Two brothers sold their flock of sheep. They sold each sheep for as many dollars as there were sheep in the flock. They shared the revenue, giving each other 10 dollars at a time. First, the older brother received 10 dollars, then the younger one, then again the older one, and so on. In the end, only less than 10 dollars were left for the younger brother, so the older brother gave him his pocket knife, thus they both ended up with the same amount of revenue. How much is the pocket knife worth?
In the birkanyaj, there were $n$ birka, so according to the problem, they received a total of $n^{2}$ tallers for them. This is how they divided it:

older sibling

10 tallers

$\vdots$

10 tallers

10 tallers younger sibling

10 tallers

$\vdots$

10 tallers

$m$ tallers $\quad(1 \leq m \leq 9$ integer $)$

Thus, $n^{2}=20 \cdot k+10+m(k \geq 1$ integer). The remainders of any square number when divided by 20 can only be the following numbers: $0,1,4,9,16,5$. Out of these, only $10+m=16$ can apply, so $m=6$.

Let $b$ be the value of the bicska; the older sibling gave the bicska to the younger one, and thus the income of the two siblings became equal, that is:

$$
10-b=m+b, \quad \text { hence } \quad b=2
$$

The bicska is worth 2 tallers.

Based on the work of Ildikó Bujdosó (Bp., Veres Péter Gymn., III. o.t.)