Background Consider the shape \$T(n)\$ consisting of a triangular array of \$\frac{n(n+1)}{2}\$ unit regular hexagons: Let's call \$T(2)\$ a tribone. John Conway proved that \$n = 12k + 0,2,9,11\$ if and only if \$T(n)\$ can be tiled (i.e. exactly covered without overlapping) by tribones. At...