I'm not sure why you can't use the formula you suggested, but even though the
suggestions based on the column number (mod 2) will work, I wouldn't use it.
If you decide to add a column (for descriptions???) or delete a column or put a
date into one of those columns, you may find that it doesn't give you the
results you want.
I would insert an extra row (and hide it later). I'd put an indicator in that
row for each column that needed to be summed.
Then I could use:
=sumif(1:1,"x",3:3)
(where row 1 is my hidden row with the X's and row 3 is the row I want to sum)
It may seem like more work to add those indicators, but when you share the
workbook with others and they start making changes, you may be happier.