We solve problems

Problems Algebra and arithmetic Arithmetics. Mental maths Geometry Solid geometry Volume Ratio of volumes

When Gulliver came to Lilliput, he found that there all things were exactly 12 times shorter than in his homeland. Can you say how many Lilliputian matchboxes fit into one of Gulliver’s matchboxes?

Problem #PRU-103019

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

10–10 2.0

If the Humpbacked Horse does not eat or sleep for seven days, it will lose its magical powers. Suppose he did not eat or sleep for a week. What should he do first of all by the end of the seventh day – eat or sleep, so as not to lose powers?

Problem #PRU-103749

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

10–12 2.0

Know-it-all came to visit the twin brothers Screw and Nut, knowing that one of them never speaks the truth, and asked one of them: “Are you Screw?”. “Yes,” he replied. When Know-it-all asked the second brother the same question, he received an equally clear answer and immediately determined who was who.

Who was called Screw?

Problem #PRU-103800

Problems Set theory and logic Joke problem

10–12 2.0

In two purses lie two coins, and one purse has twice as many coins as the other. How can this be?

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-103947

Problems Geometry Plane geometry Area

10–12 2.0

Find the area of the figures shown below.

Problem #PRU-103987

Problems Methods Pigeonhole principle Pigeonhole principle (other)

10–12 2.0

a) Prove that in any football team there are two players who were born on the same day of the week.

b) Prove that in the population of London, which is almost 9 million, there will be ten thousand people who celebrate their birthday on the same day.

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-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-115374

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

10–12 2.0

In Neverland, only elves and gnomes live. Gnomes lie about their gold, but in any other instances they tell the truth. Elves lie when talking about gnomes, but in other instances they tell the truth. One day two neverlandians said:

\(A\): All my gold I stole from the Dragon.

\(B\): You’re lying.

Determine whether each of them is an elf or a gnome.