Three hedgehogs divided three pieces of cheese of mass of 5g, 8g and 11g. The fox began to help them. It can cut off and eat 1 gram of cheese from any two pieces at the same time. Can the fox leave the hedgehogs equal pieces of cheese?
Solve the rebus: \(AX \times UX = 2001\).
A rectangle is cut into several smaller rectangles, the perimeter of each of which is an integer number of meters. Is it true that the perimeter of the original rectangle is also an integer number of meters?
Arrange brackets and arithmetic signs around these numbers so that the correct equality is obtained: \[\frac{1}{2}\quad \frac{1}{6}\quad \frac{1}{6009} \ = \ 2003.\]
The number \(A\) is positive, \(B\) is negative, and \(C\) is zero. What is the sign of the number \(AB + AC + BC\)?
a) A 1 or a 0 is placed on each vertex of a cube. The sum of the 4 adjacent vertices is written on each face of the cube. Is it possible for each of the numbers written on the faces to be different?
b) The same question, but if 1 and \(-1\) are used instead.
Gerard says: the day before yesterday I was 10 years old, and next year I will turn 13. Can this be?
Solve the equation: \[x + \frac{x}{x} + \frac{x}{x+\frac{x}{x}} = 1\]
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?
In a chess tournament, each participant played two games with each of the other participants: one with white pieces, the other with black. At the end of the tournament, it turned out that all of the participants scored the same number of points (1 point for a victory, \(\frac{1}{2}\) a point for a draw and 0 points for a loss). Prove that there are two participants who have won the same number of games using white pieces.