3. A real number $x$ is called interesting if, by erasing one of the digits in its decimal representation, one can obtain the number $2x$. Find the largest interesting number.
Answer: 0.375.

Solution. When a digit from the integer part of a real number $x$ is erased, the number cannot increase, and when a digit from the fractional part is erased, it can only increase by a number less than 1. Therefore, the number $x$ must be less than 1, and if its first digit after the decimal point is not 0 (otherwise, the number would not be interesting), then this digit should be erased. Let this first digit be $y$, and let $x$ $\overline{0, y}=z$. Then, after erasing the digit $y$, the resulting number is $10z$, from which we have $10z=2(y/10+z)$ or $40z=y$. Since $z<0.1$, we have $y \leq 3$. Substituting $y=3$, we find $z=0.075$, from which the answer follows.

Comment. The correct answer is obtained by a complete and justified enumeration - 7 points. The correct answer is obtained by an incomplete enumeration, and the case where the first digit after the decimal point is 4 is not explained - 3 points. The correct answer is given, it is shown that the number is interesting, but it is not justified that it is the largest - 2 points. Examples of interesting numbers are provided - 1 point.