Source: 2012 AMC10A Problem #23 and AMC12A Problem #19
February 8, 2012
AMCAMC 12AMC 10 Ageometric transformationrotationAMC 12 Agraph theory
Problem Statement
Adam, Benin, Chiang, Deshawn, Esther, and Fiona have internet accounts. Some, but not all, of them are internet friends with each other, and none of them has an internet friend outside this group. Each of them has the same number of internet friends. In how many different ways can this happen?<spanclass=′latex−bold′>(A)</span>60<spanclass=′latex−bold′>(B)</span>170<spanclass=′latex−bold′>(C)</span>290<spanclass=′latex−bold′>(D)</span>320<spanclass=′latex−bold′>(E)</span>660