## Task 1 - 301211

Determine whether there exist natural numbers $a, b, c, d$ that satisfy the following two conditions (1) and (2):

$$
\begin{aligned}
a \cdot b \cdot c \cdot d & =111111111111 \\
a+b+c+d & <11111
\end{aligned}
$$

If this is the case, provide such numbers.
It suffices to provide an example of natural numbers $a, b, c, d$ and to confirm (1), (2) for the given numbers. One such example is

$$
a=37, \quad b=3 \cdot 11 \cdot 13=429, \quad c=7 \cdot 101=707, \quad d=9901
$$

which can be verified by calculating $a+b+c+d=11074$ and

$$
3 \cdot 37=111, \quad 7 \cdot 11 \cdot 13=1001, \quad 101 \cdot 9901=1000001
$$

thus

$$
3 \cdot 7 \cdot 11 \cdot 13 \cdot 37=111 \cdot 1001=111111
$$

$$
a \cdot b \cdot c \cdot d=3 \cdot 7 \cdot 11 \cdot 13 \cdot 37 \cdot 101 \cdot 9901=111111 \cdot 1000001=111111111111
$$

Taken from $[5]$