The New Sudoku Players' Forum

[Papy]

I have allready publish ths idea butI don't had any comments

The idea is if we cannot fill a bloc with 16 clues we cannot also fill a grid (3 blocs)

The princip seems logical.
So to demonstrate this théory I write code to enumerate all the combinaisons of 16 clues in a bloc.
Just like I think no solution.
So if no blocs with 16 clus no susoku also.
But is it possible to fill a block with 17? Good verificatio No?
I take back my code and compute with 17 clues and
same result no solution. So at this time the question:is my code wrong?

To verify 18 clues
And a this time I get solutions. So the generator and the filter seem goods A surprise witjh every valids blocks always the same dispositions!!!!! You can change all the clues you still have 14084 dispositions

So the coclusion is

a band with 16 cues : impossible
a band with 17 clues impossible
a band with 18 clues possible
But a grid with 17 clues possible
a grid with 16 clues : always a mystery!!


But for me that means that the values of the digits have no impact on the solution.there give differents problems but cannot help us to solve them

Take a box alone:impossible to have less than 8 clues. On each 362880 boxes possibles?

Take 2 boxes also 8 clues but the set of possibility are less than for one
1 2 3 4 5 6
4 5 6 7 8 9
7 8 ? 1 2 ?

You can scramble the digits never you could solve a box wit 7 clues!!!
So for me no mùatter for the digits. More if we always have the same numbers of solutionswith 18 it's for the same reason.

What do you think of that concept
But I still don't know why 18 clues for a block and 17for a sudoku

Papy

[Papy]

Hi,

I have continued my seach and the answer is that a grid is not 3 blocks!
It's easy to demonstrarte that uyou cannot make a valid grid with a band and
16,17,18,19,20 reveleds but it's easy to do a valid grid 81 cells with 20 reveleds.

So I cannot say :
Mae a 16 block is impossible so make a 81 grid is iompossible
In fact a 81 cannot be separate in parts a Grid is indivisible so
the demonstration must work with a total Grid

Papy