Elves and Goblins

Logic Level 2

On a certain island there elves who always tell the truth and goblins who always lie; other than that, you cannot tell what type an islander is. You come across 4 islanders, Alice, Bob, Cam, and Dina. After asking them how many elves and goblins there are among them, they each say the following:

Alice: There are exactly 2 elves among us.

Bob: There are at most 3 goblins among us.

Cam: There is only one goblin among us.

Dina: Alice is telling the truth.

If we know that there is at least one elf, how many goblins are there?

The answer is 3.

2 solutions

Jay B
Jun 25, 2020

If Dina and Alice are telling the truth, then they are the two elves. This means that there would be 2 goblins, i.e., at most 3 goblins. This makes Bob an elf giving us 3 elves contrary to what Alice said. Then Alice and Dina are goblins. But then there are 2 goblins > 1 goblin so that Cam lied. Then we have 3 goblins. Since there is at least one elf, that would be Bob.

Same logic

Elijah Frank - 6 months, 3 weeks ago

I have a question: the question ask for the num of goblins and we know it has at least 1 of four elves can't we just try 1, 2, 3 after realizing bob would always tell the truth unless there were 4 goblins and because it is false( at least 1 elf so he is lying) and based on that people can guess it was btwn 1 and 3

Ken Falken - 4 months, 1 week ago

Saya Suka
Mar 17, 2021

Bob is definitely telling the truth by the statement told to us about "there is at least one elf", while Alice and Dina is obviously from the same tribe. By Alice statement, they can't be be together with Bob else their teammates number exceed the 2 mentioned by herself, so they must be lying as two goblins and Bob is the elf. By this discovery, Cam is another goblin since there are more than one goblin found in Dina and Alice.

Answer = 3 goblins, Cam, Alice and Dina, plus an elf Bob.

Elves and Goblins

The answer is 3.

2 solutions

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