$\mathrm{Na}$ two families with a total of six children, aged $2, 3, 4, 5, 6$ and 8 years, met. The sum of the ages of the children from one family was the same as the sum of the ages of the children from the other family.

How old could the children from each family have been? Determine all possibilities.

(E. Novotná)
The sum of the ages of all the children was

$$
2+3+4+5+6+8=28
$$

thus the sum of the ages of the children from each family was $28: 2=14$.

Exactly one family had the oldest, 8-year-old child. We can therefore consider how to express the sum of 14 using the given numbers, with one of the addends being 8. This can be either $14=8+6$, or $14=8+4+2$. Therefore, the following two possibilities could have occurred:

a) the children from one family were 8 and 6 years old, the children from the other family were 5, 4, 3, and 2 years old,

b) the children from one family were 8, 4, and 2 years old, the children from the other family were 6, 5, and 3 years old.

Scoring suggestion. 2 points for determining the sum of the ages of the children from each family; 2 points each for determining each of the valid possibilities.

A solution with both possibilities but without any justification should be scored no more than 3 points.