Problem 8.3. Four children were walking along an alley and decided to count the number of firs planted along it.

- Anya said: "There are a total of 15 firs along the alley."
- Borya said: "The number of firs is divisible by 11."
- Vера said: "There are definitely fewer than 25 firs."
- Gena said: "I am sure that their number is divisible by 22."

One boy and one girl were right, while the other two were wrong. How many firs grow along the alley?
Answer: 11.

Solution. Let $N-$ be the number of elms along the alley.

Suppose Genya told the truth, and $N$ is divisible by 22. But then $N$ is also divisible by 11, i.e., Borya also told the truth. But according to the problem, one of the boys was wrong. Therefore, Genya must have been wrong, but Borya was right. So, $N$ is divisible by 11 but not by 22.

Since 15 is not divisible by 11, Anya must have been wrong. Then Vera told the truth, and $N<25$. But there is exactly one number less than 25 that is divisible by 11 and not by 22, which is 11. It is easy to verify that $N=11$ satisfies all the conditions of the problem.