sopadeajo wrote:
In fact your 29-permutable set is not unique, neither your 11-permutable; and so your disproof is invalid.
What?!?! Go and re-read your own conjecture. "Given a p(n) solutions-sudoku ..." -- I gave you a 29-permutable set. It didn't have a 23-permutable subset. So your conjecture is false.
You are right, it should be :" There exists at least a p(n) solutions-sudoku... to n max"
define a set of clues to be n-FPPS if it is p(n)-permutable and it contains at least one p(k)-permutable subset for each k=1,...,n-1
we seek the maximum n such that there exists at least one n-FPPS set of clues
Yes.We seek *all the successive* n-FPPS from n=4 (1,2,3 are already known) to maximum n-FPPS found ,for each n (n=4,5,6,7,8,..,max n). In S-1 or S-2 or S-3,... (Just use S-1, if this suffices).
Though i was thinking too in a n-FPPS that would contain at least one k-FPPS for each k=1,...,n-1. But this would be probably too difficult or might be impossible.
