ronk, thank you for the interesting example, with 3 deviations from standard SK loop: the 123's in row 7 linking boxes 7 & 8, the linking 479's in box 4, and the single linking 6 in box 7. Never-the-less, it still conforms with my results.

I have simply been making observations, and haven't as yet found the logical framework to explain it. The observations however are rather compelling as I can't find an exception having studied over a dozen examples of 'almost SK loops'. In all cases where there is a single deviation, ie 3 digits linking the chain in one of the 4 boxes, the following holds: the 3 digits end up in 3 of the 4 cells that are part of the chain in the box. In the other 3 boxes, the 2 linking digits end up in 2 of the 4 cells. Thus the usual eliminations in the 4 boxes of the loop can be made. The problem is that one of the digits of the pairs of digits linking the row or column is 'squeezed' out because the 3 digits have been accommodated, so one row or column does not end up with the two row or column linking digits in the 4 cells, thus in one row or column the usual eliminations cannot be made. At present I don't know how to predict which one without the hindsight of seeing the solution.

I think this has implications for manual solving as these loops are relatively easily seen.

pjb