With a non-zero number, the following operations are allowed:
Prove that if the irreducible rational fraction
There are 8 glasses of water on the table. You are allowed to take any two of the glasses and make them have equal volumes of water (by pouring some water from one glass into the other). Prove that, by using such operations, you can eventually get all the glasses to contain equal volumes of water.
A function
Author: I.I. Bogdanov
Peter wants to write down all of the possible sequences of 100 natural numbers, in each of which there is at least one 3, and any two neighbouring terms differ by no more than 1. How many sequences will he have to write out?
Author: I.I. Bogdanov
Peter wants to write down all of the possible sequences of 100 natural numbers, in each of which there is at least one 4 or 5, and any two neighbouring terms differ by no more than 2. How many sequences will he have to write out?
Author: G. Zhukov
The square trinomial
Can the discriminant of the trinomial
At what value of
The bus has
On a particular day it turned out that every person living in a particular city made no more than one phone call. Prove that it is possible to divide the population of this city into no more than three groups, so that within each group no person spoke to any other by telephone.