Ed asks: << 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?

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This is an intriguing question! One thing I'm not sure I understand is what kind of step one is allowed to take. Must it be N,S,E,W ? Or does it also include NE, SE, NW, SW ? Another question is how would one meet 119 other people in only 60 steps? I must be misunderstanding something. (Or is the real question how each person could meet 60 others in 60 steps?) A third question I have is: Is it obvious that (whatever the goal) there is necessarily some way to achieve it in the allotted time? ------------------------------------------------------------------------------------ I think that at any stage there are supposed to be two people in each of 60 squares, with 4 empty squares. (Is that right, Ed?) (Another possible avenue is to use a symmetrtic network with exactly 120 nodes, like T_15.) --Dan