Some thoughts now that zebras and butterflies disappeared for a while

Havard wrote:In the same way, one should keep a 1off2on list of 18's from gordons list in order to reduce the amount of 18's that get searched for 17, and I think that was your point JPF? If anyone is interested I could generate such a list.

Yes, in some way.

My point was that doing a {-2+1} on a 18, which is a long process, does not take into account the fact that the set

G of the actual 17s is

almost closed for the 2 operators {-1+1} and {-2+2}.

So can we eliminate a 18 only by a quick check with

G?

I agree with gsf and coloin that the list of 18s ={-1+2}

G will be large.

coloin mentionned 40000 x 250 =10^7.

[edited, thanks to coloin]other idea :

Why not trying a {-2+1} on 18 clues puzzles with more than 1 solution (2,3,..)?

kjellfp wrote:What do we know about Gordons current list? Is it closed for n=1 or n=2?

Gordons current list

G is supposed to be kept closed for n=1 and n=2, from time to time (by Havard and now by gsf, and maybe by others).

I did a full {-1+1} a week ago.

kjellfp wrote:How many equivalence classes do we get?

I think it's an information which could be of interest.

More precisely, what are the properties of the 17s within classes with many equivalent.

gsf, how is it possible to list, for each 17 of

G, the equivalents modulo {-1+1} and {-2+2} ?

- Code: Select all
` sudoku -go{-1+1} G.dat`

eliminates the duplicates.

kjellfp wrote:And a completely different question: What is the biggest number N for which we have proven that there is no N-clue Sudoku puzzle. We all believe that N=16 is the maximum, and it's obvious that N must be at least 7. But what do we know?

That is a recurrent question.

see

hereThe results are still poor.

JPF