The New Sudoku Players' Forum

[udosuk]

Is this shape possible?

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TTT
TT.
T..

[JPF]

Is this shape possible?

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TTT
TT.
T..

For the wat-boxes :

The only possible shapes are :
shape 1

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TTT
TTT
...


(270 solutions giving 40680 grids)
see my previous post.

shape 2

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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

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TTT
TT.
T..


is not possible with the wat-boxes

Here is an example for the shape 2 :

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 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

[udosuk]

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?

[JPF]

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 :

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TTT
TTT
...


984 solutions*

Example :

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 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 :

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TTT
TT.
T..


5544 solutions*

Example :

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 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 :

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TTT
TT.
..T
 

940605 solutions*

Example :

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 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

JPF

[udosuk]

Thanks JPF! Very comprehensive work...

Now I think we have to try proving mathematically why 7-boxers couldn't exist....

[beetjepeetje]

Here is a band with all 3 boxes satisfying this property:

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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%:

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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..

[udosuk]

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:

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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