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Count the Liars (Posted on 2014-12-23) Difficulty: 2 of 5
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?

  Submitted by Ady TZIDON    
Rating: 3.0000 (2 votes)
Solution: (Hide)
Solution with explanation:
…”each day one of them will send you a message” not necessarily distinct people on different days,

What is to be learned :
Mon: There is exactly one liar among us. -----only truth teller can say it, so there is at least one T.
Tue: I am not a liar.----------------------------ANYONE CAN SAY IT – no new info.
Wed: There are exactly 3 liars among us. … ..ANYONE CAN SAY IT- no new info.
Thu: There are exactly 5 liars among ……….. only liar can say it so there is at least one L.
Fri: There are exactly 4 liars among us. ANYONE CAN SAY IT – no new info.
Since the Mon + Thu statements cannot be contradicted by a new , i.e. Fri statement – we know by the end of Thursday that the composition of the group is TLXXX, a mix 1-4, or 2-3 either way.

Just by reading the text properly one can see that only the 1st and the 4th statements have resolved the issue, the rest did neither contradict them nor contributed any valuable information.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionpleaseAdy TZIDON2014-12-31 03:06:40
att: Steve Ady TZIDON2014-12-24 10:22:57
re: att: Charlie + Steve hintSteve Herman2014-12-24 07:36:28
Hints/Tipsatt: Charlie + Steve hintAdy TZIDON2014-12-24 01:16:49
re: Figures don't lie, but liars do figure (spoiler)Charlie2014-12-23 11:15:55
SolutionFigures don't lie, but liars do figure (spoiler)Steve Herman2014-12-23 10:28:16
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