Article updated on August 28, 2017

In a previous article Lookup Unique based on Multiple Conditions
and Automatically filter unique row records from multiple columns,
I presented a solution to filter unique row records.
In this article i am going to explain how to count the number of unique row records.

Here is the array formula:
=SUM(IF(((MATCH(A2:A25&B2:B25&C2:C25&D2:D25,A2:A25&B2:B25&C2:C25&D2:D25,0)) >=(ROW(A2:A25)-(MIN(ROW(A2:A25))-1)))=TRUE,1,0)) + Ctrl + Shift + Enter

MATCH(A2:A25&B2:B25&C2:C25&D2:D25,A2:A25&B2:B25&C2:C25&D2:D25,0)) >=(ROW(A2:A25)-(MIN(ROW(A2:A25))-1) This part of the formula filter out those values that are unique and return TRUE or FALSE.
{1,2,3,4,5,6,7,8,9,10,11,12,13,14,1,16,12,9,6,6,9,12,11,4}>={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24}
{TRUE,TRUE,TRUE,TRUE,TRUE,TRUE,TRUE,TRUE,TRUE,TRUE, TRUE,TRUE,TRUE,TRUE,FALSE,TRUE,FALSE,FALSE,FALSE,FALSE,FALSE,FALSE, FALSE,FALSE}

IF(((MATCH(A2:A25&B2:B25&C2:C25&D2:D25,A2:A25&B2:B25&C2:C25&D2:D25,0)) >=(ROW(A2:A25)-(MIN(ROW(A2:A25))-1)))=TRUE,1,0)) This part converts TRUE to 1 and False to 0.

Sum() sums the 1 and 0:s.