A conundrum is primarily defined as a riddle, the answer to which involves a pun or a play on words. Secondary def. is something that puzzles.

Perhaps the term oxymoron (no streets jokes now!) would be more appropriate. You know, like, Senate ethics committee, or jumbo shrimp. Then there's my automotive favorite from an all too common ad; "All original. New paint, new upholstery, mag wheels, almost new tires. Engine rebuilt 10,000 miles ago......