Page 37 - NUMINO Challenge_D2

4 Principle of Drawers

Basic Concepts Pigeonhole Principle

If ( 1) pigeons are going inside pigeonholes, there will be at least one
pigeonhole that has two pigeons in it. This is called a pigeonhole principle.
If an equilateral triangle is divided into four smaller equilateral triangles and five
dots are drawn inside as shown below, there will be at least one equilateral
triangle that has two dots drawn inside.

Example The shape of a room was made by connecting six equilateral
triangles with sides of 5 m. If seven doors are made on the floor of
the room, each leading to the basement, will there be two doors
located closer than 5 m?

5m

Class Notes

First, divide the room into equilateral triangles as shown on the

right. Then you can make a total of doors if you make one door
in each equilateral triangle.

If you make one more door in the room, there will be one equilateral triangle 5m

that will have doors. Then, the distance between the two doors

is closer than m, which is the length of a side of the equilateral triangle.

Therefore, there will be two doors that are closer than m.

34 NUMINO Challenge D2