## Weird Question

Everything about Sudoku that doesn't fit in one of the other sections
Is this shape possible?

Code: Select all
`TTTTT.T..`
udosuk

Posts: 2698
Joined: 17 July 2005

udosuk wrote:Is this shape possible?

Code: Select all
`TTTTT.T..`

For the wat-boxes :

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

shape 2
Code: Select all
`TTTTT...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
`TTTTT.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
JPF
2017 Supporter

Posts: 3755
Joined: 06 December 2005
Location: Paris, France

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

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
`TTTTTT...`
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
`TTTTT.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
`TTTTT...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

JPF
JPF
2017 Supporter

Posts: 3755
Joined: 06 December 2005
Location: Paris, France

Thanks JPF! Very comprehensive work...

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

Posts: 2698
Joined: 17 July 2005

udosuk wrote:Here is a band with all 3 boxes satisfying this property:
Code: Select all
`123|456|789894|137|265765|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 789456 789 123789 123 456234 567 891567 891 234891 234 567345 678 912678 912 345912 345 678`

This unit sudoku type can be extended to any N^2 x N^2 sudoku variant..
beetjepeetje

Posts: 9
Joined: 22 July 2006

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 789456 789 123789 123 456231 564 897564 897 231897 231 564312 645 978645 978 312978 312 645`
udosuk

Posts: 2698
Joined: 17 July 2005

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