The Prisoner's Dilemma

Christopher West (PMP) and the Georgia Southern Eagle Problem Solvers got this one. The answer is that $E$ can be any point at all on $CD$, because no matter what points $E$ and $F$ are chosen, the purple and pink areas are equal. To see this, note that by the usual area formula for triangles, each of the triangles $AFD$ and $ABE$ has area half that of rectangle $ABCD$, so the sum of their areas is equal to that of $ABCD$. On the other hand, simply looking at the regions in Figure 1, the area of $ABCD$ is the sum of triangles $AFD$ and $ABE$, plus the regions of the rectangle that they miss (precisely the purple areas), minus the area of their overlap (since that’s counted twice in the sum), which is exactly the pink area. Since the sum of $AFD$ and $ABE$ is already exactly the area of the rectangle, the purple areas and the pink area must be equal.