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?

(In reply to re: a solution? by Lisa)

Lisa's idea is interesting, but (assuming a sentence cannot start true and end false, or vice versa) then we'd have to analyze five cases: the first was said yesterday and the other four today, the first and second were said yesterday and the other three today, and so on. I'll see what comes out!

Posted by Old Original Oskar! on 2005-09-12 15:35:53