Well, it isn't the minimum for the case n=1 (8 people, 2x2 grid), where my previous posting showed a solution with the absolute minimum of 28 person moves (which were all to an adjacent cell). Franklin T. Adams-Watters -----Original Message----- From: eclark@math.usf.edu On Wed, 30 Aug 2006, Ed Pegg Jr wrote:
At a convention, 128 people all need to meet with each other, 1 on 1, for a paper exchange.
Suppose a room is divided into a 8x8 square, and a clock is set up to ding 127 times, once every 30 seconds. Each person is given a map of their starting square, and a map of their route over the next hour and 4 minutes. Only two people can be in each cell.
Here is a solution which requires 64*134 unit person moves. ... Clearly this method generalizes from 128 to any number of the form 2^(2n+1). In which case the number of unit person moves taken by this method is 2^(2n)(2^(2n+1)-4+2^(n+1)-2n) Could this be the true minimum? --Edwin ________________________________________________________________________ Check Out the new free AIM(R) Mail -- 2 GB of storage and industry-leading spam and email virus protection.