SQLite/SQLAlchemy: Check values are either NULL or the same for several columns

Question

I would like to check for several columns that: For each column the value is either NULL or the same for all records.

For example, the condition holds for the following table

+------+------+------+------+
| Col1 | Col2 | Col3 | Col4 |
+------+------+------+------+
| A    | B    | NULL | NULL |
| NULL | B    | C    | NULL |
| A    | B    | C    | NULL |
+------+------+------+------+

How can I do that, preferably with one query?

EDIT:
An alternative question would be: How can I sum the distinct values of each of the selected columns

Answer 1

You can check if the distinct number of values in each individual column is less than or equal to 1:

SELECT COUNT(DISTINCT Col1) <= 1 ok1,
       COUNT(DISTINCT Col2) <= 1 ok2,
       COUNT(DISTINCT Col3) <= 1 ok3,
       COUNT(DISTINCT Col4) <= 1 ok4
FROM tablename; 

Or, you can get a result for the the whole table:

SELECT MAX(
         COUNT(DISTINCT Col1),
         COUNT(DISTINCT Col2),
         COUNT(DISTINCT Col3),
         COUNT(DISTINCT Col4)
       ) <= 1 ok  
FROM tablename;

See the demo.