Subject: 10 friends run into each other at a bar
Name: Ken
Who are you: Other (Secondary)

10 friends run into each other at a bar. We will name them A,B,C,D,E,F,G,H,I AND J.

They all leave at the same time heading for seperate bars. However, A runs into B, C runs into D, E runs into F, G runs into H and I runs into J. These five groups leave again and the same thing keeps happening, but each time running in to someone they have not run into before. How many bars will it take, with each person meeting the others only once, until all of them have met each other again? An illistration in Excel would be great if possible. Thanks



My advice is not to use Excel. Why not use a diagram showing a regular 10-sided figure (called a decagon) with vertices labeled A through J? Meeting in a bar would be represented by a line segment joining two vertices (a diagonal or a side). Join A to B and take all diagonals (and sides) parallel to it to represent the first session. Join A to C and take all parallels for the second, joining the missing pair B with its opposite point. Continue in this way until all pairs are accounted for. How many ways are there to join A to another vertex?