Analysis of zz-google-000-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ....8.7.2.6..129......4..8.6.5.....4.9.......2..7..5.11.....6.9..25.....78....... initial

Autosolve

position: 419685732867312945523947186675...3.4391.5....2487..5.1154...6.99325...1.786....53 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # D9: 2,4 => SOL
* DIS # D9: 1 => CTR => D9: 2,4
* PRF # H5: 2,7 => SOL
* DIS # H5: 6 => CTR => H5: 2,7
* PRF # D9: 2,4 => SOL
* DIS # D9: 1 => CTR => D9: 2,4
* CNT   6 HDP CHAINS /   6 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* PRF # D9: 2,4 => SOL
* STA D9: 2,4
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

....8.7.2.6..129......4..8.6.5.....4.9.......2..7..5.11.....6.9..25.....78....... initial
419685732867312945523947186675...3.4391.5....2487..5.1154...6.99325...1.786....53 autosolve
419685732867312945523947186675128394391456278248739561154873629932564817786291453 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (22)
D4: 1,8
E4: 2,9
F4: 1,8
D5: 2,4
F5: 4,6
E6: 3,6
F6: 3,9
H4: 2,9
G5: 2,8
I5: 7,8
H6: 6,9
D7: 2,8
E7: 3,7
F7: 3,8
E8: 6,7
F8: 4,6
E9: 2,9
F9: 1,9
H7: 2,7
G8: 4,8
I8: 7,8
G9: 2,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D4,F4: 1.. / D4 = 1  =>  0 pairs (*) / F4 = 1  =>  0 pairs (X)
D9,F9: 1.. / D9 = 1  =>  0 pairs (X) / F9 = 1  =>  0 pairs (_)
D4,D9: 1.. / D4 = 1  =>  0 pairs (*) / D9 = 1  =>  0 pairs (X)
F4,F9: 1.. / F4 = 1  =>  0 pairs (X) / F9 = 1  =>  0 pairs (_)
E4,D5: 2.. / E4 = 2  =>  0 pairs (*) / D5 = 2  =>  0 pairs (X)
H7,G9: 2.. / H7 = 2  =>  0 pairs (*) / G9 = 2  =>  0 pairs (X)
E4,H4: 2.. / E4 = 2  =>  0 pairs (*) / H4 = 2  =>  0 pairs (X)
D7,H7: 2.. / D7 = 2  =>  0 pairs (X) / H7 = 2  =>  0 pairs (_)
E4,E9: 2.. / E4 = 2  =>  0 pairs (*) / E9 = 2  =>  0 pairs (X)
G5,G9: 2.. / G5 = 2  =>  0 pairs (*) / G9 = 2  =>  0 pairs (X)
E6,F6: 3.. / E6 = 3  =>  0 pairs (*) / F6 = 3  =>  0 pairs (X)
E7,F7: 3.. / E7 = 3  =>  0 pairs (X) / F7 = 3  =>  0 pairs (_)
E6,E7: 3.. / E6 = 3  =>  0 pairs (*) / E7 = 3  =>  0 pairs (X)
F6,F7: 3.. / F6 = 3  =>  0 pairs (X) / F7 = 3  =>  0 pairs (_)
D5,F5: 4.. / D5 = 4  =>  0 pairs (*) / F5 = 4  =>  0 pairs (X)
F8,D9: 4.. / F8 = 4  =>  0 pairs (*) / D9 = 4  =>  0 pairs (X)
G8,G9: 4.. / G8 = 4  =>  0 pairs (X) / G9 = 4  =>  0 pairs (_)
F8,G8: 4.. / F8 = 4  =>  0 pairs (*) / G8 = 4  =>  0 pairs (X)
D9,G9: 4.. / D9 = 4  =>  0 pairs (X) / G9 = 4  =>  0 pairs (_)
D5,D9: 4.. / D5 = 4  =>  0 pairs (*) / D9 = 4  =>  0 pairs (X)
F5,F8: 4.. / F5 = 4  =>  0 pairs (X) / F8 = 4  =>  0 pairs (_)
F5,E6: 6.. / F5 = 6  =>  0 pairs (*) / E6 = 6  =>  0 pairs (X)
H5,H6: 6.. / H5 = 6  =>  0 pairs (X) / H6 = 6  =>  0 pairs (_)
E8,F8: 6.. / E8 = 6  =>  0 pairs (*) / F8 = 6  =>  0 pairs (X)
F5,H5: 6.. / F5 = 6  =>  0 pairs (*) / H5 = 6  =>  0 pairs (X)
E6,H6: 6.. / E6 = 6  =>  0 pairs (X) / H6 = 6  =>  0 pairs (_)
E6,E8: 6.. / E6 = 6  =>  0 pairs (X) / E8 = 6  =>  0 pairs (_)
F5,F8: 6.. / F5 = 6  =>  0 pairs (*) / F8 = 6  =>  0 pairs (X)
H5,I5: 7.. / H5 = 7  =>  0 pairs (*) / I5 = 7  =>  0 pairs (X)
E7,E8: 7.. / E7 = 7  =>  0 pairs (*) / E8 = 7  =>  0 pairs (X)
H7,I8: 7.. / H7 = 7  =>  0 pairs (X) / I8 = 7  =>  0 pairs (_)
E7,H7: 7.. / E7 = 7  =>  0 pairs (*) / H7 = 7  =>  0 pairs (X)
E8,I8: 7.. / E8 = 7  =>  0 pairs (X) / I8 = 7  =>  0 pairs (_)
H5,H7: 7.. / H5 = 7  =>  0 pairs (*) / H7 = 7  =>  0 pairs (X)
I5,I8: 7.. / I5 = 7  =>  0 pairs (X) / I8 = 7  =>  0 pairs (_)
D4,F4: 8.. / D4 = 8  =>  0 pairs (X) / F4 = 8  =>  0 pairs (_)
G5,I5: 8.. / G5 = 8  =>  0 pairs (X) / I5 = 8  =>  0 pairs (_)
D7,F7: 8.. / D7 = 8  =>  0 pairs (*) / F7 = 8  =>  0 pairs (X)
G8,I8: 8.. / G8 = 8  =>  0 pairs (*) / I8 = 8  =>  0 pairs (X)
D4,D7: 8.. / D4 = 8  =>  0 pairs (X) / D7 = 8  =>  0 pairs (_)
F4,F7: 8.. / F4 = 8  =>  0 pairs (*) / F7 = 8  =>  0 pairs (X)
G5,G8: 8.. / G5 = 8  =>  0 pairs (X) / G8 = 8  =>  0 pairs (_)
I5,I8: 8.. / I5 = 8  =>  0 pairs (*) / I8 = 8  =>  0 pairs (X)
E4,F6: 9.. / E4 = 9  =>  0 pairs (X) / F6 = 9  =>  0 pairs (_)
H4,H6: 9.. / H4 = 9  =>  0 pairs (*) / H6 = 9  =>  0 pairs (X)
E9,F9: 9.. / E9 = 9  =>  0 pairs (*) / F9 = 9  =>  0 pairs (X)
E4,H4: 9.. / E4 = 9  =>  0 pairs (X) / H4 = 9  =>  0 pairs (_)
F6,H6: 9.. / F6 = 9  =>  0 pairs (*) / H6 = 9  =>  0 pairs (X)
E4,E9: 9.. / E4 = 9  =>  0 pairs (X) / E9 = 9  =>  0 pairs (_)
F6,F9: 9.. / F6 = 9  =>  0 pairs (*) / F9 = 9  =>  0 pairs (X)
* DURATION: 0:01:26.970310  START: 06:21:07.081017  END: 06:22:34.051327 2017-05-01
* CP COUNT: (50)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D4,D5,D7,E4,E6,E7,E8,E9,F4,F5,F6,F7,F8,F9,G5,G8,G9,H4,H6,H7,I5,I8)
* 419685732867312945523947186675...3.4391.5....2487..5.1154...6.99325...1.786....53
* PAIR D5: 2,4 COL D
D9: 2,4,1                                # reduction candidate for 2,4
D9: 2,4 => SOLVED
* 419685732867312945523947186675128394391456278248739561154873629932564817786291453
D9: 1 => CTR
* 419685732867312945523947186675...3.4391456...24873956115427.6.99325...1.786....53
* PAIR H7: 2,7 COL H
H5: 2,7,6                                # reduction candidate for 2,7
H5: 2,7 => SOLVED
* 419685732867312945523947186675128394391456278248739561154873629932564817786291453
H5: 6 => CTR
* 419685732867312945523947186675...3.4391.5..67248763591154.386799325764187864...53
* PAIR G9: 2,4 ROW 9
D9: 2,4,1                                # reduction candidate for 2,4
D9: 2,4 => SOLVED
* 419685732867312945523947186675128394391456278248739561154873629932564817786291453
D9: 1 => CTR
* 419685732867312945523947186675...3.4391456...24873956115427.6.99325...1.786....53
* INCONCLUSIVE
* SAVE PR GRAPH zz-google-000-base-pr-000.dot
* REASONING
* PRF # D9: 2,4 => SOL
* DIS # D9: 1 => CTR => D9: 2,4
* PRF # H5: 2,7 => SOL
* DIS # H5: 6 => CTR => H5: 2,7
* PRF # D9: 2,4 => SOL
* DIS # D9: 1 => CTR => D9: 2,4
* CNT   6 HDP CHAINS /   6 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D4,D5,D7,E4,E6,E7,E8,E9,F4,F5,F6,F7,F8,F9,G5,G8,G9,H4,H6,H7,I5,I8)
* 419685732867312945523947186675...3.4391.5....2487..5.1154...6.99325...1.786....53
* PAIR D5: 2,4 COL D
D9: 2,4,1                                # reduction candidate for 2,4
D9: 2,4 => SOLVED
* 419685732867312945523947186675128394391456278248739561154873629932564817786291453
* DURATION: 0:00:02.527109  START: 06:22:42.910942  END: 06:22:45.438051 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-google-000-base-pr-001.dot
* REASONING
* PRF # D9: 2,4 => SOL
* STA D9: 2,4
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

* PAIR REDUCTION ..
* ROUND 1: 419685732867312945523947186675...3.4391.5....2487..5.1154...6.99325...1.786....53
D4: 1,8
E4: 2,9
F4: 1,8
D5: 2,4
D9: 1,2,4                                # reduction candidate for 2,4
D9: 2,4 => SOLVED
* 419685732867312945523947186675128394391456278248739561154873629932564817786291453
* SOLVED!

--------------------------------------------------
--------------------------------------------------
Pairs
F5: 4,6
F8: 4,6
* DISABLE VALUE:: F6 != 6
* DISABLE VALUE:: F9 != 4
E4: 2,9
E9: 2,9
* DISABLE VALUE:: E6 != 9
* DISABLE VALUE:: E7 != 2
E4: 2,9
H4: 2,9
* DISABLE VALUE:: D4 != 2
* DISABLE VALUE:: F4 != 9

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

D5: 2,4
D9: 1,2,4
G9: 2,4
* DISABLE VALUE:: D9 != 1
=> D5,D9: 2,4
=> D5,G9: 2,4

* DISABLE VALUE:: D7 != 2
D7: 8                 # naked single
* DISABLE VALUE:: E9 != 2
E9: 9                 # naked single

* ANALYZE ..
* SOLVED!

F9: 1..               # hidden single
D9: 2..               # hidden single
H7: 2..               # hidden single
D4: 1..               # hidden single
E4: 2..               # hidden single
D4: 1                 # naked single
E4: 2                 # naked single
H7: 2                 # naked single
D9: 2                 # naked single
F9: 1                 # naked single
F4: 8..               # hidden single
F6: 9..               # hidden single
F8: 4..               # hidden single
I8: 7..               # hidden single
H4: 9..               # hidden single
E7: 7..               # hidden single
G9: 4..               # hidden single
D5: 4..               # hidden single
H5: 7..               # hidden single
F4: 8                 # naked single
H4: 9                 # naked single
D5: 4                 # naked single
H5: 7                 # naked single
F6: 9                 # naked single
E7: 7                 # naked single
F8: 4                 # naked single
I8: 7                 # naked single
G9: 4                 # naked single
E6: 3..               # hidden single
G5: 2..               # hidden single
H6: 6..               # hidden single
F7: 3..               # hidden single
E8: 6..               # hidden single
G8: 8..               # hidden single
F5: 6..               # hidden single
I5: 8..               # hidden single
F5: 6                 # naked single
G5: 2                 # naked single
I5: 8                 # naked single
E6: 3                 # naked single
H6: 6                 # naked single
F7: 3                 # naked single
E8: 6                 # naked single
G8: 8                 # naked single

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

|:step:| OOPS
--------------------------------------------------

Quad with common value: 2 # |:check:||:info:| this is wrong!
D5:   2,4
G5:   2,  8
D9: 1,2,4
G9:   2,4
=> D,G,5,9 is covered for value 2

D7: 2,8
H5: 2,6,7
E9: 2,9
* DISABLE VALUE:: D7 != 2
D7: 8                 # naked single
* DISABLE VALUE:: H5 != 2
* DISABLE VALUE:: E9 != 2
E9: 9                 # naked single

* ANALYZE ..
* SOLVED!

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

D9: 2..               # hidden single
H7: 2..               # hidden single
E4: 2..               # hidden single
E4: 2                 # naked single
H7: 2                 # naked single
D9: 2                 # naked single
F6: 9..               # hidden single
F9: 1..               # hidden single
F8: 4..               # hidden single
I8: 7..               # hidden single
H4: 9..               # hidden single
E7: 7..               # hidden single
G9: 4..               # hidden single
D4: 1..               # hidden single
D5: 4..               # hidden single
H5: 7..               # hidden single
D4: 1                 # naked single
H4: 9                 # naked single
D5: 4                 # naked single
H5: 7                 # naked single
F6: 9                 # naked single
E7: 7                 # naked single
F8: 4                 # naked single
I8: 7                 # naked single
F9: 1                 # naked single
G9: 4                 # naked single
E6: 3..               # hidden single
F4: 8..               # hidden single
G5: 2..               # hidden single
H6: 6..               # hidden single
F7: 3..               # hidden single
E8: 6..               # hidden single
G8: 8..               # hidden single
F5: 6..               # hidden single
I5: 8..               # hidden single
F4: 8                 # naked single
F5: 6                 # naked single
G5: 2                 # naked single
I5: 8                 # naked single
E6: 3                 # naked single
H6: 6                 # naked single
F7: 3                 # naked single
E8: 6                 # naked single
G8: 8                 # naked single

Solution

position: 419685732867312945523947186675128394391456278248739561154873629932564817786291453 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:

* PRF # D9: 2,4 => SOL
* DIS # D9: 1 => CTR => D9: 2,4
* PRF # H5: 2,7 => SOL
* DIS # H5: 6 => CTR => H5: 2,7
* PRF # D9: 2,4 => SOL
* DIS # D9: 1 => CTR => D9: 2,4
* CNT   6 HDP CHAINS /   6 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # D9: 2,4 => SOL
* STA D9: 2,4
* CNT   1 HDP CHAINS /   1 HYP OPENED