Make a triangle by connecting three points from these points.
Noted that three sides of triangle do not pass through any other points except vertexes of the triangle.
How many triangles containing three points inside are there in all?
Answer
18 pieces
Solution
As shown below, it is possible to make two pieces around the equilateral triangle shaded.
It's also possible to make two pieces respectively in the same way around 5 equilateral triangles as shown in a figure below.
It's also possible to make six triangles as shown in a figure below.
Therefore altogether, it's 2 × 6 + 6 = 18 pieces.
