Since i saw, that a couple of good mathematicians is watching this forum, let me ask a question. I am not that good in combimatorics, so it might be easy to answer.

The background is, that i wondered, if it could be a good measure to rate a puzzle, how much units you have to look at to make an elimination. It soon turned out not to be a good idea, because an 18 cell xy-chain could need 9 units, as much as the hardest possible step.

But the question remained: How many unit combinations are there in this respect ? That means, all combinations of max. 9 units out of the rows, columns and boxes, but you must not count

- duplicates, e.g. the 3 rows and 3 boxes of a band

- combinations with "isolated units", e.g. box 1 and box 9 (the hard part for me)

Routine or challenge ?