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 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: 1906
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
2018 Supporter
 
Posts: 710
Joined: 01 June 2010
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: 1906
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
2016 Supporter
 
Posts: 1784
Joined: 24 May 2010

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
Serg
2018 Supporter
 
Posts: 710
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: 1906
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...
123456789456......789......2.......35..92....8.....6..3...1.4..6..5.....9........
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.
123456789456......789......2.......65...7....8..9.....3....25..6.....2..9..6.....
123456789456......789......2.......65...74...8....1...3........6.....1..9...8..3.
123456789456......789......2.......65..14....8...3....3.....1..6....9...9......3.
123456789456......789......2.......65..14....8..3.....3.....1..6....9...9......3.
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....
123456789456......789......2.......65..7..4..8...9....3..1..2..6........9...8....
123456789456......789......2.......65..71....8.......33.......16.....5..9..8.....
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
 
Posts: 1906
Joined: 05 May 2005

Re: Ask for patterns that they dont have puzzles 2

Postby JPF » Sat Jun 27, 2020 4:09 pm

coloin wrote:And these are ? unproven patterns with n clues to be added - in order of possible ease !
Probably they are all correct ! Apologies if they have indeed been proven in former posts.....

The fact that we havnt got proof probably means that it is not an easy task !

Code: Select all
Adding 4 clues is never enough ?                                     
                                                                                                                                     
 7+---+---+---+       +---+---+---+                                 
  |...|...|...|       |...|...|781|                                 
  |...|...|...|       |96.|...|...|                                 
  |...|...|...|       |...|...|...|                                 
  +---+---+---+       +---+---+---+                                 
  |...|xxx|...|       |...|123|...|                                 
  |...|xxx|...|       |...|456|...|                                 
  |...|xxx|...|       |...|789|...|                                 
  +---+---+---+       +---+---+---+                                 
  |xxx|...|xxx|       |659|...|317|                                 
  |xxx|...|xxx|       |437|...|268|                                 
  |xxx|...|xxx|       |821|...|459|                                 
  +---+---+---+       +---+---+---+    valid plus 5 clues                                                                                                                                                                                                                                                     

actually, adding 4 clues may be enough:
Code: Select all
+---+---+---+
|.3.|..2|...|
|...|...|..4|
|...|...|..5|
+---+---+---+
|...|123|...|
|...|456|...|
|...|789|...|
+---+---+---+
|195|...|348|
|284|...|756|
|376|...|219|
+---+---+---+

JPF
JPF
2017 Supporter
 
Posts: 4155
Joined: 06 December 2005
Location: Paris, France

Re: Ask for patterns that they dont have puzzles 2

Postby JPF » Tue Jun 30, 2020 9:18 pm

Code: Select all
Adding 4 clues is never enough ?                                     
                                                                                           
 8+---+---+---+       +---+---+---+                                 
  |...|...|..,|       |.2.|...|...|                                 
  |...|...|..,|       |...|.5.|9..|                                 
  |...|...|..,|       |...|...|...|                                 
  +---+---+---+       +---+---+---+                                 
  |...|...|xxx|       |...|6..|123|                                 
  |...|...|xxx|       |..9|...|456|                                 
  |...|...|xxx|       |...|...|789|                                 
  +---+---+---+       +---+---+---+                                 
  |xxx|xxx|xxx|       |281|345|697|                                 
  |xxx|xxx|xxx|       |476|891|532|                                 
  |xxx|xxx|xxx|       |935|267|841|                                 
  +---+---+---+       +---+---+---+   valid  plus 5 clues 

here is one puzzle valid plus 4 clues:
Code: Select all
+---+---+---+
|...|...|...|
|...|1..|...|
|23.|...|...|
+---+---+---+
|...|.4.|562|
|...|...|731|
|...|...|849|
+---+---+---+
|678|921|453|
|451|837|926|
|923|465|178|
+---+---+---+

JPF
JPF
2017 Supporter
 
Posts: 4155
Joined: 06 December 2005
Location: Paris, France

Re: Ask for patterns that they dont have puzzles 2

Postby coloin » Wed Jul 01, 2020 7:13 pm

Excellent ..... those two puzzles are valid and show that there is [as ever] always incidences in the sudoku puzzle space which surprise us ! I will update the posts...
Evidently in these cases I did not search as hard as I should have ! Well done !
I wonder were there many examples that you found ? if there were very few found this would increase the likelihood that the limit was reached.

Of course as touched on before, there are the patterns plus n ( where n>1) clues as we have here , which are more of a generalization, rather than some of the specific patterns which are "maximal and have no puzzles" - whereby the addition of a single clue anywhere in the remaining cells now would give a valid puzzle.

I would be interested if you looked at the other cases which had very few puzzle examplars and whether you found any more !!!
eg
Code: Select all
+---+---+---+                                     
|123|456|789|                                     
|...|...|..1|                                     
|...|.9.|...|                                     
+---+---+---+                                     
|891|243|567|                                     
|4..|...|...|                                     
|...|...|9..|                                     
+---+---+---+                                     
|...|..1|...|                                     
|...|...|...|                                     
|965|872|413|                                     
+---+---+---+ valid plus 5 clues  [only one found]
coloin
 
Posts: 1906
Joined: 05 May 2005

Re: Ask for patterns that they dont have puzzles 2

Postby JPF » Wed Jul 01, 2020 9:49 pm

you wrote:
Code: Select all
+---+---+---+                                     
|123|456|789|                                     
|...|...|..1|                                     
|...|.9.|...|                                     
+---+---+---+                                     
|891|243|567|                                     
|4..|...|...|                                     
|...|...|9..|                                     
+---+---+---+                                     
|...|..1|...|                                     
|...|...|...|                                     
|965|872|413|                                     
+---+---+---+ valid plus 5 clues  [only one found]

I'm not sure I understand your point.
I found easily more than 1000 valid puzzles with the same pattern.
Here are some examples:

Code: Select all
+---+---+---+   +---+---+---+   +---+---+---+
|123|456|789|   |123|456|789|   |123|456|789|
|...|...|..5|   |...|...|..1|   |...|...|..1|
|...|.9.|...|   |...|.8.|...|   |...|.8.|...|
+---+---+---+   +---+---+---+   +---+---+---+
|895|243|167|   |891|263|547|   |981|563|247|
|6..|...|...|   |4..|...|...|   |4..|...|...|
|...|...|2..|   |...|...|2..|   |...|...|5..|
+---+---+---+   +---+---+---+   +---+---+---+
|...|..1|...|   |...|..7|...|   |...|..1|...|
|...|...|...|   |...|...|...|   |...|...|...|
|914|872|653|   |768|592|413|   |865|792|413|
+---+---+---+   +---+---+---+   +---+---+---+

Here are 2 valid puzzles with different patterns:
Code: Select all
+---+---+---+   +---+---+---+
|123|456|789|   |123|456|789|
|...|...|...|   |...|...|...|
|5..|..2|...|   |5..|1..|...|
+---+---+---+   +---+---+---+
|341|827|695|   |839|625|147|
|...|...|...|   |...|...|...|
|7..|..9|...|   |.6.|.9.|...|
+---+---+---+   +---+---+---+
|692|145|873|   |458|739|216|
|...|...|...|   |...|...|...|
|...|...|1..|   |...|...|5..|
+---+---+---+   +---+---+---+

I'm pretty sure that this pattern is invalid:
Code: Select all
+---+---+---+   +---+---+---+
|xxx|xxx|xxx|   |123|456|789|
|...|...|...|   |...|...|...|
|x..|x..|x..|   |5..|1..|6..|
+---+---+---+   +---+---+---+
|xxx|xxx|xxx|   |879|621|543|
|...|...|...|   |...|...|...|
|.x.|...|...|   |.6.|...|...|
+---+---+---+   +---+---+---+
|xxx|xxx|xxx|   |417|893|256|
|...|...|...|   |...|...|...|
|...|...|x..|   |...|...|9..|
+---+---+---+   +---+---+---+
Min=2 sol.           2 sol.

JPF
JPF
2017 Supporter
 
Posts: 4155
Joined: 06 December 2005
Location: Paris, France

Re: Ask for patterns that they dont have puzzles 2

Postby coloin » Wed Jul 01, 2020 10:34 pm

JPF wrote:I'm not sure I understand your point.....

Well your methods now are oviously superior to mine. The more examples of a pattern that you can make the more likely that there will be a superflous clue in the added clues [stating the obvious I suppose]
It was some time ago and perhaps methods have improved !!
We are well short of any proof however and the number and ease of puzzles found is probably a good guide to the lower limit
Have updated with your new finds ...
coloin
 
Posts: 1906
Joined: 05 May 2005

Re: Ask for patterns that they dont have puzzles 2

Postby JPF » Sat Jul 04, 2020 12:11 pm

B1B5B9 + 3 clues
The only valid 3 empty box patterns are:
Code: Select all
00X   0XX
XX0   X0X
XXX   XX0

and here is the only valid 4 empty box pattern:
Code: Select all
X0X
0X0
X0X

Therefore for B1B5B9 + 3 clues, there exists only 5 possible ed-patterns:
Code: Select all
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+
|XXX|...|...|   |XXX|...|...|   |XXX|...|...|   |XXX|...|...|   |XXX|...|...|
|XXX|...|...|   |XXX|...|...|   |XXX|.X.|...|   |XXX|...|..X|   |XXX|...|XX.|
|XXX|...|...|   |XXX|...|...|   |XXX|...|...|   |XXX|...|.X.|   |XXX|...|...|
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+
|...|XXX|...|   |...|XXX|...|   |...|XXX|...|   |...|XXX|...|   |...|XXX|...|
|...|XXX|.X.|   |...|XXX|.X.|   |...|XXX|.X.|   |...|XXX|...|   |...|XXX|...|
|...|XXX|...|   |...|XXX|...|   |...|XXX|...|   |...|XXX|...|   |...|XXX|...|
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+
|...|...|XXX|   |...|...|XXX|   |...|...|XXX|   |...|...|XXX|   |...|...|XXX|
|...|.X.|XXX|   |.X.|.X.|XXX|   |.X.|...|XXX|   |...|...|XXX|   |.X.|...|XXX|
|.X.|...|XXX|   |...|...|XXX|   |...|...|XXX|   |X..|...|XXX|   |...|...|XXX|
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+

The first four patterns are valid.
Here is an example for each of them :
Code: Select all
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+
|123|...|...|   |123|...|...|   |123|...|...|   |123|...|...|
|456|...|...|   |456|...|...|   |456|.7.|...|   |456|...|..7|
|789|...|...|   |789|...|...|   |789|...|...|   |789|...|.4.|
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+
|...|347|...|   |...|769|...|   |...|213|...|   |...|324|...|
|...|986|.5.|   |...|453|.2.|   |...|967|.4.|   |...|157|...|
|...|512|...|   |...|218|...|   |...|845|...|   |...|689|...|
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+
|...|...|897|   |...|...|247|   |...|...|861|   |...|...|325|
|...|.7.|341|   |.1.|.9.|856|   |.3.|...|259|   |...|...|819|
|.9.|...|562|   |...|...|319|   |...|...|473|   |3..|...|476|
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+

The last pattern is probably invalid.
Here is a puzzle with 2 solutions:
Code: Select all
+---+---+---+
|123|...|...|
|456|...|23.|
|789|...|...|
+---+---+---+
|...|124|...|
|...|765|...|
|...|893|...|
+---+---+---+
|...|...|198|
|.6.|...|453|
|...|...|627|
+---+---+---+
2 sol.

JPF
JPF
2017 Supporter
 
Posts: 4155
Joined: 06 December 2005
Location: Paris, France

Re: Ask for patterns that they dont have puzzles 2

Postby Serg » Sat Jul 04, 2020 7:44 pm

Hi, coloin, JPF!
Impressive results! What methods do you use to check - has given pattern valid puzzles or not?

Serg
Serg
2018 Supporter
 
Posts: 710
Joined: 01 June 2010
Location: Russia

Re: Ask for patterns that they dont have puzzles 2

Postby JPF » Sat Jul 04, 2020 8:34 pm

coloin wrote:
Code: Select all
 6+---+---+---+        +---+---+---+                                 
  |x..|...|..x|        |9..|...|..7|                                 
  |x..|...|..x|        |3..|87.|..2|                                 
  |x..|...|..x|        |64.|...|..3|                                 
  +---+---+---+        +---+---+---+                                 
  |x..|...|..x|        |46.|...|..8|                                 
  |x..|...|..x|        |2..|.3.|..1|                                 
  |x..|...|..x|        |5..|...|..4|                                 
  +---+---+---+        +---+---+---+                                 
  |x..|...|..x|        |7..|...|..6|                                 
  |x..|...|..x|        |8..|...|..5|                                 
  |xxx|xxx|xxx|        |123|456|789|                                 
  +---+---+---+        +---+---+---+    valid 25plus5 clues  [only one found]   


Here is an other one with symmetry:
Code: Select all
 2 . . | . . . | . . 8
 7 . . | 3 . 9 | . . 6
 5 . . | . . . | . . 1
-------+-------+-------
 6 . . | . 8 . | . . 7
 3 . . | . . . | . . 2
 4 . 9 | . . . | 3 . 5
-------+-------+-------
 8 . . | . . . | . . 4
 9 . . | . . . | . . 3
 1 2 3 | 4 5 6 | 7 8 9

JPF
JPF
2017 Supporter
 
Posts: 4155
Joined: 06 December 2005
Location: Paris, France

PreviousNext

Return to General