How do I count the number of cells in a row that are either not blank or above zero in a non sequential range?

For example, I want a column in a golf course chart to count the applicable "Par" columns of each of the course holes. Although my sheet has provisions for 18 holes across the page, some courses are only 9 hole courses, so the remaining holes 10-18 are blank in their Par columns.

In my course summary table, I want a column to be "Number of Holes" which is a calculation of how many Par cells have data in them.

The par for each course is within the following cells:
($C3,$F3,$I3,$L3,$O3,$R3,$U3,$X3,$AA3,$AD3,$AG3,$AJ3,$AM3,$AP3,$AS3,$AV3,$AY3,$BB3)
Pic to help explain:
Excel_Count_Non_Blanks.jpg