How many states can the US have and keep a flag with a reasonably close to
square arrangement of stars like it currently has?
(take-while #(<= % 100)
(sort
(distinct
(for [m (range 3 20)
n (range (int (* m 3/4)) (inc m))]
(- (* 2 m n) m n -1)))))
(8 13 18 23 25 32 39 41 50 59 61 72 83 85 94 98)
The next close-to-squarish possibility is 59 states. The stars would be a
7x5 grid with a superposed 6x4 grid, versus the present 6x5 and 5x4. But
just two states after that it could be exactly square, with 6x6 and 5x5
arrays. :)
Also: the flag would have to change if the US annexed either of its large
neighbors. Canada has 13 internal divisions which would become new states,
but 63 is not a solution. Mexico's 31 internal states would give the US 81
in total, but that is not a solution either. Both miss solutions by 2, but
in opposite directions. Mexico, plus graduating Puerto Rico and the U.S.
Virgin Islands to full statehood, would give 83, allowing a flag with 8x6
and 7x5 arrays of stars. (Of course, the GOP would never stand for anything
like this that would make such a large fraction of US voters Latino.)
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