Two park rangers at a Civil War battle site are assigned the job of counting a pile of cannonballs arranged in the shape of a regular tetrahedron. The first ranger says, “We will have to disassemble the pile to count the cannonballs in the middle.”

The second ranger replies, “That won’t be necessary. Just tell me the number n of balls along one side of the bottom layer, and I can calculate the total number in the stack.”

What closed-form formula did he use?