## Can any grid be fiendish

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

### Can any grid be fiendish

can this always be reduced to a very hard puzzle?
Does anyone know?
Pi

Posts: 389
Joined: 27 May 2005

As a complete guess with zero substantiating evidence, I'm going to say yes.
PaulIQ164

Posts: 533
Joined: 16 July 2005

This is undoubtedly true, yet impossible to prove.

There are such vast numbers of puzzles contained within a single grid that the grid would have to be outstandingly special for every one of those puzzles to be easy. And this just won't happen.

But there is no way of ever proving it...

Gordon
gfroyle

Posts: 214
Joined: 21 June 2005

### fiendish

I agree but still I would like to see a fiendish set of clues for that one.
Code: Select all
`+-------+-------+-------+| 1 2 3 | 4 5 6 | 7 8 9 | | 4 5 6 | 7 8 9 | 1 2 3 | | 7 8 9 | 1 2 3 | 4 5 6 | +-------+-------+-------+| 2 3 1 | 5 6 4 | 8 9 7 | | 5 6 4 | 8 9 7 | 2 3 1 | | 8 9 7 | 3 1 2 | 5 6 4 | +-------+-------+-------+| 3 1 2 | 6 4 5 | 9 7 8 | | 6 4 5 | 9 7 8 | 3 1 2 | | 9 7 8 | 2 3 1 | 6 4 5 | +-------+-------+-------+`
bennys

Posts: 156
Joined: 28 September 2005

here the hardest according to
http://magictour.free.fr/suexrat9.exe
from 1000 randomized minimal sudokus over this grid:
rating: 281

...4.....
..6.8.12.
.....3.5.
..1.6..97
...8.72..
8.73.2...
.12...9..
.4.......
..8...6..

I think, it could be feasable to proof that there is a fiendish over each
grid. Suppose e.g. you fill in 2 bands and only consider all puzzles
over the 3rd band. Just 416 possibilities, can they all be made fiendish ?
(I don't know how exactly fiendish is defined)

Or take a 3-rookery, can it be fiendish ? Well, there are lots of
nonisomorphic 3-rookeries, though.

Or how about B5689s ? Only 2865 grids to examine.

-Guenter
dukuso

Posts: 479
Joined: 25 June 2005

### thanks

thanks
bennys

Posts: 156
Joined: 28 September 2005