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# liar and truth-teller

## Question

You meet 4 persons, at least one of them always tell the truth, and the other always lie.

Then you have conversation with them.

Andre  : I, Brian and Cole are truth-tellers, Diego is a liar.
Brian  : I'm truth-teller, Andre and Cole are liars.
Cole   : I, and Andre are truth-tellers, other are liars.
Diego  : I, and Andre are truth-tellers, Brian is a liar.

Identify the liars and truth-tellers.

Edited by jasen

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Spoiler

If Andre is a truth teller, then so are Brian and Cole,
but they disagree, so Andre is not a truth teller.

Brian is the only one who says Andre is a liar, so Brian is the only truth teller.

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Spoiler

Before the conversation, there are fifteen possible permutations of the truth-tellers and liars.
Such that T = truth-teller and F = liar, and the order of the set is {Andre, Brian, Cole, Diego}, these are (non-deliniated): {TTTT}, {TTTF}, {TTFT}, {TTFF}, {TFTT}, {TFTF}, {TFFT}, {TFFF}, {FTTT}, {FTTF}, {FTFT}, {FTFF}, {FFTT}, {FFTF}, {FFFT}.

From Andre's statement the following can be eliminated as possibilities: {TTTT}, {TTFT}, {TTFF}, {TFTT}, {TFTF}, {TFFT}, {TFFF}; leaving: {TTTF}, {FTTT}, {FTTF}, {FTFT}, {FTFF}, {FFTT}, {FFTF}, {FFFT}.

Then, from Brian's statement the following can be eliminated as possibilities: {TTTF}, {FTTT}, {FTTF}; identifying Andre as a liar and leaving: {FTFT}, {FTFF}, {FFTT}, {FFTF}, {FFFT}.

Subsequently, from Cole's statement the following can be eliminated as possibilities (and Cole is identified as a liar): {FFTT}, {FFTF}; leaving {FFFT}. {FTFT}, {FTFF}.

Finally, from Diego's statement, {FFFT} and {FTFT} are eliminated, identifying Diego as a liar, leaving {FTFF}.

Brian is the only truth-teller, and Andre, Cole, and Diego are liars.

Captain Ed's solution is equally correct, but more concisely stated.

Edited by DejMar
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Brian is truth teller

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