1. A $10 \times 10$ table is filled with numbers from 1 to 100: in the first row, the numbers from 1 to 10 are written in ascending order from left to right; in the second row, the numbers from 11 to 20 are written in the same way, and so on; in the last row, the numbers from 91 to 100 are written from left to right. Can a fragment of 7 cells in the shape $\quad$ be found in this table, the sum of the numbers in which is $455?$ (The fragment can be rotated.)
1. Answer: Yes. If $x$ is in the center of the fragment, then the sum of the numbers in it is $7x$ and then with 646566 $x=65$ the sum will be exactly 455 (see figure).