Until very recently, the small island nation of Scromitia had not had any contac

Question

Until very recently, the small island nation of Scromitia had not had any contact with the rest of the world. The Scromitians were a highly educated people, yet very fond of superstitions. The weirdest superstition they follow is that each Scromitian is given a different colored necklace at birth, but they are forbidden from knowing what color their necklace is. This neckalce, called a Scromitor, comes in two different colors, t omitors are magenta, and m Scromitors are turqoise. The Scromitians know that there are two colors available for Scromitors, and they can see everyone else's Scromitor, except for their own. If a Scromitian learns the color of their own necklace, they suffer massive organ failure, and they scromit t ough the Scromitians see each other's Scromitors they never talk about the color of anyone's Scromitor. One day, an explorer lands on the island. She is given a warm welcome, and the Scromitians throw a lavish feast for her which is attended by everyone on the island. While giving a toast, the explorer makes the following remark: urqoise and magenta. Assume that n Scr o death. Because of this threat, even th Thank you for your very warm welcome! I am very impressed by your culture, and I never thought I would see someone wear such a nice magenta Scromitor! Prove that n days later, all the Scromitians scromit to death.

Explanation / Answer

m is used for magenta

t is used for turquoise

Let's take the case of 1 magenta and 1 turquoise in this when they came to know that there is one magenta then when the magenta one sees the other color it is confirmed that his color is magenta it dies and hence to the other it is confirmed that its color is turquoise hence it dies also.

Now take case 1 m and 2 t

here similarly as above all will die as only one person has m necklace

Now 1t and 2m

In this case there will be doubt that whether the person who is seeing the other one wearing m necklace whether his color is also m or not so they wait out for the first day.

Then as they find out that they are again waiting the next day which implies that those wearing m necklace are facing the same situation hence they both are in doubt because of that hence they come to know that the color of their necklace is m hence they die.

The third person with t necklace will be sure that if they are dead then he has t necklace because they were watching each other and were in doubt.

Now we can generalise that this pattern will repeat and depending on n the number of scormitians wearing magenta necklace the days after which all will die.

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