Counting distinct values in MDX

How many elements in the set have distinct values ? This sounds like a simple question. Apparently, this is well known problem in Excel, and there is a classic solution for it. There are plenty of sites in Internet (for example here and here) which give the following solution:

=SUM(1/COUNTIF(A1:A6,A1:A6)))

(note that this formula needs to be entered with Ctrl-Shift-Enter to indicate that this is array formula, or it won’t give right result – one of the Excel quirks)

When someone showed me this solution, I just stared at it and I couldn’t understand how it worked. Only rewriting it in MDX clarified what was going on. Let’s take the following example based on Adventure Works – we want to count how different letters the product names start from (just wanted to pick something for which Product dimension didn’t have dedicated attribute, because otherwise it would’ve been too simple). The MDX which performs the same algorithm as Excel formula above in these conditions will look like following...