Two classes with the same number of students took a test. Having checked the test, the strict teacher Mr Jones said that he gave out 13 more twos than other marks (where the marks range from 2 to 5 and 5 is the highest). Was Mr Jones right?
Write the first 10 prime numbers in a line. How can you remove 6 digits to get the largest possible number?
In one move, it is permitted to either double a number or to erase its last digit. Is it possible to get the number 14 from the number 458 in a few moves?
Is the number \(10^{2002} + 8\) divisible by 9?
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.
Find the largest six-digit number, for which each digit, starting with the third, is equal to the sum of the two previous digits.
Find the largest number of which each digit, starting with the third, is equal to the sum of the two previous digits.
In the equation \(101 - 102 = 1\), move one digit in such a way that that it becomes true.
Find a two-digit number that is 5 times the sum of its digits.
Will the quotient or the remainder change if a divided number and the divisor are increased by 3 times?