I don't know where to start.
i know that I am supposed to use some sort of probability principal.
2026-04-09 17:06:36.1775754396
Show that if five points are placed in a Equilateral triangle with sides of 2, two points will always be closer than 1
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Try to divide an equilateral triangle into four equal parts, each of which is an equilateral triangle of side $1$.
Now, if there are five points, then two of these must lie within the same equilateral triangle, since we have five points, which is more than four triangles.
Prove that any two points within an equilateral triangle of side $1$ cannot be separated by more than $1$ unit. Then you would be done.