## Task 1 - 270831

During a children's birthday party, they play "Guess the Birthday." Katrin, the birthday girl, explains to each of her play partners:

"Divide your birth date into a day number and a month number! (My birthday today, the 24th of May, would be divided into the day number 24 and the month number 5.) Double the day number of your birth date, add 7 to the result, multiply the sum by 50, and increase the product by the month number of your birth date!"

After the result was named, Katrin was able to name the relevant birth date. Explain how the birth date can always be found from the result of the calculation Katrin requested!
For each birthdate with day number $x$ and month number $y$, the required calculation leads successively to the numbers

$$
2 x, \quad 2 x+7, \quad(2 x+7) \cdot 50=100 x+350
$$

thus resulting in $100 x+350+y$.

From this result, the desired numbers $x$ and $y$ can be found as follows:

Subtract 350 to obtain the number $100 x+y$. Since $y$, as the month number, is less than 100, $y$ must be the number formed by the tens and units digits of $100 x+y$ (where, if the tens digit is 0, it should be omitted); and if one removes the tens and units digits from $100 x+y$, the (digit representation of the) number $x$ remains.