At a circular table, 5 people are sitting: Arnaldo, Bernaldo, Cernaldo, Dernaldo, and Ernaldo, each in a chair. Analyzing in a clockwise direction, we have:

I. Between Arnaldo and Bernaldo there is 1 empty chair;

II. Between Bernaldo and Cernaldo are 5 chairs;

III. Between Dernaldo and Ernaldo are 4 chairs, almost all empty;

IV. Between Dernaldo and Cernaldo are 2 chairs;

V. Between Ernaldo and Bernaldo are 3 chairs, not all empty.

How many chairs are there around the table?
Solution

Let's position Arnaldo in the chair we will call 1, and by information $I$, Bernaldo should sit in chair 3, and consequently, by information $II$, Cernaldo should sit in chair 9. Since there are 6 chairs between Dernaldo and Ernaldo and 2 chairs between Dernaldo and Cernaldo, Cernaldo is between Dernaldo and Ernaldo, with Dernaldo sitting in chair 6 and Ernaldo in chair 11. Since there are 3 chairs between Ernaldo and Bernaldo, Arnaldo is between them, with one empty chair between Ernaldo and Arnaldo, which is chair 12, the last chair. Therefore, there are 12 chairs in total.

![](https://cdn.mathpix.com/cropped/2024_05_01_e67c0440f1fa8bc62cdcg-08.jpg?height=590&width=595&top_left_y=789&top_left_x=612)