How to count exclusive values in Google Sheets

Question

Ok, so I have data in this format:

      A     B     C     D
 2    X     X     X
 3    X           X
 4    X           X     X
 5          X         
 6                X     X
 ...

I have a formula that helps with a total count per column:

 =COUNTA(A2:A)

But how do I calculate “exclusives”? In this case, the expected answer for A, C & D is 0, while B should yield 1 (row 5).

The results will be laid out per column, so my pseudocode logic for column B would be:

 if (count(A)=0 and count(C)=0 and count(D)=0)
 then count(B)

Alternatively:

 count(b) where count(a)=0, count(c)=0, count(d)=0

Is my logic correct in the given context (Google Sheets)? What formula (or combinations of formulae) would I need to achieve the desired result in Google Sheets?

Edit: I'm using named ranges in my sheet, just in case that makes a difference as far as the formula is concerned.

Answer 1

Assuming that A is in Cell A1, flag the rows in which you are interested with, in a spare column (E assumed), something like :

=(counta(A2:D2)=1)*1 

copied down to suit. Count the rows in each column that are flagged and contain X with something like:

 =countifs(A1:A10,"X",$E1:$E10,1) 

in ColumnA and copied cross to suit.

Answer 2

English isn't my first language, I didn't comprehend everything you wrote, but now I think I've got it.

Counting first in columns won't work, counting rows will. Then count the columns.

      A     B     C     D     F
 2    X     X     X           3*
 3    X           X           2
 4    X           X     X     3
 5          X                 1
 6                X     X     2
 7    X                       1
 8          X     X           2
 9          X           X     2                 

                              2**

I made it like this, pretty easy I hope.

^* Count the X’s in the rows in another column (for example column "F") =count(B2:E2) → and drag it down.

^** Here we only count the 1’s (so you only count the rows where there is just one "X" =sumproduct(F2:F=1).

I hope this works for you.