Using Multiple, Noncontiguous Ranges in COUNTIF?
 

I have data in several non-contiguous ranges that I need to summarize with
COUNTIF. No matter what I do, though, I get a VALUE! error. I know the
problem isn't the source data, since the COUNTF formula works fine if I use
just one of any of the ranges. I've tried this:

=COUNTIF((Q4:Q20,S4:S20,X4:X20),"9/1/2006")

and this:

=COUNTIF((Q4:Q20+S4:S20+X4:X20),"9/1/2006")

and this:

=COUNTIF(Q4:Q20,S4:S20,X4:X20,"9/1/2006")

But these either return VALUE! or (in the last example) are simply plain
wrong because the formula interprets the second two ranges as new arguments.

Help! What am I doing wrong?