  We prove that the sum of entries of the suitably normalized groundstate
vector of the O(1) loop model with periodic boundary conditions on a periodic
strip of size 2n is equal to the total number of n x n alternating sign
matrices. This is done by identifying the state sum of a multi-parameter
inhomogeneous version of the O(1) model with the partition function of the
inhomogeneous six-vertex model on a n x n square grid with domain wall boundary
conditions.
