We solve problems

Problems Algebra Arithmetics. Mental maths Set theory and logic Joke Problems

Gerard says: the day before yesterday I was 10 years old, and next year I will turn 13. Can this be?

Problems Set theory and logic Joke Problems

We call a natural number “amazing” if it has the form \(a^b + b^a\) (where \(a\) and \(b\) are natural numbers). For example, the number 57 is amazing, since \(57 = 2^5 + 5^2\). Is the number 2006 amazing?

Problem #PRU-104041

Problems Set theory and logic Joke Problems

12–13 2.0

Homework. Cut a hole in an exercise book of a size so that you yourself can climb through it.

Problem #PRU-104046

Problems Combinatorics

10–13 2.0

A toddler has \(25\) lego pieces in a box:

In how many ways are there to choose three pieces to play with?
In how many ways can he choose three pieces for the foundation, main walls and roof? Note that the order is important.

Problem #PRU-104057

Problems Algebra Arithmetics. Mental maths

10–12 2.0

Doctor Smith gave out 2006 miracle tablets to four sick animals. The rhinoceros received one more tablet than the crocodile. The hippopotamus got one more tablet than the rhino. The elephant got one more tablet than the hippo. How many tablets did the elephant have to eat?

Problem #PRU-104058

Problems Combinatorics Geometry on grid paper

12–13 2.0

Cut the shape (see the figure) into two identical pieces (coinciding when placed on top of one another).

Problem #PRU-104060

Problems Set theory and logic Algorithm Theory Algorithm Theory

11–13 2.0

Gabby is standing on a river bank. She has two clay jars: one – for 5 litres, and about the second Gabby remembers only that it holds either 3 or 4 litres. Help Gabby determine the capacity of the second jar. (Looking into the jar, you cannot figure out how much water is in it.)

Problem #PRU-104069

Problems Algebra Algebraic equations and systems of equations Arithmetics. Mental maths

10–12 2.0

There are two numbers \(x\) and \(y\) being added together. The number \(x\) is less than the sum \(x+y\) by 2000. The sum \(x+y\) is bigger than \(y\) by 6. What are the values of \(x\) and \(y\)?

Problem #PRU-104072

Problems Set theory and logic Mathematical logic Mathematical logic (other)

10–12 2.0

On Brennan’s birthday, the postman Daniel wants to find out how old Brennan is. Sarah says that Brennan is over 11 years old, and Matt claims that he is more than 10 years old. How old is Brennan, if it is known that exactly one of them was mistaken? Justify your answer.

Problem #PRU-104074

Problems Set theory and logic Set theory Inclusion-exclusion principle

11–13 2.0

In the garden of Sandra and Lewis 2006 rose bushes were growing. Lewis watered half of all the bushes, and Sandra watered half of all the bushes. At the same time, it turned out that exactly three bushes, the most beautiful, were watered by both Sandra and Lewis. How many rose bushes have not been watered?