I'mpossible... At least I think so.

Logic Level 2

There are 100 people at a party, they are either truth-tellers or liars. Everybody shakes hands with one another. Liars always lie and truth-tellers always tell the truth. Everybody knows if another is a liar or a truth-teller. Everybody is asked one question, "How many truth-tellers did you shake hands with tonight?" Their answers were 0, 1, 2, 3, 4... all the way to 99. How many liars are there at the party?

1 49 99 Not enough information 10 50

Jonathan Tse by Jonathan Tse , 20, Hong Kong

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1 solution

Jonathan Tse
Apr 18, 2019

Let's say that person 99 shook hands with 99 people, 98 with 98 , 97 with 97...1 with 1, with 0

If person 99 was a truth-teller, then everyone must be truth-tellers.

This includes person 0 who has claimed to have shaken hands with 0 truth-tellers. 

   Either person 99 and person 0 did not shake hands(99 is a liar), or
   Person 0 only shook hands with liars(99 is also a liar).

There are no other possibilities, so 99 is a liar. This sequence can continue because 99 has already been deduced as a liar, so if person 98 was a truth-teller, then 0-98 must be truth-tellers e.t.c.

So 99-1 are liars. Person 0 is telling the truth because there are 99 liars, so he couldn't possibly have shook hands with any of them.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

but one of the "assumed" liars answered 1 which is the truth so they cannot be the liar.This situation seems like a paradox.

Anirudh Sreekumar - 2 years, 1 month ago

Ya you are right (although I didn't notice it before and got correct :-p)

Mr. India - 2 years, 1 month ago

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