Ask for patterns that they dont have puzzles 2

Everything about Sudoku that doesn't fit in one of the other sections

Re: Ask for patterns that they dont have puzzles 2

Postby JPF » Sat Mar 25, 2023 11:04 pm

I checked that your puzzles are not in my list, which is therefore incomplete.
So my count is also incorrect.
I will try to see where my mistake is.
Thank you for checking.

JPF
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Re: Ask for patterns that they dont have puzzles 2

Postby coloin » Sun Mar 26, 2023 5:10 pm

blue wrote:The correct number is 27*27 = 729.
-- 27 ways to choose two rows in different bands.
-- 27 ways to choose two columns in different stacks.

Indeed that is a better and correct way to look at it !
blue wrote:"More homework": find 3 more "frame + 2" puzzles.

I suspect enough energy has been burned with my randon generation approach !!
Hopefully thats the lot !
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Re: Ask for patterns that they dont have puzzles 2

Postby coloin » Sun Mar 26, 2023 5:16 pm

As a subset of the outside perimeter puzzles
we can easily find the middle frame plus 2 puzzles
Code: Select all
+---+---+---+
|...|...|...|
|.64|798|31.|
|.7.|...|.5.|
+---+---+---+
|.5.|...|.6.|
|.3.|...|.4.|
|.8.|...|.7.|
+---+---+---+
|.2.|...|.9.|
|.91|547|82.|
|...|...|...|
+---+---+---+

here are the 5 possible patterns, with over 300 puzzles
Code: Select all
..........6479831..7.....5..5.2...6..3..5..4..8.....7..2.....9..9154782..........       
..........1254679..9.....3..5.....8..3..9..25.7.....4..8.....7..2983761..........       
..........1345679..9.....2..8.....7..5..3.21..2.....3..6.....4..3172895..........       
..........1246579..5.....6..6.....59.4..7..1..3.....8..9.....4..7189652..........       
..........1245679..6.....4..5....97..4..2..3..9.....1..2.....5..3178946..........       
                                                                                       
                                                                                       
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+           
|...|...|...|   |...|...|...|   |...|...|...|   |...|...|...|   |...|...|...|           
|.64|798|31.|   |.12|546|79.|   |.13|456|79.|   |.12|465|79.|   |.12|456|79.|           
|.7.|...|.5.|   |.9.|...|.3.|   |.9.|...|.2.|   |.5.|...|.6.|   |.6.|...|.4.|           
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+           
|.5.|2..|.6.|   |.5.|...|.8.|   |.8.|...|.7.|   |.6.|...|.59|   |.5.|...|97.|           
|.3.|.5.|.4.|   |.3.|.9.|.25|   |.5.|.3.|21.|   |.4.|.7.|.1.|   |.4.|.2.|.3.|           
|.8.|...|.7.|   |.7.|...|.4.|   |.2.|...|.3.|   |.3.|...|.8.|   |.9.|...|.1.|           
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+           
|.2.|...|.9.|   |.8.|...|.7.|   |.6.|...|.4.|   |.9.|...|.4.|   |.2.|...|.5.|           
|.91|547|82.|   |.29|837|61.|   |.31|728|95.|   |.71|896|52.|   |.31|789|46.|           
|...|...|...|   |...|...|...|   |...|...|...|   |...|...|...|   |...|...|...|           
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+    28plus2

Serg's patterns have already shown tht one clue added to the outside frame and this middle frame is never enough.
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Re: Ask for patterns that they dont have puzzles 2

Postby coloin » Sun Mar 26, 2023 5:47 pm

And as a natural follow-up
these frames have an as yet unelucidated minima
Code: Select all
+---+---+---+       +---+---+---+       +---+---+---+       +---+---+---+       +---+---+---+       +---+---+---+     
|...|...|...|       |...|...|...|       |...|...|...|       |...|...|...|       |...|...|...|       |...|...|...|     
|.12|345|6..|       |.12|354|6..|       |...|...|...|       |...|...|...|       |...|...|...|       |...|...|...|     
|.4.|...|7..|       |.4.|...|5..|       |.61|234|5..|       |..1|234|5..|       |..1|234|...|       |...|123|...|     
+---+---+---+       +---+---+---+       +---+---+---+       +---+---+---+       +---+---+---+       +---+---+---+     
|.7.|...|8..|       |.6.|...|3..|       |.1.|...|6..|       |..6|...|4..|       |..2|..5|...|       |...|8.4|...|     
|.5.|...|9..|       |.7.|...|2..|       |.2.|...|8..|       |..5|...|3..|       |..3|..6|...|       |...|2.5|...|     
|.2.|...|1..|       |.5.|...|4..|       |.3.|...|4..|       |..2|...|1..|       |..8|..7|...|       |...|3.6|...|     
+---+---+---+       +---+---+---+       +---+---+---+       +---+---+---+       +---+---+---+       +---+---+---+     
|.9.|...|2..|       |.89|576|1..|       |.45|678|9..|       |..4|751|6..|       |..6|498|...|       |...|987|...|     
|.87|436|5..|       |...|...|...|       |...|...|...|       |...|...|...|       |...|...|...|       |...|...|...|     
|...|...|...| 7x6   |...|...|...| 6x6   |...|...|...| 6x5   |...|...|...| 5x5   |...|...|...| 5x4   |...|...|...|  5x3
+---+---+---+ 22    +---+---+---+ 20    +---+---+---+ 18    +---+---+---+ 16    +---+---+---+ 14    +---+---+---+  12
Last edited by coloin on Tue Mar 28, 2023 4:39 pm, edited 1 time in total.
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Re: Ask for patterns that they dont have puzzles 2

Postby coloin » Sun Mar 26, 2023 5:47 pm

Code: Select all
+---+---+---+                +---+---+---+         
|...|...|...|                |...|...|...|         
|.12|345|6..|                |.12|456|9..|         
|.6.|...|7..|                |.9.|...|4..|         
+---+---+---+                +---+---+---+         
|.2.|...|8..|                |.8.|...|6..|         
|.5.|.78|9..|                |.5.|.3.|2.1|         
|.4.|..9|1.2|                |.4.|...|3.5|         
+---+---+---+                +---+---+---+         
|.3.|...|28.|                |.6.|...|1.4|         
|.98|764|3..|                |.31|728|5..|         
|...|...|...|                |...|...|...|         
+---+---+---+   22plus5      +---+---+---+   22plus4
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Re: Ask for patterns that they dont have puzzles 2

Postby JPF » Sun Mar 26, 2023 8:10 pm

the "frame" could be:
Code: Select all
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+
|xxx|xxx|xxx|   |xxx|xxx|xx.|   |.xx|xxx|xx.|   |.xx|xxx|xxx|   |.xx|xxx|xx.|   |...|...|...|
|x..|...|..x|   |x..|...|.x.|   |.x.|...|.x.|   |.x.|...|..x|   |.x.|...|.x.|   |.xx|xxx|xx.|
|x..|...|..x|   |x..|...|.x.|   |.x.|...|.x.|   |.x.|...|..x|   |.x.|...|.x.|   |.x.|...|.x.|
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+
|x..|...|..x|   |x..|...|.x.|   |.x.|...|.x.|   |.x.|...|..x|   |.x.|...|.x.|   |.x.|...|.x.|
|x..|...|..x|   |x..|...|.x.|   |.x.|...|.x.|   |.x.|...|..x|   |.x.|...|.x.|   |.x.|...|.x.|
|x..|...|..x|   |x..|...|.x.|   |.x.|...|.x.|   |.x.|...|..x|   |.x.|...|.x.|   |.x.|...|.x.|
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+
|x..|...|..x|   |x..|...|.x.|   |.x.|...|.x.|   |.x.|...|..x|   |.x.|...|.x.|   |.x.|...|.x.|
|x..|...|..x|   |x..|...|.x.|   |.x.|...|.x.|   |.xx|xxx|xxx|   |.xx|xxx|xx.|   |.xx|xxx|xx.|
|xxx|xxx|xxx|   |xxx|xxx|xx.|   |.xx|xxx|xx.|   |...|...|...|   |...|...|...|   |...|...|...|
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+
9x9              9x8             9x7             8x8             8x7             7x7

JPF
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Re: Ask for patterns that they dont have puzzles 2

Postby coloin » Sun Mar 26, 2023 8:16 pm

indeed but they can all be a subset of the 9x9 .... remove one clue per row/column

in the 7x7 example above , it allows 2 clues per r/c to be removed and still be valid
Code: Select all
+---+---+---+     +---+---+---+      +---+---+---+
|654|798|321|     |6.4|798|3.1|      |...|...|...|
|1..|...|..8|     |...|...|...|      |.64|798|31.|
|7..|...|..5|     |7..|...|..5|      |.7.|...|.5.|
+---+---+---+     +---+---+---+      +---+---+---+
|5..|2..|..6|     |5..|2..|..6|      |.5.|2..|.6.|
|3..|.5.|..4|     |3..|.5.|..4|  ->  |.3.|.5.|.4.|
|8..|...|..7|     |8..|...|..7|      |.8.|...|.7.|
+---+---+---+     +---+---+---+      +---+---+---+
|2..|...|..9|     |2..|...|..9|      |.2.|...|.9.|
|4..|...|..3|     |...|...|...|      |.91|547|82.|
|931|547|862|     |9.1|547|8.2|      |...|...|...|
+---+---+---+     +---+---+---+      +---+---+---+

So these examples are possible
Code: Select all
|xxx|xxx|xxx|   |xxx|xxx|xx.|   |.xx|xxx|xx.|   |.xx|xxx|xxx|   |.xx|xxx|xx.|
|x..|...|..x|   |x..|...|.x.|   |.x.|...|.x.|   |.x.|...|..x|   |.x.|...|.x.|
|x..|...|..x|   |x..|...|.x.|   |.x.|...|.x.|   |.x.|...|..x|   |.x.|...|.x.|
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+
|x..|...|..x|   |x..|...|.x.|   |.x.|...|.x.|   |.x.|...|..x|   |.x.|...|.x.|
|x..|...|..x|   |x..|...|.x.|   |.x.|...|.x.|   |.x.|...|..x|   |.x.|...|.x.|
|x..|...|..x|   |x..|...|.x.|   |.x.|...|.x.|   |.x.|...|..x|   |.x.|...|.x.|
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+
|x..|...|..x|   |x..|...|.x.|   |.x.|...|.x.|   |.x.|...|..x|   |.x.|...|.x.|
|x..|...|..x|   |x..|...|.x.|   |.x.|...|.x.|   |.xx|xxx|xxx|   |.xx|xxx|xx.|
|xxx|xxx|xxx|   |xxx|xxx|xx.|   |.xx|xxx|xx.|   |...|...|...|   |...|...|...|
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+                                                                             
     9x9             9x8             9x7             8x8             8x7     
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+
|654|798|321|   |654|798|31.|   |.64|798|31.|   |.64|798|321|   |.64|798|31.|
|1..|...|..8|   |1..|...|.8.|   |.1.|...|.8.|   |.1.|...|..8|   |.1.|...|.8.|
|7..|...|..5|   |7..|...|.5.|   |.7.|...|.5.|   |.7.|...|..5|   |.7.|...|.5.|
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+
|5..|2..|..6|   |5..|2..|.6.|   |.5.|2..|.6.|   |.5.|2..|..6|   |.5.|2..|.6.|
|3..|.5.|..4|   |3..|.5.|.4.|   |.3.|.5.|.4.|   |.3.|.5.|..4|   |.3.|.5.|.4.|
|8..|...|..7|   |8..|...|.7.|   |.8.|...|.7.|   |.8.|...|..7|   |.8.|...|.7.|
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+
|2..|...|..9|   |2..|...|.9.|   |.2.|...|.9.|   |.2.|...|..9|   |.2.|...|.9.|
|4..|...|..3|   |4..|...|.3.|   |.4.|...|.3.|   |.91|547|862|   |.91|547|82.|
|931|547|862|   |931|547|82.|   |.91|547|82.|   |...|...|...|   |...|...|...|
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+
Last edited by coloin on Tue Mar 28, 2023 4:16 pm, edited 1 time in total.
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Re: Ask for patterns that they dont have puzzles 2

Postby JPF » Sun Mar 26, 2023 11:20 pm

just in case, one more:
Code: Select all
1234567896.......18.......35.......82...3...64.......23....2..47.......5956184237

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Re: Ask for patterns that they dont have puzzles 2

Postby blue » Mon Mar 27, 2023 4:15 am

coloin wrote:rect way to look at it !
blue wrote:"More homework": find 3 more "frame + 2" puzzles.

I suspect enough energy has been burned with my randon generation approach !!
Hopefully thats the lot !

That was my way of saying that I thought that at 97, you guys had found all but 3 of them.
Good work all around !
JPF has found #98. Nice !

Spoiler (homework hint):
Hidden Text: Show
If it's really true that only two remain, then they both have 2 clues in the center box.
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Re: Ask for patterns that they dont have puzzles 2

Postby JPF » Mon Mar 27, 2023 10:29 am

Here they are:
Code: Select all
+---+---+---+   +---+---+---+
|123|456|789|   |123|456|789|
|8..|...|..1|   |6..|...|..3|
|7..|...|..6|   |9..|...|..2|
+---+---+---+   +---+---+---+
|6..|3..|..8|   |4..|2..|..6|
|5..|.7.|..2|   |7..|.3.|..5|
|9..|...|..5|   |5..|...|..1|
+---+---+---+   +---+---+---+
|2..|...|..4|   |3..|...|..8|
|3..|...|..7|   |2..|...|..7|
|478|621|953|   |851|679|324|
+---+---+---+   +---+---+---+

Code: Select all
1234567898.......17.......66..3....85...7...29.......52.......43.......7478621953
1234567896.......39.......24..2....67...3...55.......13.......82.......7851679324

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Re: Ask for patterns that they dont have puzzles 2

Postby coloin » Tue Mar 28, 2023 4:34 pm

Great work , well found. It would have been a long time fishing for those last 2 !
We now have 100 9x9 frame plus 2 clues puzzles [ presumable the total by exhaustive search]
I wonder was it easier to scan the 3 patterns - or add 2 clues to all the 9x9 frames !!!!

Code: Select all
+---+---+---+              +---+---+---+              +---+---+---+
|...|...|...|              |...|...|...|              |...|...|...|         
|.12|345|6..|              |.12|456|9..|              |.12|435|6..|         
|.6.|...|7..|              |.9.|...|4..|              |.4.|6..|3..|         
+---+---+---+              +---+---+---+              +---+---+---+         
|.2.|...|8..|              |.8.|...|6..|              |.7.|...|58.|         
|.5.|.78|9..|              |.5.|.3.|2.1|              |.3.|.4.|2..|         
|.4.|..9|1.2|              |.4.|...|3.5|              |.2.|...|7..|         
+---+---+---+              +---+---+---+              +---+---+---+         
|.3.|...|28.|              |.6.|...|1.4|              |.5.|...|9..|         
|.98|764|3..|              |.31|728|5..|              |.63|187|4..|         
|...|...|...|              |...|...|...|              |...|...|...|         
+---+---+---+  22plus5     +---+---+---+  22plus4     +---+---+---+  22plus3  7x6 plus 3 [minimum]

It seems that 22 plus 2 clues [7x6] is impossibe
There is no 9x9 plus 2 which allows 4 clues to be removed from r1c89 and r9c89. [I found only one which allows 3 of the 4 clues to be removed]

Likewise the 7x7 case
Code: Select all
+---+---+---+      +---+---+---+                                         
|xx.|xxx|x..|      |123|456|7..|                                         
|x..|...|x..|      |9.8|...|2..|                                         
|x..|...|x..|      |4..|...|5..|                                         
+--.+---+---+      +---+---+---+                                         
|x..|...|x..|      |8..|...|6.1|                                         
|x..|...|x..|      |5..|7..|3..|                                         
|x..|...|x..|      |3..|...|8..|                                         
+---!---+---+      +---+---+---+                                         
|xx.|xxx|x..|      |795|128|4..|                                         
|...|...|...|      |...|.6.|...|                                         
|...|...|...|      |...|...|.7.|                                         
+---+---+---+      +---+---+---+   7x7A plus5 ....prob not minimum       
     7x7A                                                                 
                                                                         
                                                                         
+---+---+---+      +---+---+---+                                         
|...|...|...|      |...|...|...|                                         
|xxx|xxx|x..|      |182|435|6..|                                         
|x..|...|x..|      |4..|6..|3..|                                         
+---+---+---+      +---+---+---+                                         
|x..|...|x..|      |7..|...|58.|                                         
|x..|...|x..|      |3..|.4.|2..|                                         
|x..|...|x..|      |2..|...|7..|                                         
+---+---+---+      +---+---+---+                                         
|x..|...|x..|      |5..|...|9..|                                         
|xx|xxx|x..|       |693|187|4..|                                         
|...|...|...|      |...|...|...|                                         
+---+---+---       +---+---+---+    7x7B plus3 [minimum]                 
     7x7B                                                                 
                                                                         
                                                                         
+---+---+---+      +---+---+---+                                         
|...|...|...|      |...|...|...|                                         
|.xx|xxx|xx.|      |.12|435|6..|                                         
|.x.|...|.x.|      |.4.|6..|3..|                                         
+---+---+---+      +---+---+---+                                         
|.x.|...|.x.|      |.7.|...|58.|                                         
|.x.|...|.x.|      |.3.|.4.|2..|                                         
|.x.|...|.x.|      |.2.|...|7..|                                         
+---+---+---+      +---+---+---+                                         
|.x.|...|.x.|      |.5.|...|9..|                                         
|.xx|xxx|xx.|      |.63|187|4..|                                         
|...|...|...|      |...|...|...|                                         
+---+---+---+      +---+---+---+    7x7C plus2 [minimum]                 

Only the 7x7C is solvable with plus2 clues
coloin
 
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Joined: 05 May 2005
Location: Devon

Re: Ask for patterns that they dont have puzzles 2

Postby JPF » Tue Mar 28, 2023 6:17 pm

As a by-product of the previous study and if blue confirms it, the following pattern is invalid:
Code: Select all
+---+---+---+
|xxx|xxx|xxx|
|x..|...|..x|
|x..|...|..x|
+---+---+---+
|x..|...|..x|
|x..|xx.|..x|
|x..|...|..x|
+---+---+---+
|x..|...|..x|
|x..|...|..x|
|xxx|xxx|xxx|
+---+---+---+

It is even a maximum invalid pattern i.e. the addition of any clue makes it valid:
Code: Select all
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+
|123|456|789|   |123|456|789|   |123|456|789|   |123|456|789|
|5..|...|..2|   |9..|...|..6|   |4..|...|..6|   |8..|...|..2|
|8..|7..|..6|   |5..|..3|..2|   |8..|...|1.3|   |6..|...|..4|
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+
|7..|...|..5|   |7..|...|..3|   |6..|...|..7|   |4..|...|3.1|
|9..|52.|..4|   |6..|98.|..4|   |9..|38.|..4|   |9..|28.|..5|
|6..|...|..1|   |4..|...|..1|   |3..|...|..2|   |7..|...|..6|
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+
|4..|...|..8|   |2..|...|..7|   |7..|...|..1|   |2..|...|..8|
|2..|...|..3|   |3..|...|..8|   |2..|...|..5|   |5..|...|..3|
|359|861|247|   |861|327|495|   |594|167|238|   |386|529|147|
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+

Code: Select all
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+
|123|456|789|   |123|456|789|   |123|456|789|   |123|456|789|
|4..|...|..6|   |7..|...|..2|   |6..|...|..3|   |4..|...|..6|
|9..|...|..2|   |6..|...|..4|   |7..|...|..4|   |9..|...|..5|
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+
|5..|...|..4|   |4..|.7.|..6|   |4..|..7|..6|   |7..|...|..3|
|6..|21.|5.7|   |9..|24.|..7|   |9..|32.|..5|   |5..|174|..2|
|8..|...|..3|   |5..|...|..3|   |5..|...|..8|   |6..|...|..8|
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+
|7..|...|..1|   |2..|...|..1|   |8..|...|..7|   |3..|...|..7|
|2..|...|..5|   |3..|...|..8|   |2..|...|..1|   |8..|...|..4|
|316|597|428|   |876|321|495|   |316|978|542|   |246|738|591|
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+

JPF
JPF
2017 Supporter
 
Posts: 6122
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Location: Paris, France

Re: Ask for patterns that they dont have puzzles 2

Postby blue » Wed Mar 29, 2023 8:56 am

JPF wrote:As a by-product of the previous study and if blue confirms it, the following pattern is invalid:

Confirmed. (I had done an exhaustive search -- two, actually, using different methods)

It is even a maximum invalid pattern i.e. the addition of any clue makes it valid:

Amazing ! Nice work.
blue
 
Posts: 975
Joined: 11 March 2013

Re: Ask for patterns that they dont have puzzles 2

Postby blue » Wed Mar 29, 2023 9:07 am

For Colin:

Code: Select all
+---+---+---+
|714|356|2..|
|8..|...|7..|
|3..|...|5..|
+---+---+---+
|2..|4..|1.9|
|6..|...|3..|
|5..|...|4..|
+---+---+---+
|167|943|8..|
|...|...|...|
|...|2..|..7|
+---+---+---+   7x7A plus 4

One with an empty frame ...

Code: Select all
+---+---+---+
|391|682|5..|
|7..|...|9..|
|5..|...|8..|
+---+---+---+
|2..|...|45.|
|1..|...|7.9|
|8..|...|1..|
+---+---+---+
|672|415|3..|
|...|2..|...|
|...|.9.|...|
+---+---+---+   7x7A plus 4
blue
 
Posts: 975
Joined: 11 March 2013

Re: Ask for patterns that they dont have puzzles 2

Postby Serg » Wed Mar 29, 2023 10:50 pm

Congratulatons to JPF for finding new maximum invalid pattern! It was great to see so fast confirmation of this by blue! Could you biefly describe your method, blue?

Serg
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Location: Russia

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