# How can a liar and a truthteller prove their identities? [closed]

You come across two people. One is a liar who always lies and the other is a truthteller who always tell the truth. You don't know who is who though.

Both these people are allowed to say one sentence each. What shall each of them say to prove their identity?

Note: Both need to prove their identities individually. Just the truthteller proving his identity or just the liar proving his identity is not enough.

Source: I made this question up myself.

• Are you allowed to say anything to them? Jul 4 at 14:42
• @bobble , no, you cannot speak. Jul 4 at 14:42
• This seems really trivial: just have one say "<true fact> is true" and the other "<true fact> is false" - am I missing something? Jul 4 at 14:47
• @bobble , you are right ..you can post this as your answer and I will accept it . Jul 4 at 14:48

Truthteller:

"One of us two is a truthteller" is true

Liar:

"One of us two is a truthteller" is false

This depends on the fact that

"One of us two is a truthteller" is true according to the premise of the problem. Any truth (or for that matter, any lie - we just need to know the truthiness) would work, but I opted to use a fact given in the premise, in case e.g. the way this world defines numbers means 2+2 doesn't equal 4.

So the truthteller says an obvious truth and the liar an obvious lie.

• Another, and simpler, set of statements could be : Truthteller says, "2+2 = 4" . Liar says, "2+2= 5" . Jul 4 at 15:05
• More humorously: "Mask works" for truthteller, and "Mask works" for a liar. Jul 4 at 21:25