<< I'm interested in starting with the highly symmetric 7 x 7 hexagonal torus network of 49 nodes, each connected to 6 others. We can ask this question: Given 98 people, two on each node of this network at each stage, we want each one to have an itinerary (moving to an adjacent node, or staying put, on each step) such that each person shares a node with each of the other ***49***, such that the least total number of moves-to-an-adjacent-node are used. (Making no assumptions about the number of steps necessary.)

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(asterisks added for emphasis) Of course, silly me, this should read 97, not 49. Gareth: Your solution looks promising, but I'm not sure exactly what you mean by n. --Dan