Ask for patterns that they dont have puzzles 2

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Re: Ask for patterns that they dont have puzzles 2

Postby coloin » Thu Aug 28, 2014 10:24 pm

revisiting the 2 clue in a band scenario .... which has not been totally clear
Code: Select all
        p123
+-----+-----+-----+
|. . .|. 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|
+-----+-----+-----+


tells us that
029
199
199 is invalid

therefore
033
199
199 is needed

Code: Select all
       p110
+-----+-----+-----+
|. . .|. . 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|
+-----+-----+-----+


099
119
199 is invalid

therefore
033
122
122 is at least required - as concluded by serg above ......

however
Code: Select all
        P114             
 +-----+-----+-----+     
 |. . .|. 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|     
 +-----+-----+-----+


means that

033
132
123

or

033
132
132

is a requirement

and here is one example of a puzzle of the first pattern
Code: Select all
+---+---+---+
|...|...|2..|
|...|498|...|
|...|...|.15|
+---+---+---+
|...|9..|...|
|...|.52|...|
|.8.|...|.36|
+---+---+---+
|...|.8.|59.|
|...|...|...|
|2..|..6|..7|
+---+---+---+  18 clues

and here is one example of a puzzle of the second pattern
Code: Select all
+---+---+---+
|...|...|...|
|...|345|...|
|...|...|671|
+---+---+---+
|...|9..|...|
|...|.16|...|
|.2.|...|.84|
+---+---+---+
|...|4..|.9.|
|...|.27|...|
|1..|...|..5|
+---+---+---+  18 clues


I have now more than 50 18-puzzles with these 2 patterns .....

We can say now that there cannot be a 17-puzzle with 2 clues in a band.

c
Last edited by coloin on Thu Oct 16, 2014 9:11 am, edited 2 times in total.
coloin
 
Posts: 1547
Joined: 05 May 2005

Re: Ask for patterns that they dont have puzzles 2

Postby Serg » Fri Aug 29, 2014 2:56 pm

Hi, coloin!
coloin wrote:revisiting the 2 clue in a band scenario .... which has not been totally clear
Code: Select all
        p123
+-----+-----+-----+
|. . .|. 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|
+-----+-----+-----+


tells us that
029
199
199 is invalid

Right.
coloin wrote:therefore
033
199
199 is needed

Why?
coloin wrote:therefore
Code: Select all
       p110
+-----+-----+-----+
|. . .|. . 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|
+-----+-----+-----+


099
119
199 is invalid

Right.
coloin wrote:therefore
033
122
122 is at least required - as concluded by serg above ......

Why? When did I say it?
coloin wrote:
however
Code: Select all
        P114             
 +-----+-----+-----+     
 |. . .|. 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|     
 +-----+-----+-----+


means that

033
132
123

or

033
132
132

is a requirement

I don't understand your point. Please, clarify your considerations.

Serg
Serg
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Posts: 499
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Location: Russia

Re: Ask for patterns that they dont have puzzles 2

Postby coloin » Sat Aug 30, 2014 11:49 am

Serg wrote:I agree with your logic. If a map has band 011 (i.e. 1 empty box and 2 boxes containing exactly 1 clue each), then each remaining band must have 322 configuration, at least....


033
122
122 has 16 clues

I have only extended it to show that

033
123
132 has 18 clues and has valid puzzles

033
122
132 has 17 clues and has no valid puzzles

this shows that in patterns with 2 clues only in a band
- there are no 17-puzzles
- there are no 9plus14 puzzles [9 clues in central box]

it doesnt change the remaining maps needed to search for {3+4} clues in two bands [as already {2+5} is disproved]

contemplating an exaustive grid solution search might be reduced by
only search grids which have a band completable in 3 clues - and we know the clues

c
coloin
 
Posts: 1547
Joined: 05 May 2005

Re: Ask for patterns that they dont have puzzles 2

Postby dobrichev » Sat Aug 30, 2014 1:35 pm

coloin wrote:contemplating an exaustive grid solution search might be reduced by
only search grids which have a band completable in 3 clues - and we know the clues

But a band completable in 2 clues is easy to complete with 3 clues, right?
dobrichev
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Posts: 1302
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Re: Ask for patterns that they dont have puzzles 2

Postby Serg » Sat Aug 30, 2014 11:26 pm

Hi, coloin!
coloin wrote:
Serg wrote:I agree with your logic. If a map has band 011 (i.e. 1 empty box and 2 boxes containing exactly 1 clue each), then each remaining band must have 322 configuration, at least....


033
122
122 has 16 clues

Yes, it was my point. Sorry, I fogot my own considerations :oops: .

coloin wrote:I have only extended it to show that

033
123
132 has 18 clues and has valid puzzles

033
122
132 has 17 clues and has no valid puzzles

I agree with you. Your propositions are right.
coloin wrote:this shows that in patterns with 2 clues only in a band
- there are no 17-puzzles

Yes! Impressive expectation! But you should add (for the sake of completeness) evident consideration - band having 2 empty boxes and the third box containing 2 clues cannot participate valid puzzles.
coloin wrote:- there are no 9plus14 puzzles [9 clues in central box]

Sorry, I don't catch your idea, please post your conclusion path in details.
coloin wrote:it doesnt change the remaining maps needed to search for {3+4} clues in two bands [as already {2+5} is disproved]

Surely.
coloin wrote:contemplating an exaustive grid solution search might be reduced by
only search grids which have a band completable in 3 clues - and we know the clues

Yes, it is right thought!(It is assumed that band configurations 012 and 111 should be checked while searching for new 17-clue puzzles, but band configuration 003 (having 3 clues though) is impossible in any valid puzzles.)

Good work!

Serg
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Posts: 499
Joined: 01 June 2010
Location: Russia

Re: Ask for patterns that they dont have puzzles 2

Postby coloin » Sun Aug 31, 2014 11:07 pm

dobrichev wrote:But a band completable in 2 clues is easy to complete with 3 clues, right?

welcome to the discusssion, indeed the sole band which solves with 2 clues has many combinations which solve with 3 clues.
however unless we get rid of many grids its all hypothetical
its quite possible that most grids have a band solvable with 3 clues - given that 100/416 bands are solvable in 3 - from your work here

splitting it up into just the ED 2 band [54 clue] combinations might be a potential way
but not sure how many million there are [? 500 million !]
all those not having a band completable with 3 clues can be discarded ..... this gets rid of ~ 42% [assuming band freq is similar.]
the other band will need to be solvable in 4 clues - this excludes another ~8% [58/416 bands need more than 4 clues]

Serg wrote:Yes! Impressive expectation! But you should add (for the sake of completeness) evident consideration - band having 2 empty boxes and the third box containing 2 clues cannot participate valid puzzles.

yes
099
099
299 is invalid

you showed that this pattern did not have valid puzzles
Code: Select all
+-----+-----+-----+
|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|
+-----+-----+-----+

Serg wrote:Sorry, I don't catch your idea, please post your conclusion path in details.

well i have been trying to generate 9plus12-puzzles
it probably precipitated this thread ....
at least 4 clues in any one band is the norm. i probably have found all but a few 9plus12s, and many of the 9plus13s.
C
coloin
 
Posts: 1547
Joined: 05 May 2005

Re: Ask for patterns that they dont have puzzles 2

Postby coloin » Wed Oct 26, 2016 11:08 pm

Reopening this thread as I have investigated a little more
Code: Select all
Adding 6 clues is never enough ?
 
9+---+---+---+
 |...|...|..x|
 |...|...|..x|
 |...|...|..x|
 +---+---+---+
 |...|...|..x|
 |...|...|..x|
 |...|...|..x|
 +---+---+---+
 |...|...|xxx|
 |...|...|xxx|
 |xxx|xxx|xxx|
 +---+---+---+

3 examples of a valid puzzle with 7 more clues
Code: Select all
                                                                   
+---+---+---+         +---+---+---+         +---+---+---+           
|123|456|789|         |123|456|789|         |123|456|789|           
|456|...|...|         |456|...|...|         |457|...|.2.|           
|789|...|...|         |789|...|...|         |869|...|...|           
+---+---+---+         +---+---+---+         +---+---+---+           
|2..|9..|.3.|         |2..|.18|...|         |2..|8..|.5.|           
|5..|3..|...|         |6..|...|5..|         |3..|...|...|           
|8..|...|6..|         |8..|...|..4|         |6..|.9.|...|           
+---+---+---+         +---+---+---+         +---+---+---+           
|3..|..7|...|         |3..|..9|.2.|         |5..|...|..6|           
|6..|.2.|5..|         |5..|...|...|         |7..|..3|.4.|           
|9..|...|...|         |9.1|...|...|         |9..|...|...|           
+---+---+---+ 816     +---+---+---+  202    +---+---+---+  3       


I searched and found only 1021 essentially different of these 21plus7 puzzles
None could be reduced to a 21plus6 - not proof but very unlikely to be found.

816/1021 puzzles had the repeating minirow band in both directions.
202/1021 puzzles had the repeating minirow band in one direction.
3/1021 puzzles had no repeating minirow band in either direction.

here is 200 of them
Hidden Text: Show
Code: Select all
123456789456......789......2........3......258..7.9...5...4..1.6.7......9........
123456789456......789......2........5.......48..9..6..3...25...6....1...9......5.
123456789456......789......2........5.......68..2.7...3..1..2..6....9...9.....3..
123456789456......789......2........5......218..9...3.3...1....6.....5..9..7.....
123456789456......789......2........5......238...7....3....2..56.......49...8....
123456789456......789......2........5......4.8..9....63...25.6.6...1....9........
123456789456......789......2........5......638..1.....3..2..1.76........9.......5
123456789456......789......2........5......688..1....43..2..1..6........9.......5
123456789456......789......2........5.....3..8..7....13......2.6.....5..9..8.3...
123456789456......789......2........5.....3..8..7....43......2.6.....5..9..8.3...
123456789456......789......2........5.....41.8..9.2...3........6.....52.9...1....
123456789456......789......2........5.....42.8..39....3........6...4.1..9..2.....
123456789456......789......2........5.....6.38..7.....3........6...23..19.....4..
123456789456......789......2........5.....6.38..74....3......7.6....1...9.....4..
123456789456......789......2........5.....6.38..74....3....1...6......7.9.....4..
123456789456......789......2........5.....9..8...21...3...4..2.6.......19..7.....
123456789456......789......2........5.....9..8..3....43...7..2.6.......59..1.....
123456789456......789......2........5....1..38..3...6.3..9.....6...8.2..9........
123456789456......789......2........5....1..38..3..6..3..9.....6...8..2.9........
123456789456......789......2........5....3.1.8.......43..8..2..6...4....9...7....
123456789456......789......2........5....36..8......7.3.......86..7.....9...8..2.
123456789456......789......2........5....36..8....4...3.......86..7.....9...8..2.
123456789456......789......2........5....4...8..2...133........6.....4..9...8.6..
123456789456......789......2........5....7..48...9....3....1...6..3.....9......25
123456789456......789......2........5....96..8......9.3.....4.16...2....9...8....
123456789456......789......2........5....96..8......9.3..2..4..6.......19..8.....
123456789456......789......2........5....96..8..7.....3.....4.16....8...9...2....
123456789456......789......2........5....98..8..7.....3.....4.16....8...9...2....
123456789456......789......2........5...1...48.....6..3.....1..6.....4..9...3..2.
123456789456......789......2........5...1...48..32....3......2.6....8..59........
123456789456......789......2........5...1..4.8.....6..3.....1..6....2...9....8..2
123456789456......789......2........5...1.6.48........3..8...2.6....7.9.9........
123456789456......789......2........5...1.6.48.....9..3..8...2.6....7...9........
123456789456......789......2........5...1.9..8...2.6..3......2.6....8...9..7.....
123456789456......789......2........5...1.9.48.....6..3..8...2.6....7...9........
123456789456......789......2........5...14...8......6.3..9....56.....4..9...8....
123456789456......789......2........5...17...8.......33...29...6.....1..9.....4..
123456789456......789......2........5...17...8.......33..2.9...6.....4..9.....1..
123456789456......789......2........5...2...48.......73.....2..6..9.8...9..7.....
123456789456......789......2........5...27...8.....6.33...89...6.....4..9........
123456789456......789......2........5...27...8.....6.33...98...6.....4..9........
123456789456......789......2........5...27...8.....63.3....8...6..1..4..9........
123456789456......789......2........5...3....8....14..3.......56......329....4...
123456789456......789......2........5...3....8....16..3.......26....4...9......35
123456789456......789......2........5...3....8....74..3.......56......329....4...
123456789456......789......2........5...3....8..9....43.....2..6.....5..9..8.3...
123456789456......789......2........5...3....8..9....73.....2..6.....53.9..8.....
123456789456......789......2........5...3....9..8....73.....2..6.....53.8..7.....
123456789456......789......2........5...3...68...1....3.....2..6....8...9..7....3
123456789456......789......2........5...4.6..8..7.....3.....4.16........9...82...
123456789456......789......2........5...6.8..8..7.....3.....4.16...8....9....2...
123456789456......789......2........5...7....8......363....8...6..2.....9.....5.7
123456789456......789......2........5...7....8......463...1....6........9..83.5..
123456789456......789......2........5...7....8......643...1....6........9..83.2..
123456789456......789......2........5...7....8.....6233.....4..6...8....9....2...
123456789456......789......2........5...7....8.....6323.....4..6...8....9....2...
123456789456......789......2........5...7....8....9.3.3....8...6.....5..9..23....
123456789456......789......2........5...7....8...9..3.3....2...6.......49.....5.7
123456789456......789......2........5...7....8..1...323...8....6.....5..9..2.....
123456789456......789......2........5...7....8..9.1.3.3....2...6.....5..9.......4
123456789456......789......2........5...7.1..8..9...6.3...8....6....24..9........
123456789456......789......2........5...7.6..8......3.3....2...6.....4..9..38....
123456789456......789......2........5...71...8...9...23.....1..6.....4..9...2....
123456789456......789......2........5...74...8......3.3...8....6..3..4..9.....1..
123456789456......789......2........5...9...78....1...3...82...6.....1.49........
123456789456......789......2........5..1.....8.......63..2..1..6....9...9...8..2.
123456789456......789......2........5..1....68..3.....3.....8..6....9...9...8..2.
123456789456......789......2........5..1...4.8.....6..3.....1..6....2...9....8..2
123456789456......789......2........5..1..3.48...9...63..7..1..6........9........
123456789456......789......2........5..1..4..8......363.....17.6........9....8...
123456789456......789......2........5..1..4..8....3..63.....12.6...4....9........
123456789456......789......2........5..1..4..8....9...3..7..15.6........9...8....
123456789456......789......2........5..1..4..8...9...63..7..1..6........9...8....
123456789456......789......2........5..1..4..8..3....63.....2..6....9...9...8....
123456789456......789......2........5..1..4..8..3....63.....2..6...9....9...7....
123456789456......789......2........5..14....8...3...63.....4..6....9...9......3.
123456789456......789......2........5..17....8......363..2...1.6........9...8....
123456789456......789......2........5..17....8.....3.63..2...1.6........9...8....
123456789456......789......2........5..17....8...3...63.....1..6....9...9......3.
123456789456......789......2........5..2..3..8..3....63...7.1..6...9....9........
123456789456......789......2........5..24....8.....6.33........6...7.4..9....8...
123456789456......789......2........5..27....8.....6.33.....4..6...8....9....2...
123456789456......789......2........5..27....8.....63.3.....4..6...8....9....2...
123456789456......789......2........5..3..4..8...9...63..2..1..6........9...8....
123456789456......789......2........5..31.4..8.....6..3......1.6.....3..9....8...
123456789456......789......2........5..7.....8...9..3.3....2...6.....41.9.......7
123456789456......789......2........5..7.....8..9.1.3.3........6....25..9.......4
123456789456......789......2........5..7....48....1...3......2.6.....5..9..8.3...
123456789456......789......2........5..7....68..3.....3.....8..6....9...9...8..2.
123456789456......789......2........5..7..1..8......363.....41.6........9....8...
123456789456......789......2........5..7..1..8...9...63..1..2..6........9...8....
123456789456......789......2........5..7..2..8.......33...98...6.....5..9......4.
123456789456......789......2........5..7..2..8......563.....4..6...98...9........
123456789456......789......2........5..7..4..8...9...63..1..2..6........9...8....
123456789456......789......2........5..71....8......363...4..1.6........9..8.....
123456789456......789......2........5..71....8.....3.63...4..1.6........9..8.....
123456789456......789......2........5..72....8.....63.3....8...6..1..4..9........
123456789456......789......2........5..74....8......363.....5..6..9.....9....2...
123456789456......789......2........5..74....8......363...2..1.6........9..8.....
123456789456......789......2........56...7...8......323.....1..6....8...9...2....
123456789456......789......2........56..7....8......323.....1..6...8....9..2.....
123456789456......789......2........6.....5.28....9...3...2....5..16.4..9........
123456789456......789......2.......15........8..9...6.3.....2..6.....5..9..8.3...
123456789456......789......2.......15..7.....8..9....33....25..6......4.9........
123456789456......789......2.......35........8....74..3..8.1...6....2...9.......5
123456789456......789......2.......35........8...4.6..3.....4..6.....1..9..2.3...
123456789456......789......2.......35....4...8....1...3...7....6.....1..9...8..2.
123456789456......789......2.......35....7...8....4.9.3.....5..6......7.9..2.....
123456789456......789......2.......35....7...8....9.6.3.....5..6......7.9...2....
123456789456......789......2.......35....74..8......9.3........6.....1..9..23....
123456789456......789......2.......35...4....8.....62.3........6...7.4..9....2...
123456789456......789......2.......35...7....8.....62.3........6...1.4..9....2...
123456789456......789......2.......35...71...8......2.3..89....6.....4..9........
123456789456......789......2.......35...74...8.....6..3.....4..6....2...9...8....
123456789456......789......2.......35...9....8.....6.23.....4..6...82...9........
123456789456......789......2.......35..1.4...8......9.3.....4..6.......19...8....
123456789456......789......2.......35..17....8......2.3..98....6.....4..9........
123456789456......789......2.......35..17....8......6.3..98....6.....4..9........
123456789456......789......2.......35..29....8.....6..3.....4..6...82...9........
123456789456......789......2.......35..29....8.....6..3..1..4..6...2....9........
123456789456......789......2.......35..29....8.....6..3..1..4..6...7....9........
123456789456......789......2.......35..29....8.....6..3..1..4..6...8....9........
123456789456......789......2.......35..29....8.....6..3..1..5..6...8....9........
123456789456......789......2.......35..7.....8......2.3......7.6....25..9....3...
123456789456......789......2.......35..7.....8.....69.3.....4..6........9...23...
123456789456......789......2.......35..7..6..8......9.3.....4..6........9...32...
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123456789456......789......2.......35..92....8.....6..3...1.5..6....8...9........
123456789456......789......2.......356...4...8........3.....4..6.....5..9..32....
123456789456......789......2.......356.7.....8........3.....5..6.....4..9...32...
123456789456......789......2.......45........6....7...3..2..5..8......7.9..14....
123456789456......789......2.......45..6..1..8...9....3...8....6.....4..9....2...
123456789456......789......2.......53..8.....8....7...5......146....8...9...2....
123456789456......789......2.......55.....6..8..7.....3.....4.16....8...9...2....
123456789456......789......2.......55.....6..8..7.....3.....4.16....9...9...2....
123456789456......789......2.......55.....6..8..7.....3..1...4.6...2.8..9........
123456789456......789......2.......55...3....8......6.3.....2..6....9...9....41..
123456789456......789......2.......55..1..4..8....3...3....71..6........9...8....
123456789456......789......2.......65........8....74..3....2...6..8.1...9.......5
123456789456......789......2.......65........8....74..3..8.1...6....2...9.......5
123456789456......789......2.......65.....2..8..9.....3...721..6....1...9........
123456789456......789......2.......65.....23.8...7....3.......46...1....9....2...
123456789456......789......2.......65.....23.8..7.....3...8....6.......49....2...
123456789456......789......2.......65.....3..8...17...3...7..1.6....9...9........
123456789456......789......2.......65...1.2..8..7.....3.......46......7.9....2...
123456789456......789......2.......65...47...8....9.3.3.....1..6........9...2....
123456789456......789......2.......65...7....8........3...8.1..6.......49..2.3...
123456789456......789......2.......65...7....8......233.....4..6...1....9....2...
123456789456......789......2.......65...7....8......3.3....2...6.......49..38....
123456789456......789......2.......65...7....8......3.3....2...6.....3.49...8....
123456789456......789......2.......65...7....8......323.....6..6...9....9....2...
123456789456......789......2.......65...7....8..9.....3....21..6...8....9......4.
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123456789456......789......2.......65..17....8.......33.......16.....4..9...8....
123456789456......789......2.......65..7..3..8...9....3..1..2..6........9...8....
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123456789456......789......2.......65..8.....8...7....3......646....2...9...8....
123456789456......789......2.......65..8.....8...9....3....1..46....2...9.....1..
123456789456......789......2.......65..8.....8..7...2.3....2...6...8....9.......4
123456789456......789......2.......65..8.....8..7..2..3....2...6...8....9.......4
123456789456......789......2.......65..8.....8..7..3..3....2...6...8....9.......4
123456789456......789......2.......65..8.....8..7..4..3....2...6...8....9.......4
123456789456......789......2.......65..8..1..8..7.....3....2...6...8....9.......4
123456789456......789......2.......65..89....8......3.3...8....6....2...9.......4
123456789456......789......2.......65..89....8.....3..3...82...6........9.......5
123456789456......789......2.......75...7.1..8..9.....3....24..6...8....9........
123456789456......789......2.......85..7.....8......563..1..4..6....8...9........
123456789456......789......2......1.5.......48...9....3..7.....6..1.....9......25
123456789456......789......2......1.5.....6..8...7....3.....4.66...2....9...8....
123456789456......789......2......1.5....3..68....2...3..8.....6......2.9...7....
123456789456......789......2......1.5....36..8....2...3..8.....6......2.9...7....
123456789456......789......2......1.5...8....8...9..3.3....2...6.......49.....5..
123456789456......789......2......1.5..7.....8..9...3.3....2...6.......49.....5..
123456789456......789......2......135...7....8........3.....4..6....25..9....3...
123456789456......789......2......135..7.....8........3.....4..6....25..9....3...
123456789456......789......2......143........8..7.9...5...4..3.6.7......9........
123456789456......789......2......143..7.9...8........5...1..3.6.7......9........
123456789456......789......2......143..7.9...8........5...4..3.6.7......9........
123456789456......789......2......153........8..7.9...5...4..3.6.7......9........
123456789456......789......2......153...79...8........5..1...3.6.7......9........
123456789456......789......2......153...79...8........5..1...4.6.7......9........
123456789456......789......2......153..7.9...8........5...4..3.6.7......9........
123456789456......789......2......3.5.....6..8...7....3.....4.66...2....9...8....
123456789456......789......2......3.5....4...8...71...3.....4..6........9...8...5
123456789456......789......2......3.5...1...48...2....3......2.6..9.....9....8...
123456789456......789......2......3.5...7....8.....6.23.....4..6...8....9....2...
123456789456......789......2......3.5...7....8....3.6.3........6..2.....9.....4.5
123456789456......789......2......3.5...71...8.......63.....4..6........9...8..7.
123456789456......789......2......3.5...74...8........3...8....6..2..4..9.....1..
123456789456......789......2......3.5...74...8.....6..3.....4..6....2...9...8....
123456789456......789......2......3.5..17....8.......63....74..6...8....9........
123456789456......789......2......315..7.....8........3....25..6......2.9....1...
123456789456......789......2......315..7.....8........3....25..6....1...9.....4..
123456789456......789......2......345....1...8...7....3.....4..6........9...8...5
123456789456......789......2......353........8..7.9...5...4..1.6.7......9........
123456789456......789......2......365........8...47...3...7..1.6....8...9........
coloin
 
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