Each person in a group of ten people calculates the sum of the ages of the other nine members of the group. The ten sums obtained are $82, 83, 84, 85, 87, 89, 90, 90, 91$ and 92.

Determine the age of the youngest person.
Observe that the age of each person appears as a term in 9 of the 10 numbers. Thus, if we sum the 10 numbers, we will get nine times the sum of all the ages. Therefore, the sum of the ages of the ten people is

$$
\frac{82+83+84+85+87+89+90+90+91+92}{9}=\frac{873}{9}=97
$$

The youngest person obtained the highest sum, which corresponds to the sum of the ages of the nine oldest, so their age is $97-92=5$ years.