Suggestion for a sequence: weights on a circle

[T. D. Noe]

This problem is similar to the following:

For which n is there an equiangular polygon whose sides are some
permutation of 1,2,3,...,n.  The smallest solution is n=6, for which there
are essentially 4 permutations: (1,4,5,2,3,6), (1,5,3,4,2,6),
(1,6,2,4,3,5), and (1,6,3,2,5,4).

The problem was given on page 10 of the latest issue of MuddMath.  See
http://www.math.hmc.edu/muddmath/

Tony