There are 42 sun umbrellas installed on the beach, half of which are blue.

There are 42 sun umbrellas installed on the beach, half of which are blue. A third of all blue umbrellas are already taken. How many blue umbrellas are still free?

1) In order to solve this problem, first we need to determine how many umbrellas are blue. To do this, divide the total number of umbrellas (42) by two:
42: 2 = 21
2) Next, we need to calculate how many blue umbrellas are already taken. Since one third of all blue umbrellas are occupied, the total number of blue umbrellas should be divided by three:
21: 3 = 7
3) Now, in order to determine the number of free umbrellas, it is necessary to subtract the occupied ones from the total number of blue umbrellas:
21 – 7 = 14
Answer: 14.