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?
Taking into account Lisa's point, that all sentences need not be said on the same day...
The last one "I'm not a knight" must have been said by an odd person on an odd day, and it can be true or false.
The third one, "I'm odd" is certainly true. If it was said on the same day as the last one, the speaker is an ODD LIAR, and my solution stands. If not, the speaker is an ODD KNIGHT, who said that on an even day... but that doesn't mesh with the first sentence -- unless the speaker took over 24 hours to say all five sentences!