2. The teacher wrote a positive number $x$ on the board and asked Kolya, Petya, and Vasya to raise this number to the 4th, 5th, and 20th power, respectively. It turned out that Kolya's number has at least 8 digits before the decimal point, and Petya's number has no more than 9 digits before the decimal point. How many digits are there before the decimal point in Vasya's number?
Answer: 36.

Solution. From the condition, it follows that $x^{4} \geqslant 10^{7}$, and $x^{5}<10^{9}$. Therefore, $10^{35} \leqslant x^{20}<10^{36}$. This means that the integer part of Vasya's number is a 36-digit number.

Evaluation. 13 points for the correct solution.