The programming-puzzle tag seems a bit useless given we're called 'Programming Puzzles and Code-Golf'. It seems to be used when no other objective winning criteria is used and sometimes used in conjunction with other winning criteria tags.
15 out of the 29 questions in the tag are closed and of the remaining 14, 7 of them have other criterion that suggest the winner. This leaves a total of 7 valid programming-puzzle tags.
I propose we remove the tag from questions with another winning objective tag and on the other questions replace it with code-challenge or possible add programming-puzzle as a synonym of code-challenge
A programming puzzle includes a goal, a partially completed program, and rules outlining how the program can be modified. The program is specifically designed to make achieving the goal difficult. An answer to a programming puzzle takes the program and modifies it only in ways specified in the rules, so that the goal is achieved.
This is very clearly distinct from code challenge and golf. Just because the latter tends to be easier to do and more popular is no reason to make the former off-topic. \$\endgroup\$