A1. In the places of the asterisks, there are positive integers arranged in such a way that the multiplication table below is correct.

What is the largest number that appears more than once in the $5 \times 5$ table?
A) 6
B) 8
C) 9
D) 12
E) 18

| $\times$ | $*$ | $*$ | $*$ | 7 |
| :---: | :---: | :---: | :---: | :---: |
| $*$ | 24 | $*$ | $*$ | 56 |
| $*$ | $*$ | 36 | 8 | $*$ |
| $*$ | $*$ | 27 | 6 | $*$ |
| 6 | 18 | $*$ | $*$ | 42 |
A1. D) 12 Look at the left picture. At the place of the star, a number must stand that both 27 and 6 are divisible by. This gives two possibilities: 1 or 3. The first possibility is ruled out, because then the number 27 would stand at the place of the double star, while 36 is not divisible by it.

| $\times$ |  | $* *$ |  | 7 |
| :---: | :---: | :---: | :---: | :---: |
|  | 24 |  |  | 56 |
|  |  | 36 | 8 |  |
| $*$ |  | 27 | 6 |  |
| 6 | 18 |  |  | 42 |


| $\times$ | 3 | 9 | 2 | 7 |
| :---: | :---: | :---: | :---: | :---: |
| 8 | 24 | 72 | 16 | 56 |
| 4 | 12 | 36 | 8 | 28 |
| 3 | 9 | 27 | 6 | 21 |
| 6 | 18 | 54 | 12 | 42 |

With the second possibility, we can fill in the entire table step by step (see the right picture). We see that 12 is the largest number that appears twice.