## Task 2 - 330622

Imagine all the different numbers formed by arranging the five digits 1, 2, 3, 4, 5 in every possible order.

What is the sum of all these five-digit numbers?
For each possibility of choosing one of the digits 1, 2, 3, 4, 5 as the unit digit, there are as many numbers as there are permutations of the remaining four digits. The number of these possibilities is 24. Consequently, the sum of the unit digits is

$$
24 \cdot(1+2+3+4+5)=24 \cdot 15=360
$$

The same applies to the sum of the tens, hundreds, thousands, and ten-thousands digits. Therefore, the same result is obtained as with the following calculation:

|  |  |  |  | 3 | 6 | 0 |
| :--- | :--- | :--- | :--- | :--- | :--- | :--- |
|  |  |  | 3 | 6 | 0 |  |
|  |  | 3 | 6 | 0 |  |  |
|  | 3 | 6 | 0 |  |  |  |
| 3 | 6 | 0 |  |  |  |  |
| 3 | 9 | 9 | 9 | 9 | 6 | 0 |