Seven dwarfs were born on the same day in seven consecutive years. The sum of the ages of the three youngest dwarfs was 42 years. When one dwarf left with Snow White to fetch water, the remaining dwarfs discovered that their average age was the same as the average age of all seven.

How old was the dwarf who went with Snow White to fetch water?

(L. Hozová)

Hint. How old were the individual dwarfs?
The sum of the ages of the first three dwarfs was 42 years, so on average they were 14 years old $(42: 3=14)$. The ages of these, or the remaining four dwarfs, were $13,14,15$, and $16,17,18$, and 19 years, respectively.

The sum of the ages of all seven dwarfs was 112 years, so on average they were 16 years old $(112: 7=16)$. If the youngest dwarf left, the average age of the remaining six would be 16.5 years:

$$
(112-13): 6=16.5 .
$$

Similarly, we can determine what would happen to the average age of the remaining dwarfs if each of the other dwarfs left:

| age of the one leaving | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| average of the remaining | 16.5 | $16, \overline{3}$ | $16,1 \overline{6}$ | 16 | $15,8 \overline{3}$ | $15, \overline{6}$ | 15.5 |

The average age did not change after the middle dwarf left. The dwarf who left with Snow White was 16 years old.

Notes. The average age of the dwarfs did not change after one of them left. Therefore, that dwarf was born as the middle one, and his age was the average age of all seven. This method can replace the trial of possibilities in the second part of the solution.

The considerations in the given solution can also be approached as follows: If we denote the age of the youngest dwarf as $n$, then the sum of the ages of the first three dwarfs was

$$
n+(n+1)+(n+2)=3 n+3=42 \text {. }
$$

Thus, $3 n=39$ or $n=13$. The ages of the dwarfs were $13,14,15,16,17,18,19$ years. The sum of all seven ages was 112, and their average was $112: 7=16$. If we denote the age of the leaving dwarf as $o$, then the average of the remaining did not change:

$$
(112-o): 6=16
$$

Thus, $112-o=96$ or $o=16$.