The average age of eleven football players is 22 years. During the match, one of the players got injured and left the field. The average age of the remaining players on the field became 21 years. How old is the football player who got injured?

#
What is the total sum of the ages of 11 players on a team?

## Solution

First method. The total sum of the ages of 11 players is $11 \cdot 22 = 242$. After one player left, this sum became $10 \cdot 21 = 210$. By calculating the difference, we find that the player who left was 32 years old.

Second method. The sum of the deviations of the numbers from the mean is zero. The sum of the deviations from the old mean (22) of the remaining 10 players is -10. Therefore, the deviation of the injured player is 10, meaning he was $22 + 10 = 32$ years old.

## Answer

32 years

Find ten consecutive natural numbers, among which:

a) there is no prime number;

b) there is one prime number;

c) there are two prime numbers;

d) there are three prime numbers;

e) there are four prime numbers;

f) how many prime numbers can there be among ten consecutive natural numbers?

## Hint

Among ten consecutive natural numbers (greater than 5), there are always five even numbers, and one of the odd numbers is divisible by 5.

## Answer

a) $2312, \ldots, 2321$; b) $2325, \ldots, 2334$; c) $30, \ldots, 39$; d) $22, \ldots, 31$; e) $10, \ldots, 19$; f) no more than five.