Question

A tetrahedral puzzle is made of smaller tetrahedrons. One face of the larger tetrahedron is shown divided into smaller ones. Assuming all faces are the same, how many small tetrahedrons are there on the faces of the larger tetrahedron?

Hint:

Each face of a tetrahedron is an equilateral triangle. If divided into $n$ parts per side, number of sub-triangles = $n^2$.

Answer 1

Step 1: Count subdivisions.
From the image, one face of the tetrahedron is divided into $4^2 = 16$ small equilateral triangles.
Step 2: Number of faces.
A tetrahedron has 4 triangular faces.
Step 3: Total small tetrahedrons on faces.
\[ 16 \times 4 = 64 \] Final Answer: \[ \boxed{64} \]