daj95376 wrote:In my previous post, I was looking for confirmation that the puzzle didn't contain an acceptable SK-Loop. From the responses, I'm not sure if there's a consensus or not. So, I'll just proceed with puzzles that I consider to contain an (acceptable to me) SK-loop.

It would be interesting to have more details on which SK loops in my file of "sk loop seen" you don't recognise.

Your former example is a valid SK loop

daj95376 wrote:Consider this puzzle:

In each case, the puzzle's solution contains a single value from each side of the (ab=cd) term.

FWIW: This happens in all 1,944 (acceptable to me) SK-loops that I found in champagne's 31,804 puzzles from HARD_11.

Now, I'm probably the only one who finds this interesting.

May be we have not been clear but this is the point noticed earlier by ronk.

There is a statistical reason to have that, but we have so far no logical proof that it must be, so it has to be established in each case.

The statistical reason is very simple. each belt of your "ab" or "cd" is valid or false in bloc.

Here is the better chance to have a contradiction.