A distant planet is inhabited by creatures having more than two arms. The ones with an even number of arms are the knights who always tell the truth; the ones with an odd number of arms are the liars who always speak falsely.

Four inhabitants are conversing amongst themselves:

• The green one says, "I have ten arms. The blue one has only eight arms."
• The blue one says, "I have ten arms. The green one has nine arms."
• The red one says, "The blue one has ten arms. I have eleven arms."
• The striped one says, "None of the four of us except myself have ten arms."

Which of the four inhabitants has exactly ten arms?

The red one is definitely lying because nobody with 11 arms can claim to have 11 arms. Therefore, the red one cannot have 10 arms. Since the red one is a liar and says that the blue one has 10 arms, the blue one cannot have 10 arms. That makes the blue one's first statement false, so the blue one cannot have 8 arms. Therefore, the green one's second statement is false, so the green one's first statement must also be false. That means that the green one does not have 10 arms. Therefore, the striped one has 10 arms.

Posted by Math Man on 2012-12-21 21:58:18