denis_berthier wrote:logel wrote:From some manual case studies I know that k is at least 5.

I bet you'll find a larger k on a larger collection.

It took really much more time than expected. The reduction of planes is a severe problem. Chasing bugs too.

The answer is 6. (not 42!)

So T&E(S6) solves all known sudoku represented by 817681 puzzles of the current hardest list, all SER 10.3 or more.

S6 stands for pattern with max 6 base lines, i.e. with max 6 true nodes in the pattern.

The S6-pattern used are additionally restricted to max three planes, so its in fact < S6.

If the restriction is on two planes, only 169 are left unsolved.

But I have absolutely no clue how you might compare this to T&E(B7). Looks like apples and oranges.

Re-reading your statements in this thread, I still don't understand why you object to a universal pattern definition.

I put up a new thread proposing such a definition: universal-elimination-pattern

There you also find more details of my results.

I appreciate very much your work on nrczt-chains and braids, but these pattern don't loose their value when embedded in a larger scope.

Any comparison of size or complexity needs a common basis.

Another mystery is how you justify that T&E(Bx) build a strict hierarchy for x=2,3,4,... in whatever sense of simplicity.

The size/complexity of pattern on T&E level one does not limit the size/complexity of the primary elimination.

Some observation (more to do) rather show that smaller patterns on level one increase the complexity of the primary pattern in some cases.

I mistrust the simplest-first strategy to be valid globally.