SQL - Return count based on frequency of columns

Here is a database\query problem I have been trying to wrap my head
around for a couple days.

I have 7 columns. The first column is unique with someone's name.
The next 6 columns are products that could have been purchased.
Customer's could have been marked as having anywhere from 0 to all 6
fields tagged (not null).

Returning all the records where no fields or all 6 fields are not null
is easy. The problem I am having is doing 1 through 5 without a crazy
amount of where statements.

So basically, I would like to return all customer names that have 1 of
the 6 columns not empty, all customers that have 2 of 6 not empty. 3
of 6, etc.

I have run out of ideas and figured to try you guys for ideas. Any
hints or ideas? Or is this something not to be done via SQL?

Thanks.
Adam