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A puzzle where you have to optimize a certain objective function (maximize profit, minimize cost). There should ideally be a provable best answer, to avoid making the puzzle into an [open-ended] game.

A puzzle where you have to optimize a certain objective function. Sometimes these will be -focused, with goals such as:

However there are also many kinds of less mathematical optimization problems. Some examples:

Ideally, puzzle setters will know of a provably optimal solution before posting the puzzle. In the case where no provable best solution exists, when the "puzzle" is more of a game with no final answer, puzzles will be closed as open-ended. See here for why open-ended puzzles are off-topic: The end of open-ended puzzles