Task B-1.1. (20 points) Determine the unknown digits $a, b, c, d$ such that $\overline{a 3 b c} \cdot 45=\overline{37 d 15 b}$
Solution. The number on the right side must be divisible by 5. Therefore, $b=5$ or $b=0$.

For $b=5$ we have

$$
\overline{a 35 c} \cdot 45=\overline{37 d 155}
$$

The number on the right side must be divisible by 9, so we get $3+7+d+1+5+5=9k$ i.e. $21+d=9k$, from which $d=6$, so

$$
\overline{a 35 c} \cdot 45=376155
$$

from which $\overline{a 35 c}=376155: 45=8359$. Therefore, $a=8$ and $c=9$.

(8 points)

For $b=0$ we have

$$
\overline{a 30 c} \cdot 45=\overline{37 d 150}
$$

The number on the right side must be divisible by 9, so we get $3+7+d+1+5+0=9k$ i.e. $16+d=9k$, from which $d=2$, so

$$
\overline{a 30 c} \cdot 45=372150
$$

from which $\overline{a 30 c}=372150: 45=8270$, which does not satisfy the condition.

Therefore, there is only one solution $(a, b, c, d)=(8,5,9,6)$

(8 points)