Exampletown is a city made up of two kinds of people – nurts and blargs. Nurts a
ID: 3123234 • Letter: E
Question
Exampletown is a city made up of two kinds of people – nurts and blargs. Nurts always tell the truth, and blargs always lie. Every person is either a nurt or a blarg.
(a) There are two people, A and B. A says “At least one of us is a blarg.” Determine if each of A and B is a nurt or a blarg.
(b) Csays“EitherIamanurtorDisablarg.”DetermineifeachofCandDisanurtorablarg.
(c) E says “I am a blarg, but F isn’t.” Determine if each of E and F is a nurt or a blarg.
(d) There are three people, G, H, and J. G says “All of us are blargs”, H says “Exactly one of us is a nurt.” What are G, H, and J?
Explanation / Answer
(a) If A were to be a blarg, then he would be a liar. So his statement "Atleast one of us is a blarg" must have been false. But it is true. So we have a contradiction.
So A is a nurt. Since he is a nurt, his statement "Atleast one of us is a blarg" is true. So B is the blarg.
(b) If C is a blarg, his statement "either I am a nurt or D is blarg" would be false. This means C is a blarg and D is a nurt.
If C is a nurt, his statement "either I am a nurt or D is blarg" would be true. So D is a nurt.
From both cases, C could be blarg or nurt but D is always nurt.
(c) If E is a blarg his statement "I am a blarg but F isn't" should have been false. But since E is blarg, we have a contradiction.
If E is a nurt the statement "I am a blarg but F isn't" should have been true but it is false. We have another contradiction.
Thus we have a paradox. E and F cannot be determined.
(d) If G is a nurt, the statement "All of us are blargs" should be true. But it is false. So G is a blarg.
Further since G is a blarg, his statement "All of us are blargs" should be false. So atleast one among H and J must be a nurt.
H says "Exactly one of us is a nurt". If H is a blarg, then J must be a nurt.
But then H would be speaking the truth and we have a contradiction. So H is a nurt.
So his statement "Exactly one of us is a nurt" is true. Since H is a nurt, J must be a blarg.
So G,H and J are blarg, nurt, blarg respectively.
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