2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60673We state, discuss, provide evidence for, and prove in special cases the conjecture that the probability that a random tiling by rhombi of a hexagon with side lengths $2n+a,2n+b,2n+c,2n+a,2n+b,2n+c$ contains the (horizontal) rhombus with coordinates $(2n+x,2n+y)$ is equal to ${1/3} + g_{a,b,c,x,y}(n) {\binom {2n}{n}}^3 / \binom {6n}{3n}$, where $g_{a,b,c,x,y}(n)$ is a rational function in $n$. Several specific instances of this "1/3-phenomenon" are made explicit.16 pages, AmS-LaTeX, uses TeXDraw; a few typos correctedCombinatorics05A15 05A19 05B45 33C20 33C45 52C20text