How many 1-clue-box and 2-clue-box?

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How many 1-clue-box and 2-clue-box?

Postby Eioru » Thu Aug 17, 2006 11:05 am

For a very easy sudoku.

000 000 079
604 079 001
000 802 000
009 000 347
000 000 000
100 068 000
040 200 000
000 087 006
020 000 800

There are 4 "2-clue-box".
Because the less clue of sudoku is 17s,
there might be 9 "2-clue-box" and 7 "1-clue-box".
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Re: How many 1-clue-box and 2-clue-box?

Postby JPF » Thu Aug 17, 2006 8:24 pm

Eioru wrote:For a very easy sudoku.

000 000 079
604 079 001
000 802 000
009 000 347
000 000 000
100 068 000
040 200 000
000 087 006
020 000 800

There are 4 "2-clue-box".
Because the less clue of sudoku is 17s,
there might be 9 "2-clue-box" and 7 "1-clue-box".

Here is a post from Ocean giving stats on the clues distribution in the 17-clues gfroyle's list
He found 1405 "122222222", based on 32930 distinct 17-clue sudokus at that time.

Based on a more recent list (36628), I counted 1565 "122222222"

Now, pick one of this puzzle and add one (compatible) clue in the 1 clue-box.

For example :
Code: Select all
 8 . . | . . . | . 2 4
 . 1 . | . . 8 | . . .
 . . . | . 7 . | . . .
-------+-------+-------
 6 . . | 2 . 1 | 5 . .
 4 . . | . . . | . . 3
 . . . | . . . | . . .
-------+-------+-------
 . 7 . | . . . | 8 1 .
 5 . . | 4 3 . | . . .
 . . . | . . . | . . .

r1c1=8 has been added.

On the second point (7 one-clue boxes), i have some doubt about the existence of valid puzzles with this kind of pattern :
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 . | . . . | . . .

but who knows ?

In any case, in the gfroyle list : there are no 111111155 and the maximum of 1-clue boxes is 5.

JPF
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Postby coloin » Wed Sep 13, 2006 1:57 am

I cant do any better than 4 clues in Box 9
Code: Select all
+---+---+---+
|123|...|7..|
|456|...|...|
|789|..5|...|
+---+---+---+
|...|148|...|
|...|259|.1.|
|..8|736|...|
+---+---+---+
|...|9..|.46|
|.7.|...|1..|
|...|...|..5|
+---+---+---+


C
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Postby JPF » Wed Sep 13, 2006 5:29 pm

Here is a puzzle with 3 clues in Box 9

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


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Postby coloin » Wed Sep 13, 2006 11:23 pm

Well done ..it spurred me on to make this one.......

Which I think is the first symetrical puzzle Ive ever made:!:

Code: Select all
+---+---+---+
|.79|...|..3|
|386|...|...|
|21.|7..|...|
+---+---+---+
|..3|.46|...|
|...|879|...|
|...|21.|8..|
+---+---+---+
|...|..4|...|
|...|...|.69|
|5..|...|.7.|
+---+---+---+


No doubt Ocean is waiting in the wings with an improvement !
C
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Re: Cold case : How many 1-clue-box and 2-clue-box?

Postby JPF » Tue Aug 30, 2022 7:07 pm

coloin wrote:No doubt Ocean is waiting in the wings with an improvement !

no response from Ocean. So it's my turn now:
Code: Select all
+---+---+---+
|123|...|...|
|456|..2|...|
|789|...|.3.|
+---+---+---+
|...|148|...|
|...|369|..7|
|.4.|725|...|
+---+---+---+
|...|...|.4.|
|5..|...|2..|
|...|8..|...|
+---+---+---+

JPF
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Re: How many 1-clue-box and 2-clue-box?

Postby coloin » Wed Aug 31, 2022 12:17 am

Very nice
Must have taken a long time to make !! :)
It can be morphed to have diagonal symmetry and reduced to 20C

If there is no empty box it seems 6 clues are always necessary in the 5 boxes [B36789] in your puzzle

So with 5 clues always needed in B12369 ......can you find a smaller puzzle - removing clues from B4578 ?

Code: Select all
+---+---+---+    +---+---+---+     
|...|...|..1|    |...|...|..1|     
|...|...|.23|    |...|...|.23|     
|...|..4|...|    |...|..4|...|     
+---+---+---+    +---+---+---+     
|168|295|4..|    |.68|295|4..|     
|234|687|...|    |2..|.8.|...|     
|759|341|...|    |.5.|...|...|     
+---+---+---+    +---+---+---+     
|972|163|...|    |9.2|1.3|...|     
|581|479|...|    |..1|.7.|...|     
|346|528|...|    |34.|5..|...|     
+---+---+---+    +---+---+---+   22C
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Re: How many 1-clue-box and 2-clue-box?

Postby JPF » Wed Aug 31, 2022 10:10 am

can you find a smaller puzzle - removing clues from B4578 ?

sure!
Code: Select all
+---+---+---+   +---+---+---+
|...|...|..1|   |...|...|..1|
|...|...|.2.|   |...|...|.2.|
|...|..3|..4|   |...|..3|..4|
+---+---+---+   +---+---+---+
|482|956|7..|   |..2|.56|7..|
|539|781|...|   |.3.|7.1|...|
|176|234|...|   |1..|..4|...|
+---+---+---+   +---+---+---+
|245|168|...|   |.4.|1.8|...|
|697|325|...|   |..7|.2.|...|
|318|497|...|   |31.|.9.|...|
+---+---+---+   +---+---+---+   21C

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Re: How many 1-clue-box and 2-clue-box?

Postby coloin » Wed Aug 31, 2022 1:14 pm

Gets a bit tricky now ... !
But further to go I think ...

Code: Select all
+---+---+---+
|...|...|..1|
|...|...|.23|
|...|..4|...|
+---+---+---+
|9.6|..1|4..|
|5..|...|...|
|78.|.25|...|
+---+---+---+
|...|.38|...|
|..4|79.|...|
|.13|...|...|
+---+---+---+  20C
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Re: How many 1-clue-box and 2-clue-box?

Postby m_b_metcalf » Wed Aug 31, 2022 1:19 pm

Here are three more 21-clue puzzles, each with three empty boxes:
Code: Select all
 . . . . . . . 1 2
 . . . . . . . . 3
 . . . . . . 4 . .
 . 2 . 1 . . . . .
 . 1 . 3 5 . . . .
 . . 6 . 7 . 8 . .
 4 . . 6 8 . . . .
 9 . . . . 2 . . .
 3 8 5 . . 4 . . .   ED=2.0/1.2/1.2

 . . . . . . . 1 2
 . . . . . . . . 3
 . . . . . . 4 . .
 . 2 . 3 . . . . .
 . 5 . . 6 . . . .
 . . 1 . 7 8 9 . .
 7 . . 4 9 . . . .
 4 . . . . 7 . . .
 8 1 6 . . 5 . . .   ED=2.0/2.0/2.0

 . . . . . . . 1 2
 . . . . . . . . 3
 . . . . . . 4 . .
 . 5 . 1 . . . . .
 . 1 . 3 6 . . . .
 . . 2 . 7 . 8 . .
 4 . . 2 8 . . . .
 9 . . . . 5 . . .
 8 7 3 . . 4 . . .   ED=2.3/1.2/1.2


On the way, I picked up this too:
Code: Select all
 . . . 4 . . . . .
 . . . . . . 2 . 1
 . . . . . . 5 . 7
 4 1 . . . 7 . . .
 . 2 . 5 . . . 8 .
 . 7 . . . 2 . . .
 . . 8 3 . . . . .
 . . . . . 1 . . .
 6 . 3 . 9 . . . .   6 clues in  B12369, but only 19 overall


Regards,

Mike
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Re: How many 1-clue-box and 2-clue-box?

Postby m_b_metcalf » Wed Aug 31, 2022 2:30 pm

Code: Select all
 . . . . . . . . 6
 . . . . . . . 2 3
 . . . . . 4 . . .
 5 . . . . 6 4 . .
 2 . . . . . . . .
 8 3 . . 7 1 . . .
 . . . . 3 7 . . .
 . . 4 5 2 . . . .
 . 6 9 . . . . . .   19C

and two cousins:
Code: Select all
........1.......23.....4...5....64..2........76..81.......38.....452.....19......   19    5         
........1.......23.....4...5....64..2........76..81.......37.....452.....19......   19    5         
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Re: How many 1-clue-box and 2-clue-box?

Postby JPF » Wed Aug 31, 2022 6:14 pm

cousin of cousins...
Code: Select all
+---+---+---+
|...|...|..1|
|...|...|.23|
|...|..4|...|
+---+---+---+
|5..|..6|4..|
|2..|...|...|
|37.|.89|...|
+---+---+---+
|...|.2.|...|
|..1|37.|...|
|.48|...|...|
+---+---+---+   18C

JPF
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Re: How many 1-clue-box and 2-clue-box?

Postby JPF » Wed Aug 31, 2022 10:53 pm

There are no 17 with two empty boxes. So the game is over.

What about this one: find the minimum number of clues if B1B2B6B9=0 ?

Here is a first try:
Code: Select all
+---+---+---+
|...|...|..1|
|...|...|234|
|...|...|5..|
+---+---+---+
|...|..3|...|
|2.5|.6.|...|
|13.|4.7|...|
+---+---+---+
|...|.2.|...|
|3.6|.89|...|
|.78|..5|...|
+---+---+---+   21C

JPF
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Re: How many 1-clue-box and 2-clue-box?

Postby m_b_metcalf » Thu Sep 01, 2022 10:33 am

My first try:
Code: Select all
 . . . . . . . . 1
 . . . . . . . 4 6
 . . . . . . 8 5 9
 2 4 . 1 9 6 . . .
 . . . . 7 . . . .
 . 3 . . . 2 . . .
 . . 1 8 . . . . .
 6 . 7 . . 4 . . .
 . . 8 . . 3 . . .  21C

 . . . . . . . 3 2
 . . . . . . 4 . 6
 . . . . . . 8 5 .
 3 2 9 . . . . . .
 . 1 . 6 . . . . .
 . . . . 4 8 . . .
 1 4 8 . 6 . . . .
 . . . 5 . 9 . . .
 . 6 . . . 3 . . .  21C
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Re: How many 1-clue-box and 2-clue-box?

Postby m_b_metcalf » Fri Sep 02, 2022 2:48 pm

20C remains too elusive (for me). Here are a few more 21Cs, with patterns slightly different from those already posted:
Code: Select all
 . . . . . . . 1 2
 . . . . . . 3 . .
 . . . . . . 4 5 6
 1 2 6 . . . . . .
 . 7 . 8 . . . . .
 . . . . 3 4 . . .
 7 3 4 . 8 . . . .
 . . . 5 . 6 . . .
 . 8 . . . 1 . . .   ED=2.0/1.2/1.2

 . . . . . . . . 1
 . . . . . . . 2 3
 . . . . . . 4 5 6
 7 2 . 1 6 . . . .
 . . . . 8 . . . .
 . 9 . . 4 7 . . .
 . . 1 4 . . . . .
 3 . 8 . . 2 . . .
 . . 4 . . 9 . . .   ED=2.3/1.2/1.2

 . . . . . . . . 1
 . . . . . . 2 3 4
 . . . . . . 5 . .
 . . . . 6 3 . . .
 2 . 5 . . . . . .
 1 3 . 4 . 7 . . .
 . . . . 2 . . . .
 3 . 8 . 9 6 . . .
 . 7 9 . . 5 . . .   ED=2.5/1.2/1.2


Regards,

Mike
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