In fact, if we are only concerned with how many total person-moves there are, with no concern for distance moved, we can always achieve the theoretical minimum. At this point it is simpler to reformulate the problem. We have 2n people in n cells, with no particular arrangement to the cells. We want to have 2n-1 rounds, with each person meeting each other person in one round. Make up a schedule of who will meet whom in which round. There are many ways of doing this; any schedule will do. Assign people to cells for the first round. Now, for each subsequent round, look at the cycles in the form "A will meet B who just met C who will meet ... who just met A". Since these alternate "will meet" with "just met", the cycle length must be even. Arbitrarily have every other person in each cycle stay in place; the others move to their next meeting. Franklin T. Adams-Watters ________________________________________________________________________ Check Out the new free AIM(R) Mail -- 2 GB of storage and industry-leading spam and email virus protection.