Weird Question

Everything about Sudoku that doesn't fit in one of the other sections

Postby udosuk » Mon Jul 31, 2006 6:39 am

Is this shape possible?

Code: Select all
TTT
TT.
T..
udosuk
 
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Joined: 17 July 2005

Postby JPF » Mon Jul 31, 2006 6:33 pm

udosuk wrote:Is this shape possible?

Code: Select all
TTT
TT.
T..

For the wat-boxes :

The only possible shapes are :
shape 1
Code: Select all
TTT
TTT
...
(270 solutions giving 40680 grids)
see my previous post.

shape 2
Code: Select all
TTT
TT.
..T
(1143 solutions giving 1443 grids)
There are only 4 solutions giving 4 grids each, 288 giving 2 grids each ; the remainings are valid puzzles.

This shape
Code: Select all
TTT
TT.
T..
is not possible with the wat-boxes

Here is an example for the shape 2 :
Code: Select all
 1 2 3 | 4 5 6 | 7 8 9
 8 9 4 | 2 3 7 | 5 6 1
 7 6 5 | 1 9 8 | 4 3 2
-------+-------+-------
 4 1 2 | 7 6 5 | . . .
 5 3 9 | 8 4 2 | . . .
 6 7 8 | 9 1 3 | . . .
-------+-------+-------
 . . . | . . . | 8 7 6
 . . . | . . . | 9 2 5
 . . . | . . . | 1 4 3

(valid puzzle )


JPF
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Postby udosuk » Tue Aug 01, 2006 8:43 am

So the triangular shape is not possible with 6 wat-boxes... How about 6 T-boxes in general?

If it's all impossible I think we might be able to prove it mathematically (something to do with row/column combination)...:) How about the L-shape 5-boxer?
udosuk
 
Posts: 2698
Joined: 17 July 2005

Postby JPF » Tue Aug 01, 2006 8:49 pm

udosuk wrote:So the triangular shape is not possible with 6 wat-boxes... How about 6 T-boxes in general?

Yes, it is possible ...
Here are the different shapes fot the t-boxes in general :

Shape A :
Code: Select all
TTT
TTT
...
984 solutions*

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



Shape B :
Code: Select all
TTT
TT.
T..
5544 solutions*

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



Shape C :
Code: Select all
TTT
TT.
..T
 
940605 solutions*

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


*The number of resulting grids has to be calculated.

That's it for the t-boxes & wat-boxes:)

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Postby udosuk » Wed Aug 02, 2006 4:58 am

Thanks JPF! Very comprehensive work...

Now I think we have to try proving mathematically why 7-boxers couldn't exist....:)
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Joined: 17 July 2005

Postby beetjepeetje » Wed Aug 02, 2006 1:22 pm

udosuk wrote:Here is a band with all 3 boxes satisfying this property:
Code: Select all
123|456|789
894|137|265
765|298|134

I think the challenge is to get all 9 boxes satisfying this... Will have to work on that...:)


my sudoku generator gives as the default 'unit' sudoku this one, satisfying
the property 100%:
Code: Select all
123 456 789
456 789 123
789 123 456

234 567 891
567 891 234
891 234 567

345 678 912
678 912 345
912 345 678


This unit sudoku type can be extended to any N^2 x N^2 sudoku variant..
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Postby udosuk » Wed Aug 02, 2006 1:26 pm

You got the wrong property. It's not the one stated by liturgygeek...

Besides, your grid isn't the most canonical grid... The most canonical would be:

Code: Select all
123 456 789
456 789 123
789 123 456

231 564 897
564 897 231
897 231 564

312 645 978
645 978 312
978 312 645
udosuk
 
Posts: 2698
Joined: 17 July 2005

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