Counting and summing based on 2 columns

[inquisitor]

Variations of this have been asked before, possibly the exact same thing but I'm still struggling to get this to work right -- please do feel free to point me to another post if this has been answered.

Given a spreadsheet with two (non-adjacent, though I don't think it matters) columns. Column A has names, or may be blank. Column B has an "X" in it, or may be blank.

I'd like a single number that counts the number of X marks for the UNIQUE set of names in Column A. Preferably without using a helper column because I'd like to drag the formula across another 11 columns of Xes.

Given this table:
A B
One X
Two X
Three
Four X
Two X
Three
One X
Four

The value I'd like at the bottom of the B column should be 3 (representing that One, Two, and Four have Xes).

Thanks for any help you can provide!

 

[Aladin Akyurek]

Outstanding. I ran into a bit of trouble because my cells actually have 0 values instead of being empty but was able to identify that as the root cause and update the formulas accordingly. Thank you again so much for your patience help -- invaluable.

You are welcome.

Let's hope I don't need to add new services, though I have a disconcerting feeling that I will...

I was afraid you would say that.

 

[inquisitor]

It's like I'm a soothsayer. Now I've got A, B, and C. Fortunately, not all combinatorics are relevant today. I have five categories: A, B, C, A+B, A+B+C. Possible to extend this model, or is it fruitless and I should seek another solution?