## Task 16/66

In the newspaper "Neues Deutschland" on June 29, 1965, the following note was found:

When a small animal keeper in Christdorff in the district of Wittstock slaughtered a chicken a few days ago, it provided not only the Sunday roast but also a sum of cash as an addition. In the chicken's stomach, 17 coins were found, totaling 34 Pfennig ...

Assuming it was coins currently in circulation. Which coins were they and in what quantities?
The task leads to a readily solvable Diophantine equation. If we denote the number of 10-pfennig coins by $x$, the number of 5-pfennig coins by $y$, and the number of 1-pfennig coins by $z$ (larger coins are not considered), we obtain the following system of equations:

$$
x+y+z=17 \quad, \quad 10 x+5 y+z=34
$$

where $x, y$, and $z$ are natural numbers. Subtracting the first equation from the second yields $9 x+4 y=17$.

Since 17 is not divisible by 4, $x>0$ must hold. Since $y \geq 0$, $x<2$ must also hold. Therefore, $x=1$. Substituting this value yields $y=2$ and finally $z=14$. Thus, there was 1 10-pfennig coin, 2 5-pfennig coins, and 14 1-pfennig coins. The verification confirms the correctness of this solution.