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 mathematics-focused, with goals such as:
- maximizing bananas transported to market: A camel transporting bananas
- minimizing area of a blanket: A blanket for my baby snake
- maximizing the smallest amount that 8 coins can pay for: Eight coins for the fair king
However there are also many kinds of less mathematical optimization problems. Some examples:
- chess minimizing the "score" of chess pieces to control the whole board: How many Chess Pieces are needed to control every square on the board? No Piece Restriction
- sudoku minimizing the numbers covered by a "Sudoku net" that will always leave a solvable Sudoku: Sudoku net that is always solvable
- board-games minimizing or maximizing "shots" fired in a Battleships game, given certain constraints: Shooting them blanks (double optimization task)
- matches minimizing the number of matches removed to leave behind no triangles: How many matchsticks need to be removed so there are no equilateral triangles?
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