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?

I'm gonna take a stab at it:

There are two keys to the puzzle here, one is that you can have a Odd day followed by an Odd day (31st followed by the 1st, or the 29th followed by the 1st in the event of a leap year). So this could be a Liar on his second day of truth telling on March 1st, on a leap year:

"Today's the third" True, if he means month of the year! This was the only statement that made me groan a little.  I had to do this in order to have a 3rd preceded by an odd day.
"Trust me, I'm telling the truth" True
"I'm odd" True, he's a truth telling Liar, which is atypical
"I didn't lie yesterday" That's right, because he was a truth telling Liar yesterday too.
"I am not a Knight" True! He is a Liar!

Posted by Louise on 2005-09-13 05:24:30