How many tetrahedra?
Geometry
Level
2
If the above image is a complete model of a Sierpinski tetrahedron, then how many of the smallest tetrahedra is it composed of?
Image credit: http://thepuzzleden.blogspot.com/
The answer is 1024.
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1 solution
If you consider one of the "unit tetrahedra" in the corner of the model and work toward another corner of the model, then each time you double the length of the edge, you multiply the number of tetrahedra by four. Since, in this picture the length gets doubled five times, there are 4 5 = 1 0 2 4 tetrahedra.