Prove that it is not possible to completely cover an equilateral triangle with two smaller equilateral triangles.
A moth makes \(51\) little holes on a square cloth that is \(1\) meter on each side. Think of the holes as just tiny dots with no size. Show that you can always cover at least \(3\) of the holes with a square patch that is \(20\) centimeters on each side.
There are 7 points placed inside a regular hexagon of side length 1 unit. Prove that among the points there are two which are less than 1 unit apart.
A \(3\times 4\) rectangle contains 6 points. Prove that amongst them there will be two points, such that the distance between them is no greater than \(\sqrt5\).
There are 25 children in a class. At random, two are chosen. The probability that both children will be boys is \(3/25\). How many girls are in the class?