MathDB

Last year, the U.S. House of Representatives passed a bill which would make Washington, D.C. into the

51

st state. Naturally, the mathematicians are upset that Congress won’t prioritize mathematical interest of flag design in choosing how many U.S. states there should be. Suppose the U.S. flag must contain, as it does now, stars arranged in rows alternating between

n

and

n - 1

stars, starting and ending with rows of n stars, where

n \ge 2

is some integer and the flag has more than one row. What is the minimum number of states that the U.S. would need to contain so that there are at least three different ways, excluding rotations, to arrange the stars on the flag?

Problem Statement