1. Divide {1, 2, 9, 25, 49, 64} into two subsets so that the sum of the numbers of one of them is equal to the sum of the numbers of the other.

2. Anya and Tanya together weigh 40 kg, Tanya and Manya - 50 kg, Manya and Vanya - 90 kg, Vanya and Danya - 100 kg, Danya and Anya - 60 kg. How much does Anya weigh?

3.
a) Four merchants noticed that if they join without the first, they will collect 90 rubles, without the second - 85, without the third - 80, without the fourth - 75 rubles. How much money does anyone have?

b) Solve the system of equations: y + z + t = 90, x + z + t = 85, x + y + t = 80, x + y + z = 75.

4. The average age of the 11 players on the football team is 22 years old. During the match, one player was injured and left the field. The average age of the remaining players is 21 years old. How old is the person injured?

5. The teacher conducts a lesson in the classroom. The teacher's age is 24 years older than the average age of the students and 22 years older than the average age of everyone present in the class. How many students are there in the class?

6. Kate, Lena, Michael, Kristina took part in the concert. Each song was sung by 3 girls. Kate sang 8 songs - the most; Kristina has the least number of songs - 5 songs. How many songs were sung?

7. Is it possible to write the natural numbers from 1 to 30 in a table of 5 rows and 6 columns so that all six sums of the numbers in the columns are equal?

8. Is it possible to fill a table of size

a) 5×5 with numbers?

b) 6×6 so that the product of all numbers in any row is negative, and the product of all numbers in any column is positive?

c) Is it possible to arrange the numbers in a 19×66 table so that the sum of the numbers in each row is positive, and in each column the sum is negative?