In a triangle ABC a point D is marked on the side BC and the line AD is drawn. A second point E is then marked on the part BD, and the line AE is drawn as well. How many triangles does the completed drawing contain?

Along the base the four points now lie in the order B, E, D, C. Every triangle in the picture has A at the top and a piece of the base at the bottom, so one triangle is formed for each choice of two of those four points: BE, ED, DC, BD, EC and BC. That is 6 triangles — ABE, AED, ADC, ABD, AEC and ABC. The trap is 3: it counts only the three smallest triangles and misses the ones made by joining neighbouring pieces of the base.