Five of your friends took a week-long vacation. You know that in this group not every one is a perfect truth-teller, and if someone is a liar, he is a consistent liar.
Since they know you are an avid puzzle-solver, they decided that each day one of them will send you a message, regarding their attitude towards truth-telling.
The sequence of their messages is as follows :
Monday: There is exactly one liar among us.
Tuesday: I am not a liar.
Wednesday: There are exactly 3 liars among us.
Thursday: There are exactly 5 liars among us.
Friday: There are exactly 4 liars among us.
On Saturday you were asked:
Were you able to reason out how many of us are LIARS?
If yes, on what day; if not, at least what have you figured out?
(In reply to att: Charlie + Steve hint
by Ady TZIDON)
a) If we know that all the statements were made by a single person, then we know that there are two liars, but we don't know that until Friday. But this is not very difficult or interesting, so I don't believe it is what the puzzle author intended.
b) If we do not know how many distinct friends are messaging us, then all we know are that there are 1 to 4 liars in the group, and we can reach this conclusion on Thursday. Again, not very difficult or interesting, so I have no idea what the puzzle author intended.