MathDB

p1. Juan and Carlos draw the tadpoles in their design class (they are the ones with contour continuous). Which of the two has a greater area, if all the circles have the same radius and the equilateral triangle has a side equal to one diameter? https://cdn.artofproblemsolving.com/attachments/7/5/b8cf02ea3222f95e4e96e095ceee39d80ade94.jpg
p2. Find some positive

N

10

digits, all different from

0

and such that, by adding

N

with the product of its digits (which we will denote by

P

), we obtain a number

M

that has a sum of digits equal to

P

.
p3. In each square of a

3\times 3

square one of the numbers

1,2,3,...,9

is written . It is known that the sum of the numbers of each is equal to

15

, and that the same happens with the numbers of each column or diagonal.

\bullet

What number is in the center box?

\bullet

Give examples of configurations that verify the properties.
p4. A mathematician tells another: ''I think you can guess how many grandchildren I have and what age are, if I tell you that the product of their ages is

36

and the sum of their ages coincides with the number of floors of the front building.'' His friend thinks for a while and replies: ''Your information is not enough, Caramba!.'' Then, the first adds smiling: '' My older grandson is called Sandro .'' ''Now it is another thing! '' says the second one, and gives the correct answer. What are the ages then?
p5. Calculate the area of the triangle

ABC

, knowing that

BD = 4

DE = 2

EC = 6

BF = FC = 3

. https://cdn.artofproblemsolving.com/attachments/6/0/11bbba5770b845380cc2fbe9f03847228752f9.jpg
p6. Maca's family has

4

people: grandfather, mother, father, and herself. If we double the size of Maca's monthly scholarship, the family income will increase by

5\%

. If instead of the Maca scholarship, her mother's salary would be doubled, the family income will grow by

15\%

. The same procedure gives

25\%

in the case of Dad now. In what percentage does the family income grow, if only the grandfather's salary is doubled?
PS. Juniors P6 was also [url=https://artofproblemsolving.com/community/c4h2692089p23370183]Seniors P4.

Problem Statement