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?
(In reply to Overlooked problem
by Steve Herman)
I can do better. Take five pennies and arrange them in a row of three on top of a row of two. The center of the row of three is touching all four other pennies. Remove that penny to leave four pennies in a U-like shape. This convex hull's area is significantly greater than the area from the square or diamond configuration.