Arrange ten coins in the familiar ten-pin bowling formation (see figure). What is the smallest number of pennies you must remove so that no equilateral triangle, of any size, will have its three corners marked by the centers of three pennies that remain? Not counting rotations and reflections as different, there is only one pattern for the removal of the minimum number of pennies.
Note that the original pattern contains two equilateral triangles that are tipped so that their bases are not horizontal.
Give also a simple proof that your answer is minimal.
This problem (without the request for a proof) is from Martin Gardner's "The Colossal Book of Short Puzzles and Problems".