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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