extremal problems

Extremal problems involve finding the maximum or minimum value of a particular quantity within a specific set of rules or conditions. For example, mathematicians might ask, "What is the largest possible size of a shape with certain properties?" These problems help identify the best or worst case scenarios in fields like mathematics, physics, and computer science. They often require exploring many options to determine the extreme (highest or lowest) outcome, providing insight into the limits and capabilities of systems or structures.