Clever!

But the A:A column form did not work for me; I had to use a range:
=SUM((A1:A9="Monday")*(B1:B9<>"")) within {}.

Just checking, you didn't have the formula in one of the 2 columns did you? If you do then it creates a recursive lookup doing the A:A and so won't work. Putting it in a separate column works on Office 2010.

No, I had it in Col E.

But I'm still using Excel 95 so it might not be so "facility-rich", but it has most main things.

Maybe 95 doesn't support the ranges that way - have to say I normally use a fixed range anyway and only reason I did it this way was because that was how the OP started out. Even so, it is a very cool function of Excel that may come in useful in future (I usually only find these things when someone asks for something a little off the wall).

Excel 95 does support column range in things like VLOOKUP where a range is expected, but not in this array formula, probably cuz a range does not normally appear in an IF = test. Have found other minor quirks like this but they are usually easily surmountable.

I think this is best done with a pivot table as mentioned. (if I understand the problem)

see an example here

Already solved by ian72.