we consider the following urn model proposed by diaconis. there is an urn with $n$ balls, each ball has value 0 or 1. pick two random balls and add a new ball with their sum (modulo 2) to the urn. (thus the number of balls increases by one each time). what is the limiting distribution? in general, let $g$ be a finite additive group. we begin with an $a$ set $g_1, \dots, g_n$ of (not necessarily different) elements of $g$. (in fact, typically $n$ is much larger than $|g|$). at time $i=0,1,2,\dots,$ we choose two random elements $a$ and $b$ from the set $g_1, \dots, g_{n+i}$ and add the sum $g_{n+i+1} = a+b$ to the set. siegmund and yakir studied the distribution of the set $g_1,g_2\dots$ and showed that it converges to the uniform distribution. this result leaves open the question: how quickly does this convergence occur? in this talk we address this issue.