We solve problems

Problem #PRU-61538

Problems Set theory and logic Joke problem Algebra and arithmetic Polynomials Polynomials(other)

12–16 2.0

Find the coefficient of $x$ for the polynomial $(x - a) (x - b) (x - c) \dots (x - z)$ .

Problem #PRU-104037

Problems Algebra and arithmetic Arithmetics. Mental maths Set theory and logic Joke problem

11–13 2.0

Gerard says: the day before yesterday I was 10 years old, and next year I will turn 13. Can this be?

Problem #PRU-104039

Problems Set theory and logic Joke problem

12–14 2.0

We call a natural number “amazing” if it has the form $a^{b} + b^{a}$ (where $a$ and $b$ are natural numbers). For example, the number 57 is amazing, since $57 = 2^{5} + 5^{2}$ . Is the number 2006 amazing?

Problem #PRU-104041

Problems Set theory and logic Joke problem

12–13 2.0

Homework. Cut a hole in an exercise book of a size so that you yourself can climb through it.

Problem #PRU-104122

Problems Algebra and arithmetic Arithmetics. Mental maths Set theory and logic Joke problem

12–13 2.0

Henry did not manage to get into the elevator on the first floor of the building and decided to go up the stairs. It takes 2 minutes to rise to the third floor. How long does it take to rise to the ninth floor?

Problem #PRU-35764

Problems Algebra and arithmetic Algebraic geometry Cryptography Set theory and logic Joke problem

11–13 2.0

A message is encrypted by replacing the letters of the source text with pairs of digits according to some table (known only to the sender and receiver) in which different letters of the alphabet correspond to different pairs of digits. The cryptographer was given the task to restore the encrypted text. In which case will it be easier for him to perform the task: if it is known that the first word of the second line is a “thermometer” or that the first word of the third line is “smother”? Justify your answer. (It is assumed that the cryptographic table is not known).