Using five fours, arithmetic operations and exponentiation, form the numbers from 1 to 22.
Using five fives, arithmetic operations and exponentiation, form the numbers from 1 to 17.
Using five sixes, arithmetic operations and exponentiation, form the numbers from 1 to 14.
Using five sevens, arithmetic operations and exponentiation, form the numbers from 1 to 22.
Using five eights, arithmetic operations and exponentiation, form the numbers from 1 to 20.
Using five nines, arithmetic operations and exponentiation, form the numbers from 1 to 13.
In a room, there are three-legged stools and four-legged chairs. When people sat down on all of these seats, there were 39 legs (human and stool/chair legs) in the room. How many stools are there in the room?
One day a strange notebook was found on the stairs. It contained one hundred statements:
“There is exactly one incorrect statement in this notebook”;
“There are exactly two incorrect statements in this notebook”;
“There are exactly three incorrect statements in this notebook”;
...
“There are exactly one hundred incorrect statements in this notebook.”
Are any of these statements true, and if so, which ones?
Jack the goldminer extracted 9 kg of golden sand. Will he be able to measure 2 kg of sand in three goes with the help of scales: a) with two weights of 200 g and 50 g; b) with one weight of 200 g?
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?