Can I write a formula that returns the number of distinct entries in a range?

1) To find the number of unique items in a range you should enter the following formula
=SUM(1/COUNTIF(A1:A10,A1:A10)) or you could use the following that will not bring an error if there are some blanks
=SUM(IF(COUNTIF(A1:D100,A1:D100)=0, "", 1/COUNTIF(A1:D100,A1:D100)))

or try this one too

or even simplier =COUNTIF(A1:B12,"<>""")

2) to find specific items, then just use the COUNTIF formula.

Hope this helped, please check our exemples and templates.