Filter Problems

Showing 1 to 17 of 17 entries

On a table there are 2022 cards with the numbers 1, 2, 3, …, 2022. Two players take one card in turn. After all the cards are taken, the winner is the one who has a greater last digit of the sum of the numbers on the cards taken. Find out which of the players can always win regardless of the opponent’s strategy, and also explain how he should go about playing.

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

In the equation $101 – 102 = 1,$ move one digit in such a way that that it becomes true.

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.

Using five nines, arithmetic operations and exponentiation, form the numbers from 1 to 13.

Using five eights, arithmetic operations and exponentiation, form the numbers from 1 to 20.

Using five sevens, arithmetic operations and exponentiation, form the numbers from 1 to 22.

Using five sixes, arithmetic operations and exponentiation, form the numbers from 1 to 14.

Using five fives, arithmetic operations and exponentiation, form the numbers from 1 to 17.

Using five fours, arithmetic operations and exponentiation, form the numbers from 1 to 22.

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

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

Compare the numbers: $A=2011\times 20122012\times 201320132013$ and $B= 2013\times 20112011 \times 201220122012$.

Pinocchio correctly solved a problem, but stained his notebook.

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

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

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?

Catherine asked Jennifer to multiply a certain number by 4 and then add 15 to the result. However, Jennifer multiplied the number by 15 and then added 4 to the result, but the answer was still correct. What was the original number?