Analysis of zz-menneske-no-06093043-base.sdk

Contents

Original Sudoku
Autosolve
Pair Reduction Variants
- Pair Reduction Analysis
- Pair Reduction
Details
Solution
Appendix: Full HDP Chains
- A1. Pair Reduction Analysis
- A2. Pair Reduction

Original Sudoku

level: medium

position: .6.....9...5.....78..4..2.6.....38...4.....3..8..2..1.7......63..65........96...4 initial

Autosolve

position: .6.....9...5.....78..4..256.....38...4.....3..8..2..1.7......63..653.......96...4 autosolve

Pair Reduction Variants

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # E2: 1,9 => CTR => E2: 8
* PRF # E2: 8 => SOL
* DIS # F2: 1,9 => CTR => F2: 2,6,8
* PRF # E3: 1,9 => SOL
* DIS # E3: 7 => CTR => E3: 1,9
* DIS # B3: 1,9 => CTR => B3: 3,7
* DIS # C3: 1,9 => CTR => C3: 3,7
* DIS # D1: 1,8 => CTR => D1: 2,3,7
* DIS # E1: 1,8 => CTR => E1: 5,7
* DIS # F1: 1,8 => CTR => F1: 2,5
* DIS # G6: 6,7 => CTR => G6: 4
* PRF # G6: 4 => SOL
* DIS # G6: 6 => CTR => G6: 4,7
* PRF # E4: 4,7 => SOL
* DIS # E4: 1,5,9 => CTR => E4: 4,7
* DIS # G6: 6,7 => CTR => G6: 4
* PRF # G6: 4 => SOL
* DIS # A6: 5,9 => CTR => A6: 3,6
* DIS # F6: 5,9 => CTR => F6: 4,6
* DIS # F8: 1,8 => CTR => F8: 2,4,7
* CNT  20 HDP CHAINS /  38 HYP OPENED

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

Pair Reduction

The following important HDP chains were detected:

* DIS # E2: 1,9 => CTR => E2: 8
* PRF E2: 8 => SOL
* STA E2: 8
* CNT   2 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

`.6.....9...5.....78..4..2.6.....38...4.....3..8..2..1.7......63..65........96...4`	initial
`.6.....9...5.....78..4..256.....38...4.....3..8..2..1.7......63..653.......96...4`	autosolve
`264375198915682347873491256652143879147859632389726415798214563426537981531968724`	solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
F3: 1,9
I1: 1,8
H2: 4,8
D6: 6,7
H4: 4,7
G5: 6,7
I6: 5,9
I8: 1,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
I1,I8: 1.. / I1 = 1  =>  0 pairs (X) / I8 = 1  =>  0 pairs (_)
I4,I5: 2.. / I4 = 2  =>  9 pairs (_) / I5 = 2  =>  9 pairs (_)
H8,H9: 2.. / H8 = 2  => 10 pairs (_) / H9 = 2  =>  9 pairs (_)
B3,C3: 3.. / B3 = 3  =>  0 pairs (X) / C3 = 3  =>  9 pairs (_)
D1,D2: 3.. / D1 = 3  => 10 pairs (_) / D2 = 3  => 10 pairs (_)
G1,G2: 3.. / G1 = 3  => 10 pairs (_) / G2 = 3  => 10 pairs (_)
A6,C6: 3.. / A6 = 3  =>  9 pairs (_) / C6 = 3  =>  0 pairs (X)
D1,G1: 3.. / D1 = 3  => 10 pairs (_) / G1 = 3  => 10 pairs (_)
D2,G2: 3.. / D2 = 3  => 10 pairs (_) / G2 = 3  => 10 pairs (_)
A6,A9: 3.. / A6 = 3  =>  9 pairs (_) / A9 = 3  =>  0 pairs (X)
B3,B9: 3.. / B3 = 3  =>  0 pairs (X) / B9 = 3  =>  9 pairs (_)
E4,F6: 4.. / E4 = 4  =>  0 pairs (*) / F6 = 4  =>  0 pairs (X)
H4,G6: 4.. / H4 = 4  =>  0 pairs (X) / G6 = 4  =>  0 pairs (_)
C7,A8: 4.. / C7 = 4  =>  0 pairs (X) / A8 = 4  =>  0 pairs (_)
E4,H4: 4.. / E4 = 4  =>  0 pairs (*) / H4 = 4  =>  0 pairs (X)
F6,G6: 4.. / F6 = 4  =>  0 pairs (X) / G6 = 4  =>  0 pairs (_)
A8,F8: 4.. / A8 = 4  =>  0 pairs (*) / F8 = 4  =>  0 pairs (X)
C1,C7: 4.. / C1 = 4  =>  0 pairs (*) / C7 = 4  =>  0 pairs (X)
E4,E7: 4.. / E4 = 4  =>  0 pairs (*) / E7 = 4  =>  0 pairs (X)
H2,H4: 4.. / H2 = 4  =>  0 pairs (*) / H4 = 4  =>  0 pairs (X)
E1,F1: 5.. / E1 = 5  =>  8 pairs (_) / F1 = 5  => 11 pairs (_)
G7,G9: 5.. / G7 = 5  => 13 pairs (_) / G9 = 5  =>  9 pairs (_)
B7,G7: 5.. / B7 = 5  =>  9 pairs (_) / G7 = 5  => 13 pairs (_)
D2,F2: 6.. / D2 = 6  => 13 pairs (_) / F2 = 6  =>  8 pairs (_)
G5,G6: 6.. / G5 = 6  =>  8 pairs (_) / G6 = 6  =>  0 pairs (X)
A4,D4: 6.. / A4 = 6  =>  9 pairs (_) / D4 = 6  => 10 pairs (_)
F8,F9: 7.. / F8 = 7  =>  0 pairs (*) / F9 = 7  =>  0 pairs (X)
B3,B4: 7.. / B3 = 7  =>  0 pairs (*) / B4 = 7  =>  0 pairs (X)
I1,H2: 8.. / I1 = 8  =>  0 pairs (*) / H2 = 8  =>  0 pairs (X)
C7,C9: 8.. / C7 = 8  =>  0 pairs (*) / C9 = 8  =>  0 pairs (X)
I1,I8: 8.. / I1 = 8  =>  0 pairs (*) / I8 = 8  =>  0 pairs (X)
G7,G8: 9.. / G7 = 9  => 10 pairs (_) / G8 = 9  => 10 pairs (_)
* DURATION: 0:00:45.258854  START: 06:30:57.189837  END: 06:31:42.448691 2017-05-01
* CP COUNT: (32)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D6,F3,G5,H2,H4,I1,I6,I8)
* .6.....9...5.....78..4..256.....38...4.....3..8..2..1.7......63..653.......96...4
* PAIR F3: 1,9 BLK 2
E2: 1,9,8                                # reduction candidate for 1,9
E2: 1,9 => CTR
* .6.....9...5.....78..47.256.7...384..4.....3..8..24.1.7...4..634.653.......96...4
E2: 8 => SOLVED
* 264375198915682347873491256652143879147859632389726415798214563426537981531968724
F2: 1,9,2,6,8                            # reduction candidate for 1,9
F2: 1,9 => CTR
* .6.352.98..568.3478..47.25667.1.38...4.8...3..8.72..1.7..2...63..653.......96...4
F2: 2,6,8                                #  8 pairs
E3: 1,9,7                                # reduction candidate for 1,9
E3: 1,9 => SOLVED
* 264375198915682347873491256652143879147859632389726415798214563426537981531968724
E3: 7 => CTR
* .6.....9...5.....78..47.256.7...384..4.....3..8..24.1.7...4..634.653.......96...4
* PAIR F3: 1,9 ROW 3
B3: 1,9,3,7                              # reduction candidate for 1,9
B3: 1,9 => CTR
* .6.....9...5.....78.347.256.7...384..4.....3.389.24.157...4..634.653.....3.96...4
B3: 3,7                                  #  9 pairs
C3: 1,9,3,7                              # reduction candidate for 1,9
C3: 1,9 => CTR
* .6.....9...5.....783.47.256.7...384..4.....3..8..24.1.7...4..634.653.......96...4
C3: 3,7                                  #  9 pairs
* PAIR F3: 1,9 COL F
F5: 1,9,5,6,8                            # reduction candidate for 1,9
F5: 1,9                                  # 10 pairs
F5: 5,6,8                                #  8 pairs
* PAIR I1: 1,8 ROW 1
D1: 1,8,2,3,7                            # reduction candidate for 1,8
D1: 1,8 => CTR
* .6..5239...53.6..78..47.256.7...384..4.....3..8..24.1.7..24..634.653.......96...4
D1: 2,3,7                                #  8 pairs
E1: 1,8,5,7                              # reduction candidate for 1,8
E1: 1,8 => CTR
* .67..5.9...5.....78..47.256.7...384..4.....3..8..24.1.7.4....63..653......896...4
E1: 5,7                                  #  9 pairs
F1: 1,8,2,5                              # reduction candidate for 1,8
F1: 1,8 => CTR
* .67.5..9...5.....78..47.256.7...384..4.....3..8..24.1.7.4....63..653......896...4
F1: 2,5                                  #  9 pairs
* PAIR D6: 6,7 BLK 5
D4: 6,7,1                                # reduction candidate for 6,7
D4: 6,7                                  # 10 pairs
D5: 6,7,1,8                              # reduction candidate for 6,7
D5: 6,7                                  # 10 pairs
* PAIR D6: 6,7 ROW 6
G6: 6,7,4                                # reduction candidate for 6,7
G6: 6,7 => CTR
* 264...391..53.64878..4..256.....384..4.....3..8..24.1.7..24..634.653...8...96...4
G6: 4 => SOLVED
* 264375198915682347873491256652143879147859632389726415798214563426537981531968724
* PAIR H4: 4,7 BLK 6
G6: 4,7,6                                # reduction candidate for 4,7
G6: 6 => CTR
* .64.75391..53.64878..4..256.....384..4..8.73..8.72461.7...4..634.653...8...96...4
G6: 4,7                                  #  8 pairs
* PAIR H4: 4,7 ROW 4
E4: 4,7,1,5,9                            # reduction candidate for 4,7
E4: 4,7 => SOLVED
* 264375198915682347873491256652143879147859632389726415798214563426537981531968724
E4: 1,5,9 => CTR
* 264...391..53.64878..4..256.....384..4.....3..8..24.1.7..24..634.653...8...96...4
* PAIR G5: 6,7 BLK 6
G6: 6,7,4                                # reduction candidate for 6,7
G6: 6,7 => CTR
* 264...391..53.64878..4..256.....384..4.....3..8..24.1.7..24..634.653...8...96...4
G6: 4 => SOLVED
* 264375198915682347873491256652143879147859632389726415798214563426537981531968724
* PAIR G5: 6,7 ROW 5
D5: 6,7,1,8                              # reduction candidate for 6,7
D5: 6,7                                  # 10 pairs
D5: 1,8                                  #  9 pairs
* PAIR I6: 5,9 BLK 6
I4: 5,9,2                                # reduction candidate for 5,9
I4: 5,9                                  #  9 pairs
I5: 5,9,2                                # reduction candidate for 5,9
I5: 5,9                                  #  9 pairs
* PAIR I6: 5,9 ROW 6
A6: 5,9,3,6                              # reduction candidate for 5,9
A6: 5,9 => CTR
* 264...391..53.64878374..256.7...384..4.....3..83.24.1.7..24..634.653...83..96...4
A6: 3,6                                  #  9 pairs
F6: 5,9,4,6                              # reduction candidate for 5,9
F6: 5,9 => CTR
* .6.3751989152863478734912566..14387..4.75863.3876294157..81..63..653..8153.96...4
F6: 4,6                                  # 10 pairs
* PAIR I8: 1,8 ROW 8
F8: 1,8,2,4,7                            # reduction candidate for 1,8
F8: 1,8 => CTR
* .64....989.5.8..478734912566..143875541879632387625419758214963496538721132967584
F8: 2,4,7                                #  9 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-menneske-no-06093043-base-pr-000.dot
* REASONING
* DIS # E2: 1,9 => CTR => E2: 8
* PRF # E2: 8 => SOL
* DIS # F2: 1,9 => CTR => F2: 2,6,8
* PRF # E3: 1,9 => SOL
* DIS # E3: 7 => CTR => E3: 1,9
* DIS # B3: 1,9 => CTR => B3: 3,7
* DIS # C3: 1,9 => CTR => C3: 3,7
* DIS # D1: 1,8 => CTR => D1: 2,3,7
* DIS # E1: 1,8 => CTR => E1: 5,7
* DIS # F1: 1,8 => CTR => F1: 2,5
* DIS # G6: 6,7 => CTR => G6: 4
* PRF # G6: 4 => SOL
* DIS # G6: 6 => CTR => G6: 4,7
* PRF # E4: 4,7 => SOL
* DIS # E4: 1,5,9 => CTR => E4: 4,7
* DIS # G6: 6,7 => CTR => G6: 4
* PRF # G6: 4 => SOL
* DIS # A6: 5,9 => CTR => A6: 3,6
* DIS # F6: 5,9 => CTR => F6: 4,6
* DIS # F8: 1,8 => CTR => F8: 2,4,7
* CNT  20 HDP CHAINS /  38 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D6,F3,G5,H2,H4,I1,I6,I8)
* .6.....9...5.....78..4..256.....38...4.....3..8..2..1.7......63..653.......96...4
* PAIR F3: 1,9 BLK 2
E2: 1,9,8                                # reduction candidate for 1,9
E2: 1,9 => CTR
* .6.....9...5.....78..47.256.7...384..4.....3..8..24.1.7...4..634.653.......96...4
E2: 8 => SOLVED
* 264375198915682347873491256652143879147859632389726415798214563426537981531968724
* DURATION: 0:00:02.038416  START: 06:32:12.610940  END: 06:32:14.649356 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-menneske-no-06093043-base-pr-001.dot
* REASONING
* DIS # E2: 1,9 => CTR => E2: 8
* PRF E2: 8 => SOL
* STA E2: 8
* CNT   2 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.menneske.no/sudoku/utskrift.html?number=6093043
umulig

* PAIR REDUCTION ..
* ROUND 1: .6.....9...5.....78..4..256.....38...4.....3..8..2..1.7......63..653.......96...4
F3: 1,9
E2: 1,8,9                                # reduction candidate for 1,9
E2: 1,9 => CTR
* .6.....9...5.....78..47.256.7...384..4.....3..8..24.1.7...4..634.653.......96...4
E2: 8 => SOLVED
* 264375198915682347873491256652143879147859632389726415798214563426537981531968724
* SOLVED!

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

G6 = 4

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

Solution

position: 264375198915682347873491256652143879147859632389726415798214563426537981531968724 solved

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 # E2: 1,9 => CTR => E2: 8
* PRF # E2: 8 => SOL
* DIS # F2: 1,9 => CTR => F2: 2,6,8
* INC # F2: 2,6,8 => UNS
* PRF # E3: 1,9 => SOL
* DIS # E3: 7 => CTR => E3: 1,9
* DIS # B3: 1,9 => CTR => B3: 3,7
* INC # B3: 3,7 => UNS
* DIS # C3: 1,9 => CTR => C3: 3,7
* INC # C3: 3,7 => UNS
* INC # F5: 1,9 => UNS
* INC # F5: 5,6,8 => UNS
* DIS # D1: 1,8 => CTR => D1: 2,3,7
* INC # D1: 2,3,7 => UNS
* DIS # E1: 1,8 => CTR => E1: 5,7
* INC # E1: 5,7 => UNS
* DIS # F1: 1,8 => CTR => F1: 2,5
* INC # F1: 2,5 => UNS
* INC # D4: 6,7 => UNS
* INC # D5: 6,7 => UNS
* DIS # G6: 6,7 => CTR => G6: 4
* PRF # G6: 4 => SOL
* INC # G6: 4,7 => UNS
* DIS # G6: 6 => CTR => G6: 4,7
* PRF # E4: 4,7 => SOL
* DIS # E4: 1,5,9 => CTR => E4: 4,7
* DIS # G6: 6,7 => CTR => G6: 4
* PRF # G6: 4 => SOL
* INC # D5: 6,7 => UNS
* INC # D5: 1,8 => UNS
* INC # I4: 5,9 => UNS
* INC # I5: 5,9 => UNS
* DIS # A6: 5,9 => CTR => A6: 3,6
* INC # A6: 3,6 => UNS
* DIS # F6: 5,9 => CTR => F6: 4,6
* INC # F6: 4,6 => UNS
* DIS # F8: 1,8 => CTR => F8: 2,4,7
* INC # F8: 2,4,7 => UNS
* CNT  38 HDP CHAINS /  38 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # E2: 1,9 => CTR => E2: 8
* PRF E2: 8 => SOL
* STA E2: 8
* CNT   2 HDP CHAINS /   1 HYP OPENED