Question 18
Call a triangle big if each side is longer than $1$. Show that we can draw $100$ big triangles inside an equilateral triangle with side length $5$ so that all the triangles are disjoint. Show that you can draw $100$ big triangles with every vertex inside or on an equilateral triangle with side $3$, so that they cover the equilateral triangle, and any two big triangles either (1) are disjoint, or (2) have as intersection a common vertex, or (3) have as intersection a common side.