So this is a question that was asked in the International Kangaroo Math Contest 2017. The question is:
The faces of the following polyhedron are either triangles or squares. Each triangle is surrounded by $3$ squares and each square is surrounded by $4$ triangles. If there are $6$ square faces, how many triangular faces are there?
What I did:
Each square shares each of its four neighboring triangles with two more squares. So we can say that for 6 squares we have $6\times4\ -\ 2 \times 6 = 12$ triangles. However, I still know that this calculation of mine is quite wrong and based on an awkward thinking. So, what is the correct answer and how?
Thanks for the attention.