Problems
The population of China is one billion people. It would seem that on a map of China with a scale of 1 : 1,000,000 (1 cm : 10 km), it would be possible to fit a million times fewer people than there is in the whole country. However, in fact, not only 1000, but even 100 people will not be able to be placed on this map. Can you explain this contradiction?
Several natives of an island met up (each either a liar or a knight), and everyone said to everyone else: “You are all liars.” How many knights were there among them?
Among 4 people there are no three with the same name, the same middle name and the same surname, but any two people have either the same first name, middle name or surname. Can this be so?
In a 10-storey house, 1 person lives on the first floor, 2 on the second floor, 3 on the third, 4 on the fourth, ..., 10 on the tenth. On which floor does the elevator stop most often?
Propose a method for measuring the diagonal of a conventional brick, which is easily realied in practice (without the Pythagorean theorem).
The seller with weights. With four weights the seller can weigh any integer number of kilograms, from 1 to 40 inclusive. The total mass of the weights is 40 kg. What are the weights available to the seller?
Cutting into four parts. Cut each of the figures below into four equal parts (you can cut along the sides and diagonals of cells).
We are looking for the correct statement. In a notebook one hundred statements are written:
1) There is exactly one false statement in this notebook.
2) There are exactly two false statements in this notebook.
...
100) There are exactly one hundred false statements in this notebook.
Which of these statements is true, if it is known that only one is true?
Solve the rebus \(AC \times CC \times K = 2002\) (different letters correspond to different integers and vice versa).
Rebus. Solve the numerical rebus \(AAAA-BBB + SS-K = 1234\) (different letters correspond to different numbers, but the same letters each time correspond to the same numbers)