On 8/30/06, Ed Pegg Jr <ed@mathpuzzle.com> wrote:
At a convention, 120 people all need to meet with each other, 1 on 1.
Suppose a room is divided into a 8x8 square, and a clock is set up to ring 60 times, once per minute. Each person is given a map of their starting square, and a map of their route over the next hour.
What is the simplest set of maps? What is the length of the minimal walks people need to take?
Ed Pegg Jr
This problem does not appear to be well-defined. (1) How many people can occupy one cell simultaneously --- two? (2) Are diagonal moves permitted, or just orthogonal? (3) Are moves only to adjacent cells? (4) Why 120 rather than (say) 128? (5) What criteria constitute "simplicity" in this context? (6) Is the length of the maximum walk to be minimised? The mean? WFL