MathDB
Spies

Source: Baltic Way 1994 - 19

February 24, 2005
combinatorics unsolvedcombinatorics

Problem Statement

The Wonder Island Intelligence Service has 1616 spies in Tartu. Each of them watches on some of his colleagues. It is known that if spy AA watches on spy BB, then BB does not watch on AA. Moreover, any 1010 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 1111 spies can also be numbered is a similar manner.