Question 846969
This would be just like the "hand-shake" problem.  You would want to be able to make a polygon so that you can show 90 individual connections among all vertices.  Start with a triangle; it has 3 connections.  Next use a square (four sides); it will have 4 connections.  Next, use a pentagon; it has 7 connections.  Continue on this way...


Look at the wikipedia article, http://en.wikipedia.org/wiki/Handshake_problem
See the section about Triangular Numbers.  The given 90 gifts in your exercise would most closely correspond to 14 students.