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## Homework Statement

How many points can be placed in an equilateral triangle where each side is of length 2 such that no 2 points are within 1 of each other?

## Homework Equations

Need to use pigeon hole principle.

## The Attempt at a Solution

I know that there are at least 3. Visually, if you sketch the triangle it looks like there will be a 4. However, I don't know how to prove this.