As everyone knows, knights tell the truth all the time, and liars lie all the time. At least, this is what evenly behaved knights and liars do.

Less known is that there are also odd knights, who on odd-numbered days lie all the time. (On even-numbered days, however, they behave evenly, and tell the truth.) Also, there are odd liars, who on odd-numbered days, tell the truth about everything, while they lie the rest of the days.

Someone said: "Today's the 3rd. Trust me, I'm telling the truth. I'm odd. I didn't lie yesterday. I'm not a knight."

At first, this seemed illogical, and I thought he couldn't be either a knight or a liar, even or odd, but after a while the solution dawned on me and I found the error in my reasoning. What is he?

The person is either lying for each sentence or telling the truth for each sentence.

Suppose the person is lying. It's not the 3rd, so it could be a different odd day, or an even day. In either case the person is not odd (as he'd be lying about that) and so is even, lying every day.  But that would indeed make him an even liar, but would then be telling the truth about not being a knight.

Suppose the person is telling the truth. It is the 3rd and the person is odd, so it must be an odd liar, who tells the truth on odd days. Indeed, he's not a knight, so that's the truth.  But he says he didn't lie yesterday, the 2nd, an even day, when an odd liar would presumably lie.

The only way out of this I could think of would be that yesterday he didn't say anything, even though that violates a strict interpretation of "they lie the rest of the days."  Maybe that applies only if they speak at all.

Posted by Charlie on 2005-09-12 14:27:26