In a square carpet with a side of 4 meters, the moth ate 15 holes. Prove that it is possible to cut a rug from this carpet with a side of 1 meter, in which there will be no holes.

Leaflet #pigeonhole

In the final of the school basketball championship, the team scored 9 goals. Prove that there are 2 players of this team who scored equally goals. (There are 5 players on the basketball team.)

Leaflet #pigeonhole

Is it true that there are at least two people in your room who have the same number of friends in that room?

Leaflet #pigeonhole

There are two buckets: one with a capacity of 4 liters and the other with a capacity of 9 liters. Is it possible to use them alone to draw exactly 6 liters of water from the river?

Leaflet #transfusion

1) Is it possible to draw 4 liters of water from the tap with two 3-liter and 5-liter jars?

2) The same question if there are only 6-liter and 9-liter jars?

Leaflet #transfusion

Pour 13 liters of water from the cistern using 5-liter and 17-liter canisters.

Leaflet #transfusion

Is it possible to draw 8 liters of water from the river using two buckets with a capacity of 15 liters and 16 liters?

Leaflet #transfusion

There are three pots: 8 liters with compote, 3 liters and 5 liters empty. How do you divide the compote in half? (Compote, unlike water, cannot be poured out.)

Leaflet #transfusion

Is it possible to pour 50 liters of gasoline into three tanks so that the first tank has 10 liters more than the second, and the second tank has 21 liters more than the third?

Leaflet #transfusion

There are two hourglasses: for 7 minutes and for 11 minutes. The porridge cooks for 15 minutes. How do you use this clock to measure the right time?

Leaflet #transfusion

There are three 3L, 4L and 5L vessels, a tap with water and 3L of syrup in the smallest vessel. Is it possible to get 6 liters of a mixture of water and syrup so that there is an equal amount of water and syrup in each vessel?

Leaflet #transfusion

A man says: "I am a liar". Can he be a resident of the island of knights and liars?

The action in almost all problems of the leaflet #amazing_island takes place on an island whose inhabitants are knights and liars. Knights always tell the truth and liars always lie.

📜 Leaflet #amazing_island

More about liar's paradox.

Each of the islanders gathered in the square said to the others: You are all liars.
How many knights are there among them?

📜 Leaflet #amazing_island

Wikipedia

1) Each of the 7 residents of the island sitting at the round table said: "My neighbors are a liar and a knight."
How many knights and how many liars are sitting at the table?

2) The same question if 9 islanders were sitting at the table?

📜 Leaflet #amazing_island

What question do you have to ask an islander to find out if he has a pet crocodile living in his house?

💡 I remind you that there are knights and liars on the island. Knights always tell the truth and liars always lie.

🎯 Solution:
A question like this:
«If I asked, "Do you have a pet crocodile at home", would you say yes?»

Why:
1) A liar with a crocodile, always lies, would answer "no" to the question "Do you have a pet crocodile at home" and answer "yes" to my question;
2) A liar without a crocodile, similarly, "no."
3) A knight with a crocodile, always tells the truth, so "yes";
4) A knight without a crocodile, similarly, "no".

Bottom line: the resident of the island with a crocodile answers my question "yes", and without a crocodile - "no".

📜 Leaflet #amazing_island

A tribe of cannibals caught Robinson Crusoe. The leader said, "We would be happy to let you go, but according to our law you have to make some statement. If it turns out to be true, we'll eat you. If it turns out to be false, our lion will eat you."
What should I say to Robinson to avoid being eaten?

📜 Leaflet #amazing_island