How many matches compose the parallelogram's perimeter?
Source: Germany Bundeswettbewerb Mathematik 2008, Round 1, Problem 1
July 19, 2008
geometryperimeterparallelogramtrigonometrycombinatorics unsolvedcombinatorics
Problem Statement
Fedja used matches to put down the equally long sides of a parallelogram whose vertices are not on a common line. He figures out that exactly 7 or 9 matches, respectively, fit into the diagonals. How many matches compose the parallelogram's perimeter?