In the fairy country of Perra-Terra, among other inhabitants, Karabases and Barabases live. Each Karabas is acquainted with six Karabases and nine Barabases. Each Barabas is acquainted with ten Karabases and seven Barabases. Who is more numerous in this country - Karabases or Barabases?
Recall the problem $\underline{88268}$.

## Solution

Let's imagine stretching threads between each Karabas and the Barabas he knows. Then, from each Karabas, 9 threads will stretch, and from each Barabas, 10 threads will stretch. Therefore, the number of threads will simultaneously be 9 times the number of Karabas and 10 times the number of Barabas. Consequently, the number of Karabas is $10 / 9$ times the number of Barabas.

## Answer

Karabas.

## Author: Folklore

Prove that from any seven natural numbers (not necessarily consecutive), one can choose three numbers whose sum is divisible by 3.

## Solution

By the Pigeonhole Principle, from seven numbers, we can select three that give the same remainder when divided by 3. The sum of these three numbers is divisible by 3.