  We consider a multi-agent system where each agent has its own estimate of a
given quantity and the goal is to reach consensus on the average. To this
purpose, we propose a distributed consensus algorithm that guarantees
convergence to the average in a finite number of iterations. The algorithm is
tailored to ring networks with bidirectional pairwise communications. If the
number of agents $m$ is even, say $m=2n$, then, the number of iterations needed
is equal to $n$, which in this case is the diameter of the network, whereas the
number of iterations grows to $3n$ if the number of agents is odd and equal to
$m=2n+1$.
