Place four pennies on a table such that each touches at least one other.
For what arrangement will the area of the convex hull of this shape be maximized?
I just tried a Y shape, i.e. one central coin with three arrayed equally around it. I calculate its convex hull as Pi + 9*sqrt(3), which is .07 less than the so far winning solution of Pi + 10 + 4*sqrt(2)