Colouring a convex 18 gon and numbering the diagonals
Source:
December 6, 2010
combinatorics unsolvedcombinatorics
Problem Statement
The diagonals of a convex -gon are colored in different colors, each color appearing on an equal number of diagonals. The diagonals of one color are numbered . One randomly chooses one-fifth of all the diagonals. Find the number of possibilities for which among the chosen diagonals there exist exactly pairs of diagonals of the same color and with fixed indices .