A little brain teaser…

You are an explorer who arrived on planet Bypolar. The Bypolarians come in two species: the Falsians and the Truans. The Falsians always lie whereas the Truans always tell the truth. Alas, you do not know how to distinguish them.

In any case, two locals are waiting for you.

First Bypolarian: You are most welcome on our planet. You are safe here.

Second Bypolarian: You must leave at once. You are in danger.

First Bypolarian: Do not mind my friend, he always lie.

Second Bypolarian: Ah… we always disagree.

Should you be worried or relaxed?

Daniel Lemire, "A little brain teaser…," in Daniel Lemire's blog, September 25, 2008.

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Daniel Lemire

A computer science professor at the University of Quebec (TELUQ).

12 thoughts on “A little brain teaser…”

  1. Mmmmm…
    First Byp a liar Second Byp a liar

    Stmt 3 False True
    Stmt 4 True ****

    It cannot be that Stmt 4 by Second Byp be true if Falsians ALWAYS lie, therefore the First Byp is the Falsian => worried.

    What’s most interesting is that such a simple problem appear puzzling, there must be some step in our deductions which goes against our natural tendencies, r.e. Johnson Laird’s Mental Models.

  2. Worried.

    Case 1, Both are Truans or both are Falsians: They can not meet with different greetings. Conflict!

    Case 2, FB is Truan and SB is Falsian: SB is telling the truth at the end of the conversation but he should’t. So this can not be the case.

    Case 3, FB is Falsian and SB is Truan: All statements seem convenient, so we should be worried.

    I do not remember but there was a similar puzzle where the person should find a single question that will allow him to identify which is Truan and which is Falsian.

  3. Don’t worry, be happy !

    When asked : “Are you a Falsian ?”, they should both answer “No”. Therefore, the two Bypolarians don’t always disagree.
    Therefore, the second Bypolarians is a Falsian, and you should not worry.

  4. To Anthony, you are puzzling us, but you are wrong. “Are you a Falsian ?”,this is actually two different questions.

  5. Here’s my question: how could an explorer discover the Truthian and Falsian species and their properties in the first place? Without assuming that they always tell the truth or always lie, is there a series of questions an explorer could ask where the Truthian/Falsian nature of Bypolarians is the only valid conclusion? (I don’t know the answer to this question.)

  6. There’s one point that puzzles me: statement #4 does not necessarily need to be true. The negation of “we always disagree” is “we don’t always disagree”, not “we never disagree”. So it is plausible that Byp #2 is a Falsian.

    I go with Anthony. Although some may say the question “are you a Falsian” is another problem, it fits this problem well: both should answer “no” and we know here that they don’t always disagree. Hence Byp #2 must be the liar.

  7. İsmail Arı I do not remember but there was a similar puzzle where the person should find a single question that will allow him to identify which is Truan and which is Falsian.

    The single question is “What would the other say if I asked him if he is a liar?”

    This is easy because it is only a matter of logic, but I suspect that Daniel intent is more mischievous, to highlight the ambiguity of natural language use for stating logic/math problems.
    Because everything depends on how you define “always disagree” and this cannot be elucidated from the problem statement alone.

  8. “Are you a Falsian?”, even though both of them answer “no”, they are actually answering different questions. So it’s not a surprise they give the same answer.
    A is answering “Is A a Falsian?”
    B is answering “Is B a Falsian?”
    Of course they give the same answer “no”.

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