Let's fill in the empty cells of the diagram with numbers so that we get arithmetic sequences with the same common difference in each row and each column.

| 2 |  |  |  | 14 |
| :--- | :--- | :--- | :--- | :--- |
|  | 8 |  |  |  |
|  | 11 | 16 |  |  |
|  |  |  |  |  |
| 10 |  |  |  |  |
In the first row, from 2 to 14, the increase over 4 steps is 12, so the increase per step is 3. Similarly, in the first column, the increase per step is 2. By filling in the numbers 5, 8, 11, and 4, 6, 8 in the third row and the second column, respectively, three consecutive cells are filled. The numbers in these cells exactly meet the requirement of an increase of 5 and 3 in each step, respectively, so the remaining cells in the third row and the second column can be filled. With this, in the second, fourth, and fifth rows, which still contain empty cells, we know the first two numbers in each row. From these, the increase from term to term is 4, 6, and 7, respectively, so all remaining cells can be filled.

Meanwhile, we have not yet used the requirements for the third, fourth, and fifth columns, so we need to check if they are met. The verification shows that the requirement is met in these three columns as well. Thus, the problem is solved, and the completed table is:

| 2 | 5 | 8 | 11 | 14 |
| ---: | ---: | ---: | ---: | ---: |
| 4 | 8 | 12 | 16 | 20 |
| 6 | 11 | 16 | 21 | 26 |
| 8 | 14 | 20 | 26 | 32 |
| 10 | 17 | 24 | 31 | 38 |

Lányi Zsuzsanna (Szentgotthárd, Vörösmarty M. g. I. o. t.)

Note. Several contestants noted that the given numbers could have been left out in multiple ways, and the table could still have been filled. Some considered it essential that after leaving out two numbers, there should remain a row or column containing two given numbers. However, Exercise 771 shows that this is not necessary. - Numerous comments also noted that the table could be uniquely solved by leaving out any two of the six given numbers. This is not correct, as leaving out the pairs 8, 14 and 10, 16, for example, results in a different

| 2 | 7 | 12 | 17 | 22 | 2 | 5 | 8 | 11 | 14 |
| ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: |
| 4 | 9 | 14 | 19 | 24 | 5 | 8 | 11 | 14 | 17 |
| 6 | 11 | 16 | 21 | 26 | 8 | 11 | 14 | 17 | 20 |
| 8 | 13 | 18 | 23 | 28 | 11 | 14 | 17 | 20 | 23 |
| 10 | 15 | 20 | 25 | 30 | 14 | 17 | 20 | 23 | 26 |

filling that also meets the requirement. [^0]

[^0]:    ${ }^{1} 1$ This shows that the provision of the numbers 8 and 16 was unnecessary.