## Task B-1.5.

The PIN of Karlo's mobile phone is a four-digit natural number greater than 2021 and divisible by 5 and 6. If in this number we swap the first and third, and the second and fourth digits, we will get a number that is 3960 greater than it. Determine Karlo's mobile phone PIN.
## Solution.

Since the required number is divisible by 5 and 6, it is also divisible by 3 and 10, which means its last digit is 0.

Therefore, the PIN is a number of the form $\overline{a b c 0}$.

1 point

According to the condition in the problem, we have:

$$
\begin{aligned}
\overline{a b c 0} & =\overline{c 0 a b}-3960 & & \\
1000 a+100 b+10 c & =1000 c+10 a+b-3960 & & 1 \text { point } \\
990 a+99 b & =990 c-3960 & & \\
10 a+b & =10 c-40 & & 1 \text { point }
\end{aligned}
$$

The right side is divisible by 10, so $b$ must be 0 and we have $a=c-4$.

Additionally, the sum of the digits $a+c$ must be divisible by 3, so by substituting all possible values for $c=5,6,7,8,9$, we get the solutions $c=5, a=1$ or $c=8$ and $a=4$.

We discard the first option because the digit $a$ must be greater than or equal to 2, so the required PIN is 4080.