Expert: Bernard Hawkes - 10/2/2007

Question
I was given this riddle years ago and I never got the answer. I'm not
sure if there is one.

"There is a pilot that crash lands on an island. There is a unique
characteristic about this island and that is this: Nothing on the Island
has reflective a property. The water is not reflective, the metal from
the airplane has no reflection. There is NO WAY to view oneself.

The pilot meets the natives of the island who also carry a unique
property. Some natives have a red dot on their forehead, and some do not.
The placement of these dots is completely random, the inhabitants of the
island are born with the dot. Again it is completely random.

There are two rules on the island: If you speak of the red dot, you
have to be put to death. And If you know you have a red dot you must kill
yourself.

The pilot asks the chief about the red dots in front of the entire
village and is immediately put to death.

3 nights later everyone who had a red dot on their forehead killed
themselves on the same night. Why?

Key points:
No one broke the rules and spoke of the dots
No one pointed out the dots
no one made eye contact with the dots
There is nothing reflective on the island
the placement is completely random
everyone who had a dot killed themselves."

the guy who told me this riddle never gave me an answer and it really
bothered me.


Answer
Hi Kyle

This is a really tricky one not helped by the fact that situation is highly unlikely in the extreme. All thoughts of how the situation established itself, how do new born babies of the natives acquire this knowledge must be resolutely put to one side. You start by accepting the initial situation and that the arrival of the pilot is the catalyst for the subsequent actions (and non-actions) that culminate on the third night in three suicides.

It is necessary to assume that all the natives are brilliant logisticians and that things happen in daily cycles. I.e. during the daylight hours the natives observe certain things (or their absence) and them at night they take action, i.e. kill themselves if they have deduced that they must have a red dot.

OK, lets get started. The utterances of the pilot informs all the natives that one or more of them have a red dot. Now suppose that just one native has a red dot. This native can see that everybody else has NO red dot and can immediately conclude that he is must have a red dot. However, there is no suicide the first night, so there must be more than one native with a red dot.

Suppose that there are two natives with red dot. On the first day they each know that:-
a) One (other) person has a red dot,
b) I may or may not have a red dot,
c) Nobody else has a red spot.
From this they can predict:-
If I do NOT have a red dot the person I can see that has a red dot will commit suicide tonight (by the above logic). On the second day they observe that there has been no suicide and are then able to deduce that they DO have a red dot. They then both kill themselves on the second night. However, there are no suicides the second night, so there must be more than two natives with a red dot.

Now suppose there are three natives with a red dot. On the first day they all know nothing will happen (by the above logic). On the second day they each know that:-
a) Two (other) persons have a red dot,
b) I may or may not have a red dot,
c) Nobody else has a red spot.
From this they can predict:-
If I do NOT have a red spot the people I can see that have a red dot will commit suicide tonight (by the above logic). On the third day they observe that there have been no suicides and are then able to deduce that they DO have a red dot. They then all kill themselves on the third night.

I hope that makes some sort of sense!

Best wishes,
Bernard.