9: 5,6,7
* DIS # G9: 5,6 => CTR => G9: 4,7,8
* CNT   6 HDP CHAINS /  26 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B7,C3,C5,C7,C9,D6)
* 29..8......4...2.....4.2..7..812..69.........912..73..7..5.....13.2......2..9..1.
* PAIR C3: 1,3 BLK 1
C1: 1,3,7                                # reduction candidate for 1,3
C1: 1,3 => CTR
* 29.78.....74...2.....4.2..7..812.769..7......912..73..7..5.....13.27.....2..9..1.
* PAIR D6: 6,8 COL D
D9: 6,8,3,7                              # reduction candidate for 6,8
D9: 6,8 => SOLVED
* 297385641864719235351462897578123469643958172912647358786531924139274586425896713
* DURATION: 0:00:04.153713  START: 06:56:37.946978  END: 06:56:42.100691 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-menneske-no-06912222-base-pr-001.dot
* REASONING
* DIS # C1: 1,3 => CTR => C1: 7
* PRF C1: 7 # D9: 6,8 => SOL
* STA C1: 7 + D9: 6,8
* CNT   2 HDP CHAINS /   2 HYP OPENED

Header Info

http://www.menneske.no/sudoku/utskrift.html?number=6912222
umulig

Solution

position: 297385641864719235351462897578123469643958172912647358786531924139274586425896713 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:

* DIS # C1: 1,3 => CTR => C1: 7
* INC # C1: 7 => UNS
* INC # E3: 1,3 => UNS
* INC # E3: 5,6 => UNS
* INC # C1: 3,7 => UNS
* DIS # C1: 1 => CTR => C1: 3,7
* PRF # D9: 6,8 => SOL
* INC # D9: 3,7 => UNS
* INC # F7: 4,8 => UNS
* INC # G7: 4,8 => UNS
* DIS # H7: 4,8 => CTR => H7: 2,3,9
* INC # H7: 2,3,9 => UNS
* INC # I7: 4,8 => UNS
* INC # C8: 6,9 => UNS
* INC # C8: 5 => UNS
* INC # G7: 6,9 => UNS
* INC # G7: 4,8 => UNS
* INC # F9: 4,8 => UNS
* DIS # G9: 4,8 => CTR => G9: 5,6,7
* INC # G9: 5,6,7 => UNS
* INC # I9: 4,8 => UNS
* INC # C8: 5,6 => UNS
* INC # C8: 9 => UNS
* DIS # G9: 5,6 => CTR => G9: 4,7,8
* INC # G9: 4,7,8 => UNS
* INC # I9: 5,6 => UNS
* CNT  26 HDP CHAINS /  26 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # C1: 1,3 => CTR => C1: 7
* PRF C1: 7 # D9: 6,8 => SOL
* STA C1: 7 + D9: 6,8
* CNT   2 HDP CHAINS /   2 HYP OPENED