On the diagram below the line
How many five-digit numbers are there which are written in the same from left to right and from right to left? For example the numbers
Definition A set is a collection of elements, containing only one copy of each element. The elements are not ordered, nor they are governed by any rule. We consider an empty set as a set too.
There is a set
Does there exist a power of
Given a natural number
In a certain state, there are three types of citizens:
A fool considers everyone a fool and themselves smart;
A modest clever person knows truth about everyone’s intellectual abilities and consider themselves a fool;
A confident clever person knows about everyone intellectual abilities correctly and consider themselves smart.
There are
Draw a shape that can be cut into
There are
A equilateral triangle made of paper bends in a straight line so that one of the vertices falls on the opposite side as shown on the picture. Prove that the corresponding angles of the two white triangles are equal.
A rectangular parallelepiped of the size