"The poet only asks to get his head into the heavens. It is the logician who seeks to get the heavens into his head. And it is his head that splits." G.K. Chesterton

Saturday, May 22, 2010

Who is lying?

Here's a rather simple and fun logic puzzle.

We have three people; Alice, Bob and Cecil. One of them is a liar. You have to determine who is the liar, and give reasons for your choice, based on the following information. Alice claims that Bob is a liar. Bob claims that Cecil is a liar. Cecil claims that both Alice and Bob are liers. Who's lying and why?

Answer in comments.


Mariusz Popieluch said...

Cecil is the liar, of course!

The key step in solving this puzzle is the realization that one cannot be a non-liar whilst asserting contradictory propositions. At least in classical logic if "A" is true than "not A" is false, or if "A" is false then "not A" is true. Hence asserting both "A" and "not A", one necessarily asserts a false proposition.

Let's use the first letters of our protagonist's names to make the analysis easier to follow. B claims that C is a liar. But since A claims that B is a liar, A's statement amounts to saying that C is not a liar. Hence C by claiming that both A and B are liars, amounts to saying that she herself is both a liar and not a liar which is a contradiction.

mark said...

Nice puzzle, for sure.

Anonymous said...

One thing is sure: Denis is not a liar.

Mariusz Popieluch said...

Not quite, Zenon. The fact that one among A, B, and C is a liar does not exclude the exisence of other liars.

Anonymous said...

I agree but by the same it does not automatically make D a liar. :-) I can assure you that D does not lie, trust me on that.


Mariusz Popieluch said...

Ok, I trust you, not to trust Dennis;)