Problems

Age
Difficulty
Found: 3

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?

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?

A country is called a Fiver if, in it, each city is connected by airlines with exactly with five other cities (there are no international flights).

a) Draw a scheme of airlines for a country that is made up of 10 cities.

b) How many airlines are there in a country of 50 cities?

c) Can there be a Fiver country, in which there are exactly 46 airlines?