4. In the game "clock", at the beginning, the arrow points to one of the numbers from 1 to 7 (drawing on the right). In each step, the arrow moves in the direction of the clock hands by as many fields as the number written in the field before the start of the step. For example, in the drawing, the arrow points to the number 4, which

![](https://cdn.mathpix.com/cropped/2024_06_05_d4a9105d103058c5b923g-02.jpg?height=368&width=387&top_left_y=1301&top_left_x=1037)
means that it needs to move 4 fields and will point to the field with the number 1, and in the next step, it moves 1 field and will point to the field with the number 2, etc. After 21 moves, the arrow points to the field with the number 6. On which field did the arrow point after the first move?
Solution. Let's create a table where we will enter the current and next position of the arrow, and then a table where we will enter the current and previous position of the arrow. We have

| Current  position | Next  position |
| :---: | :---: |
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
| 4 | 1 |
| 5 | 3 |
| 6 | 5 |
| 7 | 7 |


| therefore | Current  position | Previous  position |
| :---: | :---: | :---: |
|  | 2 | 1 |
|  | 4 | 2 |
|  | 6 | 3 |
|  | 1 | 4 |
|  | 3 | 5 |
|  | 5 | 6 |
|  | 7 | 7 |

We will solve the problem by going backward. This means that for the arrow to point to 6 after the 21st step, it must point to 3 after the 20th step, then to 5 after the 19th step, to 6 after the 18th step, etc. Continuing this process, we conclude that the arrow points to 6 after the 15th, 12th, 9th, 6th, and 3rd steps. Since it points to 6 after the 3rd step, it points to 3 after the second step and finally to 5 after the first step.