Solving without pencilmarks

Advanced methods and approaches for solving Sudoku puzzles

Re: Solving without pencilmarks

Postby eleven » Wed Dec 25, 2013 11:36 pm

gearss wrote:Can Mr. RW solve the following puzzle step by step in detail? Please donot use the word like "easy to know".
If you can solve it without pencilmark, I beleive millions of player in the world must study your article as textbook.

it is out of question for me, that RW can solve this puzzle without pencilmarks. But why do you think, he should ? As i see it, it is just one of myriads uninteresting puzzles, which require a lot of time to solve manually, with or without pencilmarks. RW has already shown, that he is worth to be read by millions of players.
eleven
 
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Making easy puzzles harder

Postby Noumenon » Fri Sep 23, 2016 5:25 pm

I found a new constraint I impose on myself while solving without pencil marks. I only allow myself to fill in the grid while maintaining rotational symmetry. Here's what I do:

Stage 1 -- If the puzzle is one which contains some asymmetry, I must first only allow myself to bring the puzzle back to a symmetric state one asymmetric cell at a time. For example if there is a clue in r1c2 but not in r9c8, I must find r9c8. (Of course if there's another asymmetry in the puzzle, I have a choice on which to find first.) For example r2c2 and r8c8, or r5c1 and r5c9.
Finally I reach a state where every clue cell has its rotationally symmetric "antipode" filled; it's now a symmetric puzzle.

Stage 2 -- Next, I only allow myself to fill in two cells at a time, they must be proven and antipodes. There is one exception; the center square (which is its own antipode), if unfilled -- r5c5. Note I am not allowed to fill it until stage one is complete.

This makes many of the duller puzzles more fun and reveals much about their construction.
Noumenon
 
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Joined: 25 August 2010

Re: Solving without pencilmarks

Postby numpl_npm » Mon Sep 10, 2018 3:08 pm

gearss wrote:Postby gearss » Sat Dec 14, 2013 11:31 am
Code: Select all
 4 3 . | . . . | . 5 8
 1 . . | . 3 . | . 9 .
 6 7 . | . . 5 | 1 3 .
-------+-------+------
 . 1 . | 2 7 . | 9 8 .
 2 9 7 | . . . | 5 . 1
 8 4 6 | 5 9 1 | 3 2 7
-------+-------+------
 . . 1 | 6 . . | . 7 9
 9 2 . | . 8 . | . . 5
 7 6 . | . . . | . . 3



Code: Select all
 4 3 . | . . . | . 5 8
 1 . . | X 3 . | . 9 .
 6 7 A | A + 5 | 1 3 +
-------+-------+------
 . 1 . | 2 7 . | 9 8 .
 2 9 7 | B - B | 5 - 1
 8 4 6 | 5 9 1 | 3 2 7
-------+-------+------
 D D 1 | 6 E E | C 7 9
 9 2 . | . 8 . | o o 5
 7 6 . | . . . | C o 3


89 not in ++, so AA = 89.
38 not in --, so BB = 38.
28 not in ooo, so CC = 28.
4 not in DD, so 4 in EE and X=4.
numpl_npm
 
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Re: Solving without pencilmarks 2

Postby numpl_npm » Mon Sep 10, 2018 11:25 pm

gearss wrote:Postby gearss » Sat Dec 14, 2013 11:15 am
Puzzle 1
Code: Select all
*-----------*
|.2.|1.8|..5|
|1..|.76|.3.|
|7..|4..|...|
|---+---+---|
|..7|...|2..|
|48.|...|.59|
|..2|...|6..|
|---+---+---|
|...|..9|..1|
|.5.|74.|..6|
|6..|8.1|.7.|
*-----------*



This is a good example of the weakness of the npm method.
However, there is no problem at all.

Code: Select all
 . 2 X | 1 . 8 | 7 E 5
 1 . + | . 7 6 | . 3 .
 7 D + | 4 . . | . . .
-------+-------+-------
 . . 7 | . . . | 2 . B
 4 8 A | . . 7 | . 5 9
 . . 2 | . . . | 6 . 7
-------+-------+-------
 * 7 . | . . 9 | . . 1
 * 5 1 | 7 4 . | . . 6
 6 Y Z | 8 . 1 | . 7 .


++ = 58, ** = 28

Either A=3 or A=6, but in any case, X=4, Y=4, Z=9.
If A=3, then B=3, X=4, Y=4, Z=9.
If A=6, then D=6, E=6, X=4, Y=4, Z=9.
numpl_npm
 
Posts: 10
Joined: 10 September 2018

Re: Solving without pencilmarks 3

Postby numpl_npm » Thu Sep 13, 2018 1:12 am

gearss wrote:Postby gearss » Fri Dec 20, 2013 5:26 am
Code: Select all
*-----------*
|.59|3.6|427|
|...|..2|..3|
|2..|.9.|51.|
|---+---+---|
|7..|1..|.3.|
|3..|.6.|...|
|.6.|923|7.4|
|---+---+---|
|.87|63.|..2|
|9..|2..|...|
|612|4.9|37.|
*-----------*



The details of step by step solution are as follows.

Code: Select all
 . 5 9 | 3 . 6 | 4 2 7
 . . . | . . 2 | . . 3
 2 . A | . 9 . | 5 1 B
-------|-------|-------
 7 . . | 1 . . | . 3 .
 3 . . | . 6 . | . . .
 . 6 . | 9 2 3 | 7 . 4
-------|-------|-------
 X 8 7 | 6 3 . | . E 2
 9 . C | 2 . . | . D .
 6 1 2 | 4 . 9 | 3 7 .
 


Either A=6 or B=6, but in any case, X=5.
If A=6, then C=3, X=5.
If B=6, then D=6, E=4, X=5.

With basic techniques only, to next figure.

Code: Select all
 D 5 9 | 3 . 6 | 4 2 7
 4 7 . | . . 2 | . 9 3
 2 3 . | 7 9 4 | 5 1 E
-------|-------|-------
 7 . . | 1 4 C | . 3 .
 3 . 4 | . 6 7 | . A .
 . 6 . | 9 2 3 | 7 B 4
-------|-------|-------
 5 8 7 | 6 3 1 | 9 4 2
 9 4 3 | 2 7 . | . 6 .
 6 1 2 | 4 X 9 | 3 7 .
 


Either A=8 or B=8, but in any case, X=8.
If A=8, then C=8, X=8.
If B=8, then D=8, E=8, X=8.

With basic techniques only, the rest can be solved.
numpl_npm
 
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Joined: 10 September 2018

Re: Solving without pencilmarks 4

Postby numpl_npm » Sat Sep 15, 2018 1:55 am

gearss wrote:by gearss » Sat Dec 14, 2013 11:56 am
Code: Select all
 2 . 5 | 4 . . | 3 6 .
 . . 6 | . . 3 | . 4 2
 8 4 3 | 2 6 . | . 9 .
-------+-------+------
 5 6 . | . 4 2 | 7 1 3
 . 2 . | . 3 1 | 4 5 .
 1 3 4 | . 5 . | 2 8 .
-------+-------+------
 3 . . | . 2 6 | . 7 4
 4 . 2 | 1 . . | 6 3 .
 6 5 . | 3 . 4 | 9 2 .



Code: Select all
 2 . 5 | 4 . . | 3 6 .  Either A=5 or B=5.
 . . 6 | . . 3 | a 4 2  In any case, XY=57, so Z=1.
 8 4 3 | 2 6 X | Z 9 Y
-------+-------+------  If A=5, then a=5, so XY=57.
 5 6 . | . 4 2 | 7 1 3  If B=5, then XY=57.
 . 2 . | . 3 1 | 4 5 .
 1 3 4 | . 5 . | 2 8 .
-------+-------+------
 3 . . | A 2 6 | B 7 4
 4 . 2 | 1 . . | 6 3 .
 6 5 . | 3 . 4 | 9 2 .


Z is determined by X-wing.
However, even if Z is not found,
Another place determined by Z can be found.

Code: Select all
 2 . 5 | 4 . . | 3 6 .  Either A=5 or B=5.
 . . 6 | . . 3 | a 4 2  Then B=8 or B=5, thus X=1.
 8 4 3 | 2 6 . | . 9 . 
-------+-------+------  If A=5, then a=5, B=8.
 5 6 . | . 4 2 | 7 1 3
 . 2 . | . 3 1 | 4 5 .
 1 3 4 | . 5 . | 2 8 .
-------+-------+------
 3 . . | A 2 6 | B 7 4
 4 . 2 | 1 . a | 6 3 .
 6 5 . | 3 . 4 | 9 2 X
numpl_npm
 
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Solve Unsolveable #313 with no pencil marks - 1

Postby numpl_npm » Mon Sep 17, 2018 12:23 pm

Unsolveable #313 ( For details, see the following site. )
http://www.sudokuwiki.org/Weekly_Sudoku.asp?puz=313

With basic techniques, to next figure.

Code: Select all
 9 8 . | 7 . . | 6 . . 
 7 5 . | . . . | . 8 . 
 . . 6 | . . . | . . . 
-------|-------|-------
 . 4 . | . 3 . | . . . 
 . . 7 | 8 . . | . 5 . 
 . . . | . . . | 4 . . 
-------|-------|-------
 . . 9 | 6 . . | . 7 . 
 . 7 8 | 4 5 . | . 6 . 
 . . . | . 7 2 | 8 . 1 
-------|-------|-------
 


Code: Select all
 9 8 . | 7 . . | 6 . .  Either A=4, B=4 or C=4.
 7 5 . | . . . | . 8 .  In any case, X=6.
 . . 6 | . . . | . . . 
-------|-------|------- If A=4, then B=5, X=6.
 . 4 . | . 3 . | . . .  If B=4, then A=5, X=6.
 . . 7 | 8 . . | . 5 . 
 . . . | . . . | 4 . . 
-------|-------|-------
 . . 9 | 6 . . | . 7 . 
 . 7 8 | 4 5 . | . 6 . 
 A X B | . 7 2 | 8 C 1 
-------|-------|-------
 


If C=4, to next figure with basic techniques.

Code: Select all
 9 8 . | 7 . . | 6 . . 
 7 5 . | . . . | . 8 . 
 . . 6 | . . . | . . . 
-------|-------|-------
 . 4 . | . 3 . | . . . 
 . . 7 | 8 . . | . 5 . 
 . . . | . . . | 4 . . 
-------|-------|-------
 4 . 9 | 6 . . | . 7 . 
 . 7 8 | 4 5 . | . 6 . 
 . . . | 9 7 2 | 8 4 1 
-------|-------|-------


Code: Select all
 9 8 . | 7 . . | 6 Y .  Y<>3
 7 5 . | X c c | . 8 .  ab = XY
 a b 6 | . . . | . A . 
-------|-------|------- Because
 . 4 d | e 3 . | . B .  If 3 in ab, then
 . . 7 | 8 . . | . 5 .    X=3,
 . . d | e . . | 4 C .    Let y which is not 3 of ab, then
-------|-------|-------   y in dd and y in ee, so y not in BC, Y=y.
 4 . 9 | 6 . . | . 7 .  If 3 not in ab, then
 . 7 8 | 4 5 . | . 6 .    If X=a, Y=b.
 . . . | 9 7 2 | 8 4 1    If a in ee, Y=a, b in BC, X=b.
-------|-------|-------


Code: Select all
 9 8 . | 7 . . | 6 Y .  Y<>3
 7 5 . | X c c | . 8 .  ab = XY
 a b 6 | . . . | . A . 
-------|-------|------- Either A=3 or C=3.
 . 4 . | . 3 . | . B .  In any case, X=3.
 . . 7 | 8 . . | . 5 . 
 . . . | . . . | 4 C .  If 3 in ab, then X=3.
-------|-------|------- If 3 not in ab, then
 4 . 9 | 6 . . | . 7 .    cc = 6Y, YBC = ab9,
 . 7 8 | 4 5 . | . 6 .    so A=3, X=3.
 . . . | 9 7 2 | 8 4 1 
-------|-------|-------


Code: Select all
 9 8 . | 7 . . | 6 Y .  Y<>3
 7 5 . | 3 . . | . 8 .  ab = 3Y
 a b 6 | . . . | . . . 
-------|-------|------- Then, c=3, d=3, e=5, X=6
 . 4 . | . 3 . | . . . 
 . . 7 | 8 . . | . 5 . 
 . . . | . . . | 4 c . 
-------|-------|-------
 4 . 9 | 6 . . | . 7 . 
 . 7 8 | 4 5 . | . 6 . 
 e X d | 9 7 2 | 8 4 1 
-------|-------|-------
numpl_npm
 
Posts: 10
Joined: 10 September 2018

Solve Unsolveable #313 with no pencil marks - 2

Postby numpl_npm » Tue Sep 18, 2018 12:44 am

Unsolveable #313 ( For details, see the following site. )
http://www.sudokuwiki.org/Weekly_Sudoku.asp?puz=313

Following the previous post.

Code: Select all
 9 8 . | 7 . . | 6 . .  6 is found.
 7 5 . | . . . | . 8 . 
 . . 6 | . . . | . . . 
-------|-------|-------
 . 4 . | . 3 . | . . . 
 . . 7 | 8 . . | . 5 . 
 . . . | . . . | 4 . . 
-------|-------|-------
 . . 9 | 6 . . | . 7 . 
 . 7 8 | 4 5 . | . 6 . 
 . 6 . | . 7 2 | 8 . 1 
-------|-------|-------
 


Code: Select all
 9 8 . | 7 . . | 6 . .  Either
 7 5 . | . . . | . 8 .    A=4 or A<>4 and
 . . 6 | . . . | . . .    B=3 or B=9.
-------|-------|-------
 . 4 . | . 3 . | . . .  In any case, X=4.
 . . 7 | 8 . . | . 5 . 
 . . . | . . . | 4 . .  If A=4, then X=4.
-------|-------|------- If B=3, then a=9, X=4.
 . . 9 | 6 . . | . 7 X 
 . 7 8 | 4 5 . | . 6 . 
 . 6 A | B 7 2 | 8 a 1 
-------|-------|-------
 


If A<>4 and B=9, to next figure.

Code: Select all
 9 8 . | 7 . . | 6 . .  Z<>4
 7 5 . | . . . | . 8 . 
 . . 6 | . . . | . . . 
-------|-------|-------
 . 4 . | . 3 . | . . . 
 . . 7 | 8 . . | . 5 . 
 . . . | . . . | 4 . . 
-------|-------|-------
 . . 9 | 6 . . | . 7 . 
 . 7 8 | 4 5 . | . 6 . 
 . 6 Z | 9 7 2 | 8 . 1 
-------|-------|-------
 


Code: Select all
 9 8 . | 7 . . | 6 . .  Z<>4
 7 5 . | . . . | . 8 . 
 A B 6 | . . . | . . .  Either 3 in AB or 3 not in AB.
-------|-------|------- In any case, X=4.
 . 4 . | . 3 . | . . . 
 . . 7 | 8 . . | . 5 . 
 . . . | . . . | 4 . . 
-------|-------|-------
 . . 9 | 6 . . | . 7 X 
 . 7 8 | 4 5 . | . 6 . 
 . 6 Z | 9 7 2 | 8 . 1 
-------|-------|-------
 


Code: Select all
 9 8 . | 7 e f | 6 E F  Z<>4
 7 5 . | C D D | . 8 . 
 A B 6 | g H H | . . .  If 3 in AB, then
-------|-------|-------   C=3,
 . 4 b | c 3 . | . d .    Let a which is not 3 of AB,
 . . 7 | 8 . . | . 5 .    a in bb and a in cc, so a not in dd,
 . . b | c . . | 4 d .    E=a, F=3, f=5, DD=6a, HH=89, e=4,
-------|-------|-------   g is not a of 12,
 . . 9 | 6 . . | . 7 X    EddY = ABg9 = 3ag9, Y=3, X=4.
 . 7 8 | 4 5 . | . 6 . 
 . 6 Z | 9 7 2 | 8 Y 1 
-------|-------|-------
 


Code: Select all
 9 8 . | 7 . . | 6 b .  Z<>4
 7 5 . | a D D | . 8 . 
 A B 6 | C . . | . . .  If 3 not in AB, then
-------|-------|-------   ab = AB,
 . 4 . | . 3 . | . c .    C=3, DD =6b, bccY = AB39,
 . . 7 | 8 . . | . 5 .    Y=3, X=4.
 . . . | . . . | 4 c . 
-------|-------|-------
 . . 9 | 6 . . | . 7 X 
 . 7 8 | 4 5 . | . 6 . 
 . 6 Z | 9 7 2 | 8 Y 1 
-------|-------|-------
 
numpl_npm
 
Posts: 10
Joined: 10 September 2018

Solve Unsolveable #313 with no pencil marks - 3

Postby numpl_npm » Wed Sep 19, 2018 1:17 pm

Unsolveable #313 ( For details, see the following site. )
http://www.sudokuwiki.org/Weekly_Sudoku.asp?puz=313

Following the previous post.

Code: Select all
 9 8 . | 7 . . | 6 . .  4 is found.
 7 5 . | . . . | . 8 .  And X=5.
 . . 6 | . . . | . . . 
-------|-------|-------
 . 4 . | . 3 . | . . . 
 . . 7 | 8 . . | . 5 . 
 . . . | . . . | 4 . . 
-------|-------|-------
 . . 9 | 6 . . | X 7 4 
 . 7 8 | 4 5 . | . 6 . 
 . 6 . | . 7 2 | 8 . 1 
-------|-------|-------
 


Code: Select all
 9 8 . | 7 . X | 6 b d  In any case,
 7 5 . | a c c | . 8 .    AB = ab, cc = 6b,
 A B 6 | . . . | . . .    acc = AB6 = 6bd, X=5
-------|-------|-------
 . 4 . | . 3 . | . . . 
 . . 7 | 8 . . | . 5 . 
 . . . | . . . | 4 . . 
-------|-------|-------
 . . 9 | 6 . . | 5 7 4 
 . 7 8 | 4 5 . | . 6 . 
 . 6 . | . 7 2 | 8 . 1 
-------|-------|-------
 


Code: Select all
 9 8 . | 7 . . | 6 b .  If A=4, then b=4 and
 7 5 . | a . . | . 8 .    a=B. Because
 A B 6 | . . . | . . .      If B in 12, then
-------|-------|-------       B in ee, B in cc, B not in dd, a=B.
 . 4 c | d 3 . | . e .      If B =3, then
 . . 7 | 8 . . | . 5 .        B in cc, B not in ee, g=B, a=B.
 . . c | d . . | 4 e . 
-------|-------|------- If A=3, then ab=AB.
 . . 9 | 6 . . | 5 7 4    Because B in 12 and
 . 7 8 | 4 5 . | . 6 .    If a=B, then
 . 6 . | f 7 2 | 8 g 1      f=A, A in cc, A not in ee, b=A.
-------|-------|-------   If a<>B, then
                             B in dd, B in cc, B not in ee,
                             b=B, g=A, a=A.
 


Code: Select all
 9 8 . | 7 . . | 6 b .  If A in 12, then ab=AB.
 7 5 . | a . . | . 8 .  Because
 A B 6 | . . . | . . . 
-------|-------|------- If a=A, then
 . 4 c | d 3 . | . e .    B in dd, B in cc, B not in ee, b=B.
 . . 7 | 8 . . | . 5 . 
 . . c | d . . | 4 e .  If a<>A, then
-------|-------|-------   A in dd, A in cc, A not in ee, b=A,
 . . 9 | 6 . . | 5 7 4    B in ee, B in cc, B not in dd, a=B.
 . 7 8 | 4 5 . | . 6 .   
 . 6 . | f 7 2 | 8 g 1 
-------|-------|-------
 
numpl_npm
 
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Joined: 10 September 2018

Solve Unsolveable #313 with no pencil marks - 4

Postby numpl_npm » Wed Sep 19, 2018 1:48 pm

Unsolveable #313 ( For details, see the following site. )
http://www.sudokuwiki.org/Weekly_Sudoku.asp?puz=313

This puzzle can be solved with one Exocet technique ( See http://www.sudokuwiki.org/Exocet ).
numpl_npm
 
Posts: 10
Joined: 10 September 2018

Solve WU#314 with no pencil marks

Postby numpl_npm » Mon Sep 24, 2018 3:18 am

Unsolveable #314 ( For details, see the following site. )
http://www.sudokuwiki.org/Weekly_Sudoku.asp?puz=314
Code: Select all
A   9 8 . | 7 6 . | 5 . . 
B   7 . . | . 5 . | . 9 . 
C   . . . | . . 9 | . . 8 
   -------+-------+------ 
D   5 9 . | . . 6 | . 8 . 
E   . . 4 | . 7 . | . . . 
F   . . . | 3 . . | . . 5 
   -------+-------+*------ 
G   4 6 . | . . 7 | . 5 . 
H   . . . | . 1 . | . . 4 
J   . . . | . . . | 2 . . 

    1 2 3   4 5 6   7 8 9

Cenoman wrote:Postby Cenoman » Sunday 23-Sep-2018

WU#314 has a band exocet (1234)C45, A8, B2
* 4 cannot be a true base digit, as it false in both "mirror nodes" (A79, B13) ...
-4A8, -B2 (4 is also eliminated from the target cells which can contain only true base digits)

Code: Select all
 9 8 . | 7 6 . | 5 Y .  Let y which is not 4 in AA.
 7 X . | . 5 . | . 9 .    If 4 in AA, then X=4, Y=4.
 . . . | A A 9 | . . 8    But y<>123, so 4 not in AB.

 5 9 . | u u 6 | s 8 s  y<>1, y<>3 <-- y in ss and y in tt.
 . . 4 | . 7 . | . . .  y<>2 <-- y in uu and y in vv.
 . . . | 3 . . | . . 5 

 4 6 . | v v 7 | t 5 t 
 . . . | . 1 . | . . 4 
 . . . | . . . | 2 . . 

Code: Select all
 9 8 . | 7 6 . | 5 Y .  Let y which is not 4 in AA,
 7 X . | . 5 . | . 9 .    If 4 in X, then Y=y. So 4 not in X.
 . . . | A A 9 | . . 8    If 4 in Y, then X=y. So 4 not in Y.

 5 9 v | u u 6 | s 8 s  If 4 in X, then ...
 . . 4 | . 7 . | . . .    If y in 13, then y in ss and y in tt.
 . . . | 3 . . | . . 5    If y in 2, then y in ss.

 4 6 v | . . 7 | t 5 t  If 4 in Y, then ...
 . . . | . 1 . | . . 4    If y in 13, then y in vv.
 . . . | . . . | 2 . .    If y in 2, then y in vv.
numpl_npm
 
Posts: 10
Joined: 10 September 2018

Solve WU#314 with no pencil marks - 2

Postby numpl_npm » Mon Sep 24, 2018 12:12 pm

Unsolveable #314 ( For details, see the following site. )
http://www.sudokuwiki.org/Weekly_Sudoku.asp?puz=314
Code: Select all
A   9 8 . | 7 6 4 | 5 . . 
B   7 . . | . 5 . | . 9 . 
C   . 4 5 | . . 9 | . . 8 
   -------+-------+------ 
D   5 9 . | . . 6 | . 8 . 
E   . . 4 | . 7 . | . . . 
F   . . . | 3 . . | . . 5 
   -------+-------+------ 
G   4 6 . | . . 7 | . 5 . 
H   . . . | . 1 . | . . 4 
J   . . . | . . . | 2 . . 

    1 2 3   4 5 6   7 8 9

Cenoman wrote:Postby Cenoman » Sunday 23-Sep-2018

WU#314 has a band exocet (1234)C45, A8, B2

1. Eliminations from the exocet pattern: ...
** 6 is eliminated from B3 as non-base digit in the second cell of a mirror node
(first cell already locked with a non-base digit 7B1) => -6B3

Code: Select all
 9 8 . | 7 6 4 | 5 Y y  If X=a, then Y=b, y=a, x=b.
 7 X x | . 5 . | . 9 . 
 . 4 . | a b 9 | . . 8  If Y=a, then
-------+-------+------    either b not in ss or b not in tt,
 5 9 u | . . 6 | s 8 s    so b in uu, and X=b, x=a, y=b.
 . . 4 | . 7 . | . . . 
 . . . | 3 . . | . . 5  And either X=a or X=b.
-------+-------+------  Xx=ab=Yy.
 4 6 u | . . 7 | t 5 t 
 . . . | . 1 . | . . 4 
 . . . | . . . | 2 . . 
numpl_npm
 
Posts: 10
Joined: 10 September 2018

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