Extremal problem

An extremal problem involves finding the best, largest, smallest, or most extreme value of a quantity within a set of constraints. In mathematics, this often means identifying the maximum or minimum possible value of a function or property under certain conditions. For example, determining the shortest path connecting two points within a maze or the largest possible shape that fits inside a given boundary. These problems help us understand the limits of what is achievable and are widely used in optimization, design, and analysis across various fields.