Quiz Night

In my previous post, I made the comment:

In general, if you have a three-column index that starts with the same columns in the same order as the two-column index then the three-column index will be bigger and have a higher clustering_factor.

So what scenarios can you come up with that fall outside the general case ?
Alternatively, what argument could you put forward that justifies the general claim ?

I’ll try to respond to comments on this post a little more quickly than the last one, but I still have quite a lot of other comments to catch up on.