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 below "solution" is wrong. See Math Man's Correct Solution, in the post following this.

Green and blue must be of opposite truth types as they contradict one another.

Red must be a liar as no one with 11 arms would say so. He must have a different odd number of arms, and, more to the point, the blue one doesn't have ten arms and it is blue who is the liar (between Green and Blue), making green a truth-teller with ten arms.

At this point the puzzle is solved: Green has exactly 10 arms.

Incidentally, the striped one is lying.

Edited on December 22, 2012, 9:57 am

Posted by Charlie on 2012-12-21 12:38:50