A 35-year-old male develops involvements of PIP, DIP and metacarpophalangeal joints with sparing of the wrist and carpometacarpal joints. The probable diagnosis is -
First let me exclude the other options :


MTP joint involvement is not seen in OA.
DIP joint involvement is not seen in RA.
In pseudogout, large joints like knee, ankle are involved. Small joint are not involved.


Now we are left with psoriatic arthritis. In Psoriatic arthritis any pattern of joint involvement can be seen.
Psoriatic arthopathy
Osteoarthritis
Rheumatoid arthritis
Pseudo gout