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?

He said that he is not a knight. Neither an even knight nor an even liar can say this, so he is odd. He said that he is odd, so he is telling the truth. Therefore, all of the statements are true, so he is a liar and it is the 3rd. That means that yesterday was the 2nd. Also, he did not lie yesterday. It seems like a paradox because he is an odd liar not lying on an even day. However, it is not a paradox because he did not talk yesterday.

Posted by Math Man on 2012-06-24 21:03:13