Using five twos, arithmetic operations and exponentiation, form the numbers from 1 to 26.
Using five threes, arithmetic operations and exponentiation, form the numbers from 1 to 39.
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?