Problems

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.

Try to make a square from a set of rods:

6 rods of length 1 cm, 3 rods of length 2 cm each, 6 rods of length 3 cm and 5 rods of length 4 cm. You are not able to break the rods or place them on top of one another.

In the equation \(101 - 102 = 1\), move one digit in such a way that that it becomes true.

Try to get one billion \(1000000000\) by multiplying two whole numbers, in each of which there cannot be a single zero.

Alex laid out an example of an addition of numbers from cards with numbers on them and then swapped two cards. As you can see, the equality has been violated. Which cards did Alex rearrange?

The number \(A\) is positive, \(B\) is negative, and \(C\) is zero. What is the sign of the number \(AB + AC + BC\)?

Pinocchio correctly solved a problem, but stained his notebook. \[(\bullet \bullet + \bullet \bullet+1)\times \bullet= \bullet \bullet \bullet\]

Under each blot lies the same number, which is not equal to zero. Find this number.