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 » Sat Jul 04, 2020 8:40 pm

Of the 200 B159plus3 puzzles I have ....99% were of the 1st pattern
and to serg .... Im afraid that its a crude method - if a puzzle is not found in reasonable time the chances are that the pattern doesnt have valid puzzles ...
but a pattern either has puzzles or it doesnt ... even some 18C patterns just dont have puzzles ... even though similar patterns differing by 1 clue do !!
coloin
 
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Re: Ask for patterns that they dont have puzzles 2

Postby coloin » Sat Jul 04, 2020 8:43 pm

JPF wrote: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


very good ....
coloin
 
Posts: 1906
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Re: Ask for patterns that they dont have puzzles 2

Postby JPF » Tue Jul 07, 2020 2:36 pm

5 clues is never enough?
Code: Select all
+---+---+---+
|...|...|...|
|...|...|...|
|...|...|...|
+---+---+---+
|...|...|xxx|
|...|...|xxx|
|...|...|xxx|
+---+---+---+
|...|xxx|xxx|
|...|xxx|xxx|
|...|xxx|xxx|
+---+---+---+

It can work with 6 clues but B3 has to be 0 and at least one B5,B7 = 0

Here are examples:
Code: Select all
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+
|72.|...|...|   |...|.8.|...|   |...|...|...|   |...|..3|...|
|...|5..|...|   |..5|...|...|   |1..|7..|...|   |.65|...|...|
|..6|...|...|   |2.7|...|...|   |.26|...|...|   |..7|...|...|
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+
|...|...|217|   |...|5..|197|   |..8|...|197|   |8..|...|214|
|..4|3..|685|   |...|...|635|   |...|.2.|685|   |...|...|678|
|...|...|394|   |6..|...|284|   |...|...|324|   |...|...|395|
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+
|...|485|963|   |...|821|963|   |...|487|961|   |...|754|963|
|...|971|852|   |...|764|852|   |...|163|852|   |3..|169|852|
|...|632|741|   |...|935|471|   |...|952|743|   |...|832|741|
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+

Code: Select all
+---+---+---+   +---+---+---+
|...|6..|...|   |...|69.|...|
|9.2|...|...|   |3..|...|...|
|3..|...|...|   |74.|...|...|
+---+---+---+   +---+---+---+
|.6.|...|189|   |...|...|317|
|.8.|...|675|   |..6|...|295|
|...|...|324|   |...|...|684|
+---+---+---+   +---+---+---+
|...|514|963|   |...|821|963|
|...|793|852|   |...|764|852|
|...|862|741|   |...|953|741|
+---+---+---+   +---+---+---+

Conjecture: with 5 clues, Min sol. = 5

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

Postby m_b_metcalf » Tue Jul 07, 2020 4:52 pm

JPF wrote:Conjecture: with 5 clues, Min sol. = 5

First stab:
Code: Select all
 . . . 3 . . . . .
 4 . . . . . . . .
 9 . . . . . . . .
 . 5 . . . . 1 2 3
 . 3 . . . . 4 5 6
 . . . . . . 7 8 9
 . . . 2 7 9 8 6 4
 . . . 5 3 8 2 7 1
 . . . 1 6 4 9 3 5   14 solution(s)


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

Postby JPF » Tue Jul 07, 2020 5:09 pm

I should have given an example:
Code: Select all
+---+---+---+
|.82|...|...|
|...|...|...|
|...|.45|...|
+---+---+---+
|...|...|275|
|...|...|698|
|5..|...|314|
+---+---+---+
|...|281|936|
|...|674|852|
|...|953|741|
+---+---+---+    5 sol.

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

Postby JPF » Tue Jul 07, 2020 5:32 pm

BTW 5 clues are enough for this pattern:
Code: Select all
+---+---+---+
|xxx|...|...|
|xxx|...|...|
|xxx|...|...|
+---+---+---+
|...|...|...|
|...|...|...|
|...|...|...|
+---+---+---+
|...|xxx|xxx|
|...|xxx|xxx|
|...|xxx|xxx|
+---+---+---+

Code: Select all
+---+---+---+
|123|...|.6.|
|456|.3.|...|
|789|...|...|
+---+---+---+
|...|..1|...|
|...|...|..7|
|.3.|...|...|
+---+---+---+
|...|367|219|
|...|189|654|
|...|542|378|
+---+---+---+

EDIT : 4 clues are enough...
Code: Select all
+---+---+---+
|123|...|...|
|456|...|...|
|789|...|...|
+---+---+---+
|...|.5.|...|
|..2|...|..1|
|...|.4.|...|
+---+---+---+
|...|784|539|
|...|293|617|
|...|165|428|
+---+---+---+

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

Postby coloin » Fri Jul 10, 2020 4:12 pm

Thanks for those 2 patterns ... I will update the list,

5 clues are probably never enough
Code: Select all
+---+---+---+           
|...|...|...|           
|...|...|...|           
|...|...|...|           
+---+---+---+           
|...|...|xxx|           
|...|...|xxx|           
|...|...|xxx|           
+---+---+---+           
|...|xxx|xxx|           
|...|xxx|xxx|           
|...|xxx|xxx|           
+---+---+---+   

as 5 clues are only just needed for
Code: Select all
+---+---+---+ 
|1..|..2|...| 
|...|...|..3| 
|.4.|...|...| 
+---+---+---+ 
|...|293|651| 
|...|654|987| 
|.5.|781|432| 
+---+---+---+ 
|...|176|329| 
|...|529|148| 
|...|438|576| 
+---+---+---+   valid 36plus5

maybe Serg can show that adding 5 clues is impossible with his list of invalid crossing patterns ...

and

I suspect we have proof that 2 clues are never enough for this pattern

Code: Select all
                                                                   
+---+---+---+      +---+---+---+                                         
|xxx|xxx|...|      |123|869|...|                                         
|xxx|xxx|...|      |456|732|...|                                         
|xxx|xxx|...|      |789|415|...|                                         
+---+---+---+      +---+---+---+                                         
|...|...|...|      |2..|.4.|...|                                         
|...|...|...|      |...|...|.5.|                                         
|...|...|...|      |...|...|...|                                         
+---+---+---+      +---+---+---+                                         
|...|xxx|xxx|      |...|597|812|                                         
|...|xxx|xxx|      |...|186|534|                                         
|...|xxx|xxx|      |...|324|796|                                         
+---+---+---+      +---+---+---+    valid 36plus3 puzzle 
coloin
 
Posts: 1906
Joined: 05 May 2005

Re: Ask for patterns that they dont have puzzles 2

Postby JPF » Fri Jul 10, 2020 9:30 pm

For this pattern B1359, one is enough but in the right box:

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

+---+---+---+
|123|...|495|
|456|...|783|
|789|...|612|
+---+---+---+
|...|143|...|
|...|657|...|
|...|829|...|
+---+---+---+
|...|...|879|
|.9.|...|354|
|...|...|126|
+---+---+---+

JPF
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