In article <8hohgq$fk4$1@taliesin2.netcom.net.uk>, John Pennifold <john.pennifold@capgemini.co.uk> wrote: >Seems to me that this is what is done in marathons and bike races. One >person takes the lead for a while then slowly drifts to the back. The person >at the front is probably encountering the most wind resistance and the >others follow in the slipstream. Look at the Tour de France to see this in >action. > > This round-robin protocol is what is commonly referred to as "Indian running", but it turns out that this is not exactly the way groups of indians tried to run down opponents. Instead, they used the following rather clever strategy: Each pursuer would start out at a different pace. One of them would take off in a virtual sprint trying to catch the escapee quickly. The next one would run a slightly slower pace so that if the first pursuer failed to make the catch he would still have some endurance left. And so on. As shown by J.B. Keller in a recent article (Optimal Running Strategy to Escape from Pursuers, Amer. Math. Monthly 107(2000), 416-421), this strategy on the part of the pursuers is optimal in order to catch an opponent of equal ability who has a modest head start. Consider the plight of the escapee. He must run quite fast to evade the first pursuer. When that pursuer gives up, he must contend with another who has been running a steady (albeit slower) pace, versus his own too fast early pace. Each subsequent pursuer taxes the escapee in a different way. Keller also derives the optimal strategy for an escapee pursued by a possibly infinite number of pursuers of equal ability. Perhaps surprisingly, the escapee must not run even pace. He should run an even pace that is too fast to sustain indefinitly for an initial time period. (The length of this initial period depends on how much head start he has in a way too complicated to reproduce here.) After the initial period, he essentially "hangs on," running an ever slower pace as exhaustion sets in. For details, consult the article cited. -- ************************************************************************ Terry R. McConnell Mathematics/304B Carnegie/Syracuse, N.Y. 13244-1150 trmcconn@syr.edu http://barnyard.syr.edu/~tmc ************************************************************************