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?

Is the speaker an odd liar?

No: because if so the statement "I did not lie yesterday" cannot be true

Is the speaker an odd knight?

No: because only the statements "I am not a knight" and "I am telling the truth would be lies

Is the speaker a liar?

No: because if so the statement "I am not a knight" would be true

Is the speaker a knight?

No: because the statements " I am not a knight" and "I'm odd" would be false

Therefore: A loophole must be found where one persons statements could be consistent given certain circumstances.

Solution: It is the first of the month today. Yesterday was the 31st or the 29th of February. We are dealing with an odd liar.

My apologies to Louise. I came up with my solution before reading yours and was disappointed to discover someone else had it first. Congratulations. :)

Posted by Goldwing on 2005-09-17 00:32:40