In discrete optimization, some or all of the variables in a model are required to belong to a discrete set; this is in contrast to continuous optimization in which the variables are allowed to take on any value within a range of values. Here, we consider two branches of discrete optimization. In integer programming, the discrete set is a subset of integers.
Summary: The 15 Puzzle consists of 15 squares numbered from 1 to 15 that are placed in a 4 by 4 box with one empty position. The objective of the puzzle is to reposition the squares by sliding them one at a time into a configuration with the numbers in order.
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