Problems

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?

Find all of the natural numbers that, when divided by 7, have the same remainder and quotient.