What to do with a contest puzzle questions? Close, or leave them as they are?
Example : Apple eating problem
There are some very grey areas in the puzzle questions that make it difficult to say if something is on or off topic with them.
If someone is trying to pose a challenge to the community, that absolutely belongs on the programming puzzles and code golf stack exchange site. That is one end of the spectrum. Note that math puzzles are on topic on Math.SE: puzzles tag (logic and math puzzles fit there - islands of liars and truth tellers and the such).
On the other end of the spectrum is "I'm trying to solve this puzzle, but am having approaching it with a brute force. How can dynamic programming be applied to this?" Note that in this type of question the poster doesn't know the answer and its not so much a challenge for the community to come up with solutions but rather an issue of algorithms that happens to be applied to a puzzle.
In the middle there's the "I have this working code for this puzzle, how can I improve its performance so that it can run within the timeframe or memory allotted" which falls in the vicinity of code review.
There is also the "this code doesn't work" which still belongs on Stack Overflow, no matter if it is a puzzle or not - it is an implementation / debugging issue.
So, it is not a cut and dried thing about where puzzles belong.
For a good P.SE question about a puzzle, the following things make it a better question:
... that said, if you don't like the questions or don't think they're useful or helpful to the world at large... down votes are likely not inappropriate.