How Many Equilateral Triangles are Needed for Perfect Coverage?

[engin]

Homework Statement

We are using a drawing program in computer and we place x number of identical equilateral triangles(of same length of edges) randomly. So whenever we choose a triangle on the screen randomly(each has an equal number of possibility of being selected), we can slide the other triangles(without rotating them) in any way to cover the chosen one. In order to able to do this for each chosen triangle and for each different placements of the other triangles, what is the minimum number of triangles,that is x, placed on the screen?

Homework Equations

The Attempt at a Solution

This problem is neither homework nor coursework; it is a challenging - i think -math puzzle i saw on the internet. I didn't solve it formally but i guess that the minimum number of triangles is 4 using the symmetry(both relative and intrinsic) of the equilateral triangles.

 

[HallsofIvy]

First you will have to tell exactly what you mean by "place x number of identical equilateral triangles(of same length of edges) randomly". While we can assume that choosing one of the triangles "randomly" means using the uniform distribution, since there are only a finite number of triangles, there are an infinite number of ways to place triangles on the screen. What probability distribution are you using for "randomly"?

 

[engin]

I have thought of it as uniform distribution, too, without taking into account the technical problem that might occur with the infinite number of possibilities. I didn't take the probability and random variables at the university so i don't know what random actually means here but i doubt the puzzlewriter uses it in a technical manner, since it is not a formal math question but a puzzle.