Spies
Source: Baltic Way 1994 - 19
February 24, 2005
combinatorics unsolvedcombinatorics
Problem Statement
The Wonder Island Intelligence Service has spies in Tartu. Each of them watches on some of his colleagues. It is known that if spy watches on spy , then does not watch on . Moreover, any spies can numbered in such a way that the first spy watches on the second, the second watches on the third and so on until the tenth watches on the first. Prove that any spies can also be numbered is a similar manner.