Problem 4. Determine the four-digit number $\overline{x y z t}$ for which

$$
\overline{x y z t}+4 \cdot \overline{y z t}+2 \cdot \overline{z t}=2018
$$
Solution. From the condition of the problem, we get

$$
1000 x+500 y+70 z+7 t=2018
$$

The unit digit of the first three addends in the last equation is 0, so for the unit digit of the sum to be 8, it is necessary for the unit digit of the product $7 t$ to be 8. The only possibility is $t=4$, which means the equation takes the form

$$
1000 x+500 y+70 z=1990
$$

or

$$
100 x+50 y+7 z=199
$$

The unit digit of the first two addends in the last equation is 0, so for the unit digit of the sum to be 9, the only possibility is

$$
z=7, \text { i.e. } 100 x+50 y=150
$$

Finally, since the desired number is a four-digit number, from the last equation it follows that $x=y=1$ and therefore $\overline{x y z t}=1174$.