  It is well-known that any sequence of at least N integers contains a
subsequence whose sum is 0 (mod N). However, there can be very few subsequences
with this property (e.g. if the initial sequence is just N 1's, then there is
only one subsequence). When the length L of the sequence is much longer, we
might expect that there are 2^L/N subsequences with this property (imagine the
subsequences have sum-of-terms uniformly distributed modulo N -- the 0 class
gets about 2^L/N subsequences); however, it is easy to see that this is
actually false. Nonetheless, we are able to prove that if the initial sequence
has length at least 4N, and N is odd, then there is a subsequence of length L >
N, having at least 2^L/N subsequences that sum to 0 mod N.
