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I've seen lots of code-golf and code-challenge questions, and few code-bowling and code-curling ones that didn't go over so well. What types of puzzles are there? Why aren't we seeing them?
Rather than thinking of "programming puzzles" as a separate category my take has been that they are all puzzles.
There's also king-of-the-hill. The problem with that kind of question is best summed up by Peter Taylor's comments on this answer.