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?
There are either 3 or 4 liars.
If 3, then Tuesday and Wednesday are truthful.
If 4, then only Friday is truthful.
This conclusion (3 or 4 liars) can be reached on Thursday, at which point we know that there cannot be 2 liars (in which case Monday, Wednesday and Thursday have lied, a contradiction) and there cannot be 5 liars (in which case Thursday has told the truth, a contradiction). Friday's statement does nothing to clarify the question.