Ok, let's consider these scenarios:-

If you consider the case of just **one blue-eyed** person on the island, He looks around and sees no other blue eyed people and deduces the foreigner must be referring to him and he must commit suicide at noon on day 2.

[THEOREM 1] If there is one blue-eyed person, he will commit suicide on day 2.

If there are **two blue-eyed people**, they will each look at the other. They will each realize that "if I don't have blue eyes [HYPOTHESIS 1], then that guy is the only blue-eyed person. And if he's the only person, by THEOREM 1 he will commit suicide on day 2." They each wait and see, and when neither of them commit suicide on day 2, each realizes "HYPOTHESIS 1 was incorrect. I must have blue eyes." And each commits suicide on day 3.

So: [THEOREM 2]: If there are two blue-eyed people on the island, they will each commit suicide on day 3.

If there are **three blue-eyed people** what will happen and when?