@jbrownridge sent me this lovely puzzle yesterday….

If you choose an answer to this question at random, what is the chance that you will be correct?

a) 25%
b) 50%
c) 60%
d) 25%

As ever, please do NOT post your answers, but do say if you think you have solved the puzzle and how long it took.  Solution on Monday.

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.

68 comments

  1. This may be my favourite Friday Puzzle so far. I have that #MyBrainIsBeingMessedWith tingle. Also – how can it possibly be Friday again already? I could have sworn it was Tuesday!

    1. To add: is the random answer to this multiple choice question evaluated by a computer or a human being?

  2. If you want to avoid all the weirdness about probability I think this is a sensible rephrasing of the puzzle:

    How many option(s) contain the correct answer?
    a) 1
    b) 2
    c) 3
    d) 1

    Quite funny puzzle, it also made it to the frontpage of reddit for a short period of time ( http://www.reddit.com/r/funny/comments/lr1rw/probability_mindfuck/ don’t worry, comments don’t seem to contain any sort of actual answer).
    I think I’ve got an answer, took me a minute or two to think it through.

  3. I assume in the absence of other information we have to assume that the three values of 25%, 50% & 60% are the only possible ones and all have equal probability of being right. Also, in making a random choice, it’s not a random choice of the three values but of the four options (as two answers are identical). I know this sounds pedantic, but problems of chance like this are predicated on precise definitions.

    Given that, I have an answer (which, unusually, matches my first instinct).

  4. A couple of minutes to break out of the self-referrals.

    Speaking of which, surely the answer depends on the exact referent of “correct”.

  5. Well, what’s the question? It says “If you choose an answer to this question at random”, and it’s followed by “what is the chance that you will be correct?” But what is the question in the first place?

    1. That is the question: “what is the chance of randomly guessing the correct answer?” That is it, which is what makes this such a clever and funny puzzle. The self referral leads to all sorts of paradoxes, but I’m not sure there is actually an answer. I hope I’m wrong though.

  6. Since in the text of the question we do not have a decision criterion to evaluate the correct answer we have to assume that every answer is correct. So the chance to be correct is 100%.

  7. An interesting idea for this blog would be a way for people to provide their answers in a way that won’t be revealed until the following Monday. That way we might find out how many of those who claim to have got the right answer actually have. Or is that me being slightly cynical…

  8. Steve – that’s what Richard would love – he’s a scientist after all…
    Some kind of voting system would be perfect – there are voting platforms on the web that provide just that.

    Richard, follow up on that – you’re wasting a lot of useful data here…

    1. I’m intrigued by this. I would have given up ages ago and declared it impossible but for comments like this. I hope it’s worth persevering with.

  9. If I’m correct I got the answer by the end of the question,
    but usually I have to think a lot about the puzzles, so maybe I’m wrong.

  10. Is it me overthinking this further or could the answer keep bouncing back and forth because of the double question/answer scenario?

  11. A few seconds to come up with one answer, another few seconds to re-evaluate it and choose a different option which I believe is correct. This has to be the easiest one I’ve answered to date…

    …unless Richard’s double bluffing us!

  12. I like this puzzle. Had to give it a bit of thought this time, hence the contorted look on my face and the loud clanking noise!

  13. Oh! When I unravelled the self-referential nature of the question and answers it became obvious. Very clever. 2 minutes.

  14. If anyone follows the Post Secret Blog, they just posted this on their facebook page! Quite a few people came up with the same answer as me.

  15. note how clevver mr wiseman is.

    the question mark is before the four opttions.means the options are a complete redherring. nothing to do with the question at all.

    the fulll query is “If you choose an answer to this question at random, what is the chance that you will be correct?”

    the answer to that is [spoiler]

    1. Good point, but the same problem still exists. I.e. If you’re not restricted to one of the four possibilities, then you can basically go with any probability, which provides infinite options. Which means the chance of you getting it right is 0. But then if you choose 0, then you’ve got it right, falsifying your choice. So the question is still unanswerable in the same, self-conflicting way.

  16. This is probably the strangest coincidence I’ve ever experienced. I just saw a photograph of this exact question written on a chalkboard and it reminded me to check this blog for the weekly puzzle. Crazy weird!

  17. HAY DOS soluciones, veamos :

    A) 0% Es la respuesta a la pregunta “Cual es la probabilidad de acertar? “.
    0% No está entre las opciones así que nunca acertaria. NO pedian que marquemos una opción y ver si hemos acertado nos han pedido la probabilidad de acertar si escogieramos.

    Esta es también la respuesta lógica ante los resultados 25% y 50% que se invalidan en bucle.

    Esta opción se fortalece si partimos de que la respuesta puede no estar entre las opciones.

    B) La respuesta podría ser 25% o 1 de 4.
    Me explico y sigo respondiendo a Cuál es la probabilidad de acertar?

    Las posibilidades de que al azar marque un 25% son de 2/4 (a) y (d) o sea una probabilidad del 50% que es la opción b).

    Así que la probabilidad de que escoja b) es de 1 de 4 o sea del 25%.

    Así que 25% es la probabilidad de marcar b) y decir que tengo 50% de probabilidad de escoger la respuesta correcta 25%.

    Esta solución se refuerza si partimos de que la respuesta SI está entre las opciones:)

  18. La probabilidad de acertar es igual a 1 – la probabilidad de no acertar.
    Puesto que cualquiera de las opciones elegidas no es correcta, la probabilidad de no acertar es 1.
    Entonces la probabilidad de acertar es 1 – 1 = 0

  19. The chance of hitting is 1 – the probability of not hitting.
    Since any of the choices is not correct, the probability of not hit is 1
    Then the probability of hitting is 1-1 = 0

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