in the cabinet 2004 telephones are located
Source: Russian Olympiad 2004, problem 9.6
May 3, 2004
inductioncombinatorics unsolvedcombinatorics
Problem Statement
In the cabinet 2004 telephones are located; each two of these telephones are connected by a cable, which is colored in one of four colors. From each color there is one cable at least. Can one always select several telephones in such a way that among their pairwise cable connections exactly 3 different colors occur?