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".
Eioru
 
Posts: 182
Joined: 16 August 2006

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
JPF
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Posts: 3752
Joined: 06 December 2005
Location: Paris, France

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
coloin
 
Posts: 1632
Joined: 05 May 2005

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 . .


JPF
JPF
2017 Supporter
 
Posts: 3752
Joined: 06 December 2005
Location: Paris, France

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
coloin
 
Posts: 1632
Joined: 05 May 2005


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