Suggestion for a sequence: weights on a circle

[Ralf Stephan]

You wrote 
> Suppose you have n objects, with weights 1,2,3,...,n.
> (That is, exactly one object with each of those weights.)
> 
> How many ways are there to place these objects evenly spaced
> around the circumference of a disk so that the disk will
> exactly balance on the centre point?
> 
> In algebraic terms, how many permutations p1,p2,...,pn
> are such that the polynomial p1 + p2*x + ... + pn*x^(n-1)
> has exp(2 pi i/n) as a zero?  
> 
> An example for n=10 is [2, 9, 1, 8, 5, 7, 4, 6, 3, 10]. I don't even

Note that C = |s(n+5)-s(n)| = 5, n=1..5 where C is presumably n/2.

This reminds me of the Challenger disaster where it was found that
they measured the circleness of the tank rings by applying a ruler
and turning it around in the thing. But not only circles have a
constant diameter. See Feynman for that story.


ralf