A few years after welcoming Vermont and Kentucky, states 14
and 15 into the union (in 1791 and 1792, respectively), a new
version of the flag was created that had 15 stars and 15
stripes. As the U.S. continued to add new states, there was
concern about having to continually add additional stripes. The
solution: revert to 13 to represent the original 13 colonies,
and let the stars represent the States.
Incidentally, there have been 27 official versions of the U.S.
flag, each with a different number of stars.