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#### A segment inside the triangle is smaller than the largest side , Discrete distribution

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?

#### A segment inside the triangle is smaller than the largest side , Pythagorean theorem and its converse

A 3×4 rectangle contains 6 points. Prove that amongst them there will be two points, such that the distance between them is no greater than $\sqrt5$

#### A segment inside the triangle is smaller than the largest side , Hexagons , Pigeonhole principle (angles and lengths) , Regular polygons

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 segment inside the triangle is smaller than the largest side , Pigeonhole principle (finite number of poits, lines etc.)

51 points were thrown into a square of side 1m. Prove that it is possible to cover some set of 3 points with a square of side 20cm.

#### A segment inside the triangle is smaller than the largest side , Pigeonhole principle (angles and lengths)

Prove that it is not possible to completely cover an equilateral triangle with two smaller equilateral triangles.

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