We solve problems

Problems Geometry Solid geometry Spheres Circle on a sphere Visual geometry in space

A globe has 17 parallels and 24 meridians. How many parts is the globe’s surface divided into? The meridian is an arc connecting the North Pole with the South Pole. A parallel is a circle parallel to the equator (the equator is also a parallel).

Problem #PRU-103825

Problems Algebra and arithmetic Arithmetics. Mental maths Methods Examples and counterexamples. Constructive proofs Set theory and logic Theory of algotithms Theory of algorithms (other)

10–12 2.0

Three hedgehogs divided three pieces of cheese of mass of 5g, 8g and 11g. The fox began to help them. It can cut off and eat 1 gram of cheese from any two pieces at the same time. Can the fox leave the hedgehogs equal pieces of cheese?

Problem #PRU-103827

Problems Dissections

11–11 2.0

Cut the trapezium \(ABCD\) into two parts which you can use to construct a triangle.

Problem #PRU-103833

Problems Set theory and logic Algorithm Theory Algorithm Theory

10–12 2.0

On the island of Contrast, both knights and liars live. Knights always tell the truth, liars always lie. Some residents said that the island has an even number of knights, and the rest said that the island has an odd number of liars. Can the number of inhabitants of the island be odd?

Problem #PRU-103843

Problems Combinatorics Partitions

12–12 2.0

Cut the figure (on the boundaries of cells) into three equal parts (the same in shape and size).

Problem #PRU-103848

Problems Set theory and logic Mathematical logic Puzzles

12–13 2.0

In the line of numbers and signs \({}* 1 * 2 * 4 * 8 * 16 * 32 * 64 = 27\) position the signs “\(+\)” or “\(-\)” instead of the signs “\(*\)”, so that the equality becomes true.

Problem #PRU-103850

Problems Set theory and logic Mathematical logic Puzzles

12–13 2.0

The code of lock is a two-digit number. Ben forgot the code, but he remembers that the sum of the digits of this number, combined with their product, is equal to the number itself. Write all possible code options so that Ben could open the lock quickly.

Problem #PRU-103858

Problems Algebra and arithmetic Number theory. Divisibility The fundamental theorm of arithmetic. Prime factorisation.

12–13 2.0

Solve the rebus: \(AX \times UX = 2001\).

Problem #PRU-103869

Problems Set theory and logic Order relations Methods Pigeonhole principle Pigeonhole principle (other)

11–13 2.0

Solve the puzzle: \(BAO \times BA \times B = 2002\).

Problem #PRU-103873

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

11–12 3.0

Jessica, Nicole and Alex received 6 coins between them: 3 gold coins and 3 silver coins. Each of them received 2 coins. Jessica doesn’t know which coins the others received but only which coins she has. Think of a question which Jessica can answer with either “yes”, “no” or “I don’t know” such that from the answer you can know which coins Jessica has.