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So recently I came up with this puzzle/riddle that's really confusing me. So four people/Jokers are sitting at a table. Sometimes they tell the truth, sometimes they lie. My question is, which configurations of truth tellers are possible and how (and aren't contradictory i.e. all four can't be truthful)?

Person A says "Two of us are lying."
Person B also says "Two of us are lying."
Person C says "None of us are lying."
Person D also says "None of us are lying."

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3 Answers 3

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Person C and D cant be telling truth since there are contradictory statements so we have minimum 2 liars

That means

A and B can both be telling the truth or if one lies they would both be lying.

So combinations are

TTLL or LLLL

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  • $\begingroup$ We know that A and B are telling the truth. In cases LLLL and TTLL then at least two people are lying so the statement "Two of us are lying" is inherently true. If "Three of us are lying" were a true statement, "Two of us are lying" would still be true. $\endgroup$
    – kaine
    Oct 26, 2016 at 18:57
  • $\begingroup$ @kaine I assumed the statement was "exactly two of us are lying" in which case A and B are unknown (but always the same) as in my answer. If the statement is interpreted as "at least two of us are lying" then you are correct only TTLL would be possible. $\endgroup$
    – gtwebb
    Oct 26, 2016 at 19:09
  • $\begingroup$ Ah so if you are I are A and B respectively, then the answer could be LTLL cause I think my sentence means "at least" and you think it means "exactly". This could make a very interesting and unintuitive puzzle that looks impossible at first. $\endgroup$
    – kaine
    Oct 26, 2016 at 19:11
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Wouldn't it be

2 liars and 2 truth tellers?

if person A says what they say and person b follows their lead, wouldn't that make the statements of C and D invalid? C and D obviously contradicted themselves, which ends up making the words used by A and B the most accurate situation.

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Here are all the possibilities

A and B are always the same value. Same goes for C and D. Since their statements are the same, it's impossible for one to be true and one to be false.
Knowing that, there are only 4 possibilities. TTTT,LLLL,TTLL,LLTT
But AB and CD and opposite so TTTT is impossible.
If AB are lying, then CD is are also lying, which means that LLTT is impossible.
So only LLLL and TTLL are possible

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