368. In each cell of a $3 \times 3$ square, a number is written such that the sum of any three numbers in the same row, the same column, and on each of the two diagonals is the same. In the middle of the top row, there is a 1, and in the corner cells of the bottom row, there are 2 and 3. Find the numbers written in the other cells of the square.
$\triangle$ Let's introduce notations for the unknown numbers of the square (Fig. 43).

Since by the condition

$$
1+d+k=2+k+3
$$

then $d=4$. Since

$$
a+1+b=2+d+b
$$

where $d$ is already known, then $a=5$. Further, since

$$
5+4+3=2+4+b
$$

then $b=6$. Similarly, we find the numbers $c, e$ and $k$.

Answer: $a=5, b=6, c=5, d=4, e=3, k=7$.

| a | l | b |
| :---: | :---: | :---: |
| c | d | e |
| 2 | k | 3 |

Fig. 43