Three lines are drawn inside a triangle, one from each corner to the opposite side, and they do not pass through one point. How many triangles does the figure contain?

Sort by how many inner lines form the sides. None: the whole triangle, 1. One: each inner line splits the triangle into 2, so 6. Two: each pair of inner lines crosses and makes 3 triangles with the sides, 9. Three: the small middle triangle, 1. Total $1+6+9+1=17$.