In the summer, six grandchildren gathered at their grandmother's and we know about them that

- Martinka sometimes has to take care of her brother Tomášek, who is 8 years younger,
- Věrka, who is 7 years older than Ida, likes to tell ghost stories,
- Martinka often argues with Jaromír, who is a year younger,
- Tomášek is 11 years younger than Kačka,
- Ida often teases her 4 years older brother Jaromír,
- the boys together are 13 years old.

How old are all the mentioned children?

(M. Volfová)
Martinka is 8 years older than Tomášek and 1 year older than Jaromír, so Jaromír is 7 years older than Tomášek. Moreover, the boys together are 13 years old. If Tomášek were 7 years older (i.e., as old as Jaromír), they would be 20 years old together. Therefore, Jaromír is 10 years old and Tomášek is 3 years old.

From this, we can easily calculate the ages of the other grandchildren: Martinka is 8 years older than Tomášek, so she is 11 years old; Kačka is 11 years older than Tomášek, so she is 14 years old; Jaromír is 4 years older than Ida, so Ida is 6 years old; Věrka is 7 years older than Ida, so she is 13 years old.

Evaluation: 3 points for determining the ages of both boys (1 point for providing the method); 3 points for determining the ages of the four granddaughters (1 point for providing the method).