Tessellate S.T.E.M.S (2019) - Mathematics - Category B - Set 3 - Objective Problem 3

As shown in the picture below, three vertices of a cube form an equilateral triangle whenever the segments connecting them are all diagonals of the faces of the cube (it is impossible to form an equilateral triangle using edges of the cube or interior diagonals). There are ${8\choose3} = 56$ was to select three vertices from the cube. There are precisely $8$ equilateral triangles as described above (each vertex is a vertex in precisely three triangles, and each triangle has three vertices: $\frac{8\times 3}{3} = 8$ ). $\begin{aligned} \frac{8}{56} &= \frac{1}{7} \\ 1 + 7 &= \boxed{8} \end{aligned}$