Results with leading zero

I have a table

CREATE TABLE problem ( problem_id  integer, solution_count integer );

INSERT INTO problem VALUES (1001, 4);
INSERT INTO problem VALUES (1012, 11);

SELECT * from problem;
problem_id | solution_count
------------+---------------      1001 |             4      1012 |            11
(2 rows)


Is there a way I could write a query to produce the following?  I will
need the leading zero for solution < 10
problem_id | solution
-------------+------------       1001 | 01       1001 | 02       1001 | 02       1001 | 04       1012 | 01       1012 |
02      1012 | 03       1012 | 04       1012 | 05       1012 | 06       1012 | 07       1012 | 08       1012 | 09
1012| 10       1012 | 11
 
(15 rows)

Thanks.