Chosennumeric

Chosennumeric is a term used in recreational mathematics and theoretical computer science to designate a number selected according to a predefined scoring or selection rule from a given set. The word combines "chosen" and "numeric" to emphasize the element that a rule identifies as optimal or representative within a context.

Definition and formalization: Given a set S of numbers and a selection function f that assigns a score to each element, a chosennumeric is an element x in S such that f(x) is minimal (or maximal, depending on the convention) among all elements of S. If multiple elements share the same optimal score, any of the tied elements may be considered a chosennumeric. In some treatments, the selection function maps to simple digit-based metrics, while in others it uses more complex cost or distance measurements.

Origins and usage: The term emerged in online puzzle forums and informal mathematical discussions in the 2020s to describe optimal elements under arbitrary scoring rules. It is not a standard term in formal mathematics and lacks a single universal definition; instead, its meaning is defined by the chosen set and scoring rule in a given context.

Properties: The chosennumeric depends on both the underlying set and the scoring rule. Altering the set or the rule can change which element is chosen. The concept highlights how selection criteria influence outcomes and can vary with different representations or bases.

Examples: For S = {14, 23, 37} and f(n) = sum of digits, the sums are 5, 5, and 10, so 14 and 23 are chosennumerics under this rule. In other contexts, the rule might prefer numbers closest to a target value or with minimal digit count.

Applications: Used in puzzle design, algorithmic selection problems, and as a teaching aid for illustrating optimization concepts.