5. A $70 \times 70$ table is filled with numbers from 1 to 4900: in the first row, from left to right, the numbers from 1 to 70 are written in ascending order; in the second row, the numbers from 71 to 140 are written in the same way, and so on; in the last row, from left to right, the numbers from 4831 to 4900 are written. Can a cross of 5 cells

in the shape $\square$, the sum of the numbers in which equals $2018$, be found in this table?

(A. Solynin)
5. Answer: such a fragment does not exist. If $x$ is in the center of the fragment, the sum of the numbers in it is $5 x$, i.e., divisible by 5, and therefore cannot be equal to 2018.