There are two types of odd people: odd knights and odd liars. Odd knights lie on odd-numbered days and tell the truth on even-numbered days. Odd liars tell the truth on odd-numbered days and lie on even-numbered days.

One day in either 2012 or 2013, an odd person made the following statements.

1. Today is either the 7th or the 8th.
2. Yesterday was the 31st.
3. I did not lie yesterday.

What type is the person, and what day did he/she say these statements?

As statements 1 and 2 contradict each other -- given they are both made by either an odd knight or liar on the same day -- they are both lies. Statement 3 can only be made by an odd person if today and yesterday have the same parity, and this parity only exists at the cusp of two months in which the end of the earlier month is an odd numbered day (as the beginning of a month by definition is given as the 1st -- an odd-numbered day).  Deduced that the day is odd, the statements are made by an odd knight. The only month-end day other than the 31st which is odd, within the given parameters, is February 29, 2012, thus the day the statements are made is March 1, 2012.

Posted by Dej Mar on 2014-10-08 03:45:16