Over the weekend Jon Ronson, Rebecca Watson and I announced our Paranormal Road Trip.  It will happen towards the end of October and involve us driving from Buffalo to Nashville investigating odd stuff.  We are on the look-out for weird things to examine and visit, so please submit your ideas via the project website.

On Friday I set this puzzle……

Yesterday I met a man called Bill.  Bill said ‘I always lie’.  Was Bill lying or telling the truth?

If you have not tried to solve it, have a go now.  For everyone else the answer is after the break.

Bill is lying.  His statement cannot be true because it would be self-contradictory.  It must be the case that Bill sometimes lies and sometimes tells the truth.

Did you solve it?  Any other answers?

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle (UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.

40 comments

    1. I agree with you DD.
      I was just sitting here, totally confused, all at sixes and sevens, till Michael’s clarification came in – and, let’s face it – it was a particularly taxing conundrum last Friday.
      Hero isn’t a word I use very often, but in this case I think it is apposite.

    2. Aren’t you the least bit interested to look a little beyond the puzzle at hand? You might learn something at the link.

      While we are at it, David’s statement about “each week” is clearly wrong, as I did not do so last week. The preceding statement demonstrates, of course, the use of a counterexample.

  1. Cheers, Richard and, yep, got that one right 🙂 Thanks for another delightful brain workout. Have an excellent week 😀

    1. Maybe instead of “The Friday Puzzle” Richard should call it the “Five Second Brain Workout”?

  2. If Bill was permanently bed bound and was commenting on his state of permanent prostration, he would be telling the truth.

    1. Sorry, Jack. ‘Lie’ is the intransitive verb, and when I am in bed, I lie there. ‘Lay’ is transitive. Confusingly, the past tense of ‘lie’ is ‘lay’ (‘I lay in bed all day last Sunday’) but that doesn’t make any sense here.

  3. Not sure I like the ‘solution’. It seems to be wriggling out of facing the paradoxical nature of the situation pointed out by others on Friday.

    1. I think the solution is sound. The problem could be if people haven’t read earlier puzzles set on the street where some residents always tell the truth, others always lie and a third group do both. I assumed that Bill lived on that street, hence it being logical (to me) to assume Bill would be from one of the three groups mentioned.

    2. The paradoxical statement would

      “I am lying in this statement”

      “I always lie” doesn’t refer to itself in the same way.

    3. I don’t see any wriggling going on. This is not a paradox. It is a simple straightforward puzzle.

    4. See, someone did need Michael Sternberg’s explanation. Look above and read it. If that doesn’t work, try this:

      If Bill were telling the truth, that would be paradoxical. In fact, it would be logically impossible. You made the mistake (and I made it at first as well, but happened to realize I had inserted it when I started carefully parsing the logic) of assuming a condition that was very intentionally left out, namely that if Bill is telling the truth, then he always tells the truth. There was no reason to assume that, but familiarity with that sort of puzzles locked you in to that precondition existing when, in fact, it did not.

      There’s no wriggling here. If Bill says he always lies, that statement MUST be a lie. Nothing else matters. Therefore, he could not be telling the truth. The logic that follows is unnecessary to contemplate to have solved the puzzle, but it follows that if he is lying about that statement, then he does not always tell the truth either, but that question wasn’t asked. What was asked is whether he was lying with that one statement. From the fact that he was lying about the statement, and the nature of the statement, it follows that he sometimes lies and sometimes tells the truth: in other words, Bill is a perfectly ordinary person in terms of honesty. But you assumed a kind of person we never meet in the real world, one that only exists in convoluted logic puzzles. But this puzzle was not convoluted, it was quite straightforward.

    1. Except they got it wrong there – the robots reckon it’s unsolvable because, for some reason, they assume Kirk has to be telling the truth

    2. I just verified it.

      Kirk says: EVERYTHING Harry tells you is a lie.
      Mudd says: “Listen to this carefully, Norman, I am lying”

      That’s when the smoke starts coming out of Norman’s ears.

      The problem Richard poses is a very different one indeed.

  4. The real riddle here is: how do we even know if his name is actually Bill? How many more sleepless night will you make us endure, Richard, before ending this foul uncertainty? Oh, the lamentations! Must we be doomed to suffer our way through life thinking he might, in truth, be a Pete?

    Or Steve.

    Or Walter.

  5. I see four scenarios, but we are not told which one we are in:

    1. Bill has always told the truth before he spoke the sentence.
    2. Bill has told both lies and truths before he spoke the sentence.
    3. Bill has always lied before he spoke the sentence.
    4. Bill has said nothing before he spoke the sentence.

    Did I miss any possibilities?

    In case 1, it’s clear that he is lying when he says “I always lie”, since he doesn’t always lie.
    In case 2, it’s clear that he is lying, since he doesn’t always lie.
    In case 3, if he is lying now, it means that he is sometimes telling the truth, but that is obviously not the case since he has never said anything true. Therefore it can’t be a lie. Can it be true? Of course not, since that would directly imply that it’s actually not true.
    In case 4, if he is lying now, it means that he is sometimes telling the truth. Since this is the only sentence he has ever said, this sentence has to be the one that’s true. So can his only sentence ever be true? No, for the same reason as in case 3.

    In other words, I don’t know. He is either lying, or neither lying or telling the truth.

    1. Richard wrote “Bill is lying.” Richard seems to say that it’s impossible that Bill said something self-contradictory. Which I just showed is very possible. In other words, Richards answer is wrong. We don’t know if Bill is lying or simply said something self-contradictory.

      Maybe you can come up with a longer way of explaining why Bill couldn’t possibly have said something self-contradictory? Isn’t he allowed to have never said anything before that statement? Isn’t he allowed to have lied every time before that statement?

  6. hah! got it – between filling the washing machine and heading off to work. my, but there’s a lot of competitive horn-locking on this thread!

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