Hardest math question I've ever seen!

Question

A friend of mine ask me this question(I'm not even convinced that it is from SAT subject test Math level 2, let alone the SAT). The question states as follow: Linda is bored during his chemistry class with Mrs Victoria. He decided to draw a regular pentagon on the chemistry exercises paper his teacher gave him; he calls it ABCDE. He then connects all of its diagonals to form a star (like in this picture: [https://imgur.com/a/UFt5qBc](https://imgur.com/a/UFt5qBc)). Linda wishes to put some pebbles he previously collected inside the regular pentagon so that each pebble could neither touch the edge nor the diagonal of the shape. But he also want each triangle formed by any three point of the points A, B, C, D, E (e.g. triangle ACD, BED, ABC) to contains at least one pebble (there're a total of 10 such triangles). The minimum number of pebbles that he can place is A) 1 B) 3 C) 4 D) 5

Answer 1

It can be done with less than 5 pebbles. The ten possible triangles can be divided into two types.

Answer 2

I would say D) 5. Draw and label of diagram!