## Task 4 - 240524

Peter reports: "I wrote down a natural number. I formed a second natural number by appending the digit 0 to the first number. The sum of the two numbers is 3058."

Prove that the first number Peter wrote down can be uniquely determined from this information!

State this number!
If the sought number is $x$, then $10 \cdot x$ is the number formed by appending the digit 0. The sum is therefore $11 \cdot x$; according to Peter's statement, $11 \cdot x = 3058$.

Since $3058 : 11 = 278$, it follows that $x = 278$.

Thus, it is proven that the number Peter wrote down first can be uniquely determined from his statements. It is 278.

Solutions of the 2nd Round 1984 taken from [5]

### 2.26 25th Olympiad 1985

### 2.26.1 1st Round 1985, Class 5