Problem 1. Masha wrote a positive number on the board. It turned out that its integer part is $43\%$ less than the number itself. What number did Masha write? Find all possible options and prove that there are no others.

The integer part of a number is the greatest integer not exceeding the given number.
Solution. Answer: $1 \frac{43}{57}$.

Let $n \geqslant 0$ be the integer part of Masha's number, and $0 \leqslant \epsilon < 1$, which is impossible.

Thus, the only possible option is the number $1 \frac{43}{57}$.

## Criteria

One of the largest suitable criteria is used:

7 p. Any complete solution to the problem.

3 6. An equation of the form $n=0.57(n+\epsilon)$ is set up.

1 p. The correct answer is provided.