In the gymnasium, all students know at least one of the ancient languages – Greek or Latin, some – both languages. 85% of all children know the Greek language and 75% know Latin. How many students know both languages?
Two classes with the same number of students took a test. Having checked the test, the strict teacher Mr Jones said that he gave out 13 more twos than other marks (where the marks range from 2 to 5 and 5 is the highest). Was Mr Jones right?
Before the start of the Olympics, the price of hockey pucks went up by 10%, and after the end of the Olympics they fell by 10%.
When were the pucks more expensive – before the price rise or after the fall?
What word is encrypted: 22212221265121? Each letter is replaced by its number in the English alphabet.
Write the first 10 prime numbers in a line. How can you remove 6 digits to get the largest possible number?
Is it possible to arrange 44 marbles into 9 piles, so that the number of marbles in each pile is different?
Is it possible to cut a square into four parts so that each part touches each of the other three (ie has common parts of a border)?
In one move, it is permitted to either double a number or to erase its last digit. Is it possible to get the number 14 from the number 458 in a few moves?
Can the following equality be true: \[K \times O \times T = A \times B \times C \times D \times E \times F\] if you substitute the letters with the numbers from 1 to 9? Different letters correspond to different numbers.
A page of a calendar is partially covered by the previous torn sheet (see the figure). The vertices A and B of the upper sheet lie on the sides of the bottom sheet. The fourth vertex of the lower leaf is not visible – it is covered by the top sheet. The upper and lower pages, of course, are identical in size to each other. Which part of the lower page is greater, that which is covered or that which is not?