# Splitting an Equilateral Triangle

Geometry Level 5

Brilli the ant has a block of cheese that is in the shape of an equilateral triangle. She is hosting a party, and has invited her two-legged house mates. She insists that all of her guests get a piece of cheese that is in the shape of an isosceles triangle. What is the maximal number $$N$$ such that she cannot split the equilateral triangle block of cheese into $$N$$ non-degenerate isosceles triangles?

Details and assumptions

An equilateral triangle is also an isosceles triangle.

A degenerate triangle has 0 area, and the 3 vertices lie on a straight line.

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