Knutson, Tao, and Woodward introduced puzzle pieces
consisting of two triangles and a rhombus (with edge labels).
They proved that tilings by these puzzle pieces (allowing rotations)
of triangular regions (with edge labels)
are counted by Littlewood--Richardson coefficients.
These numbers appear naturally in many contexts,
intersection of Schubert varieties,
multiplication of Schur functions,
and tensor products of irreducible representations of general linear groups.