Just two options!

Logic Level 1

A very special island is inhabited only by knights who always tell the truth and knaves who always lie. You meet two inhabitants, Alexander and Broad, who make the following statements:

Alexander: "Broad is the knave."
Broad: "Neither of us are knaves."

Who is the knave?

Alexander Broad

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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3 solutions

Munem Shahriar
Jul 25, 2017

  • Assume Alexander's statement is true. If Broad is a knave, that means that he is lying. That would mean that one of them is a knave, which would still be true.

  • If Alexander was lying, then Broad would be telling the truth that neither of them were knaves, which would contradict Alexander's lie.

Therefore, Alexander is a knight, and Broad is a knave. \color{#3D99F6}\boxed { \text{Broad is a knave.}}

5 Helpful 1 Interesting 1 Brilliant 1 Confused
Alex Li
Jul 31, 2017

We know there is a knave since the problem asks for it. Since Broad says there are no knaves, he must be lying.

1 Helpful 1 Interesting 1 Brilliant 1 Confused
Saya Suka
Apr 25, 2021

Alexander is making an accusation against Broad, therefore they must be from different tribes. Broad statement does not reflect this fact, so he must be lying as a knave and Alexander who tells the truth about him is a Knight.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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