fourpair

Fourpair is a term used in discrete mathematics and recreational puzzle communities to denote a configuration consisting of four disjoint pairs drawn from a finite set. In practice, a fourpair refers to a collection of four unordered pairs {a1, b1}, {a2, b2}, {a3, b3}, {a4, b4} where all eight elements are distinct and no element appears in more than one pair. Variants may impose additional constraints on the relationships within each pair or among pairs.

From a graph-theory perspective, a fourpair corresponds to a matching of size four: a set of four edges with no shared endpoints. If the underlying structure is a graph on eight vertices, any perfect matching of size four is a fourpair; in larger graphs, a fourpair is any subset of four disjoint edges. This formal view highlights the conceptual connection to matchings and their properties.

Variants may require that the pairs satisfy a global property (for example, that the sum of the elements in each pair equals the same value) or that pairs form a particular pattern (for example, non-crossing pairs in a geometric representation). In puzzle contexts, fourpairs are often used to illustrate constraints in matching problems or to design exercises involving partitioning eight items into four groups of two.

Usage and scope: The term fourpair is not standard in formal literature and appears mainly in puzzle circles, educational contexts, or informal discussions. When precision is needed, editors and mathematicians typically describe the object directly as four disjoint pairs or as a matching of size four.

See also: pair, pairing function, matching (graph theory), domino tiling, partition.