3. Eight boys (Vasya, Dima, Egor, Ilya, Kolya, Petya, Temya, and Fyodor) stood in a line in some order, after which they counted from 1 to 8, with the following conditions:

- Dima's number was three times Ilya's number;
- Fyodor stood somewhere after the third boy but before Kolya;
- Vasya's number was half of Petya's number;
- the fourth boy was immediately behind Temya and somewhere before Petya.

In what order did the boys stand? Explain why you think so. (P. D. Mulyenko)
Answer: Egor, Ilya, Tema, Vasya, Fedy, Dima, Kolya, Petya.

Solution. According to the fourth condition, Tema stands in the third place. Since Dima's number is divisible by 3 according to the first condition, and the third number is occupied, Dima must have the number 6, and Ilya - number 2. From the third condition, it follows that Petya's number is even and not equal to 4 (since Ilya already has number 2), so Petya has number 8, and Vasya - 4. Then Fedy and Kolya's numbers are derived from the second condition, and Egor gets the remaining number 1.

Criteria. Correct answer without justification or only with verification of conditions 1 point.

Correct explanations of the placement of pairs of boys (Dima and Ilya, Vasya and Petya, Fedy and Kolya) - 2 points for each pair.