Lozenges in a Hexagon
A regular hexagon of side length 3 is cut by three families of parallel lines into 54 unit equilateral triangles. A lozenge is a rhombus formed by two of these unit triangles sharing an edge. In how many ways can the hexagon be tiled exactly by 27 lozenges? Tilings related by a symmetry of the hexagon count as different. Give an integer.
Related problems & prerequisites
Worth solving first
- Dominoes on the Full Chessboard 7.0/10
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Source: Counts plane partitions in a box (P. A. MacMahon, early 20th century); the lozenge-tiling interpretation is classical. Statement written for AxiomIQ.