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Default Count with merged cells

I need to count the number of blank cells, or lacking that, the number of
cells that contain either numbers or alpha characters in a range. Some cells
are merged in the range, and COUNTBLANK "counts" the merged cells as having
blanks. That is, if two cells are merged and something is entered in the
merged cell, the count functions "see" the second cell as blank. If three
cells are merged, the functions read two of the cells as blank. COUNT,
COUNTIF, and COUNTA will only return a value of "1" when the merged cells
contains data. Is there a way to count all the cells in the range that are
blank WITHOUT including the "blank" second, third, and so on cells in merged
cells among the count? Or is there a way to count the cells that have data
and include the second, third, etc. merged cells among the count?