Upper bound: One classic approach to a round-robin tournament is to arrange a line of chessboards with seats on opposite sides. One player, say X, is selected to sit still. All other players move one seat to their left, skipping past player X. A player who reaches the end of the line moves to the other side of the same table. (In other words, all players move one seat counter-clockwise, skipping X.) This approach readily translates to the checkerboard once you fix a Hamilton path. If I've counted correctly, 1 person stands still. 1 person moves 127 squares. All others move 126 squares. On 8/30/06, Ed Pegg Jr <ed@mathpuzzle.com> wrote:
Rewrite, to correct the errors.
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.
Ideally, most moves should be King moves. Not needing to move during a turn is acceptable.
Simplicity is judged by the amount of text needed to explain the choreography, and the orderliness of the room.
Alternately, the length of the maximum walk should be minimised. Ed Pegg Jr _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun