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# Is the name of this island Oahu? That depends on who is asking.

## Question

Somewhere in waters as yet uncharted is the Island named What Is The Name Of This Island?

It's a strange place by any standard: its inhabitants cannot form declarative statements.

Nor are they allowed exclamations. They can only ask questions. Yes/No questions, to be precise.

Is 2 + 2 equal to 4? But they could not ask whether that sum is 5. The other natives, (type B)

are just the opposite. They can only ask questions whose correct answer is No. They could

ask whether 2 + 2 equals 5; but not whether that sum was 4.

I met there a couple, named Sam and Janet Evening. Sam was heard to ask another native,

"Are Janet and I both type B?" What type, therefore, is Janet?

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Let us explore following possibilities;

(i) Sam – Type B, Janet – Type A
(ii) Sam – Type B, Janet – Type B
(iii) Sam – Type A, Janet – Type B
(iv) Sam – Type A, Janet – Type A

Say Sam is type B and Janet is type B, then the answer to the Q will be yes. but type B can’t ask such question. So Sam isn’t type B if Janet is type B.
Similarly another possibility of Janet and Sam both being Type A, OR Sam being type A and Janet being Type B isn’t possible, as in both cases, the answer to the Q would be NO, and such question can’t be asked by Type A.
Therefore only possibility Is that Sam is Type B and Janet is Type A.

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Say Sam is type A. That would mean that the answer to the question "Are they both type B?" would be true. However, that means that Sam is type B, which is a contradiction since he was assumed to be type A. Therefore, Sam is type B.

Since Sam is type B, the answer to the question "Are they both type B?" would be false. In order for this to be false, one of them has to be type A, and since Sam was assumed to be type B, Janet has to be type A.

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