Our little experiment was fun and interesting.  It was a kind of a wisdom of the crowds thing, and examined the accuracy of the mean of people’s guesses.  The average of the group was 44.58%.  At 10 p.m. last night 38.30% of people had chosen BLUE, so the group was reasonably accurate.  Stephen Motson was closest with 38.34% (email me and I will get a book to you).

I hope that you enjoyed it and thanks for taking part.  So, to the Friday puzzle….

You are given eight coins and told that one of them is counterfeit. The counterfeit one is slightly heavier than the other seven. Otherwise, the coins look identical. Using a simple balance scale, how can you determine which coin is counterfeit using the scale only twice?

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.

100 comments

  1. interesting variation on an old puzzle. I’m not sure I’ve seen this version of it before. It took about 30 seconds to solve

  2. By the way, I’m glad to see this competition was actually settled with a winner. I don’t think the previous one ever was

    1. That’s not the one I meant. Several weeks ago, Richard gave a puzzle, but never gave the answer. Instead, he said the one who gave the best answer would get a prize (one of his books, IIRC), but I never saw it awarded

  3. Yup I think I can do that. Solution came to me straight away. Seemed so obvious that of course now I’m worrying that there’s a catch that I’ve missed.

    1. The choice of 8 coins is probably intentional. 8 coins primes the brain to think about the problem in the wrong way.

      It would be an interesting exercise to randomly pose the question with 8 or 9 coins to individuals and then track their success rate and time.

      My guess is that individuals presented with 9 coins would solve the problem more frequently and in less time.

  4. I go to the person who told me that one was counterfeit, and I say:

    “I will give you this valuable balance scale if you tell me which is the counterfeit!”

  5. I have a solution after a couple of minutes of mulling, but, much as I hate to be one of those people, it does rather depend on what counts as one “use” of the scales.

    1. No it doesn’t. Use the scales in the conventional way with something on each side. (Put your chosen coins on in one go – not individually) And repeat once. It is not a trick question and doesn’t require any jiggery pokery.

  6. About five seconds, but have seen a variant with 12 coins, and you didn’t know if the fake was heavy or light, so got 3 weighs

  7. Wow. This takes me back. Oldie but goodie!

    Took me about 30 secs to recall the method. More a feat of defiance than a triumph of logic..!

  8. Now for a bonus : you need to determine your uses of the scale beforehand. In other words, you don’t have the result of the first weighs when you decide which coins to put on the scale the second time.

    1. And with the 12 coins version where you don’t know if the fake coin is lighter or heavier, which is fun !

  9. Initially thought I was reading the more famous “three bags” problem, which any Columbo fan knows by heart! (And I can still recall, very fondly, his tortuously drawn-out demonstration of the answer to that one). Hadn’t come across this variant before, and was initially stumped, but a quick sketch on paper illuminated the very elegant answer. Yes, it also works with nine, but I would argue that eight is the better number to set the problem with.

  10. There’s a more common version of this problem that states you have 12 coins and a simple balance and that the fake one is a different weight. What’s the minimum number of balance operations to find the fake coin and how do you do it?

  11. I initially thought it would require three weighings (4/2/1), only after cheating and looking it up did I realise the ‘trick’ (which, incidentally, does involve using the scales in the conventional manner to compare the weights of the coins).

  12. Wow! Because you told me it was slightly heavier, I got the answer in about 7 seconds (all conditions) but I have seen similar puzzles before. The harder question is where you don’t know if it is heavier or lighter…

  13. I still like this problem after 30 years,
    a more fun way to determine the forgery is by finding out which coin gets you arrested when you spend it.

  14. As several people have said the method also works for 9. I wonder if the question is posed for 8 so as to deliberately distract from the answer by hiding the symmetry hint inherent in 9?

  15. The bosses seem to appreciate when I don’t spend a lot of time on these on Friday mornings, but they like puzzles too… got it in about :30

  16. With regard to the average guess being ‘reasonably accurate’ that’s incredibly generous. Over 6% different is way out, especially when you would expect that if someone had guessed a mean value higher than 0.33, they would then probably vote blue themselves to push the mean up and improve their chances of winning the prize. I’m surprised that the actual mean didn’t end up being a lot higher.

  17. Got it, and I haven’t seen it before. I actually solved it with my brain. By doing thinking.

    In your face, universe!

  18. Thirty seconds. It can be done with nine, but it’s better with eight, as this makes it slightly more misleading.

  19. I got it immediately for once! 🙂

    It probably helped that in the past I have used this puzzle when giving interviews…

  20. Solved it in 0.006 secs and that before I’ve even read the question 😉 That’s if I’ve got the correct answer.

    1. Out of interest would you say that practicing such puzzles has had a positive impact on your puzzle solving ability? By which I guess I mean, easier to think laterally, ability to see more variations, quicker to home in on the answer?

  21. Only about as long as it took to read the question. Easier than I thought – I think I was expecting it to be nine coins not eight.

  22. Who has hijacked this website, and where has he hidden Richard Wiseman? The last three weeks’ puzzles have all been very easy and straighforward, without any of the usual naughtinesses or ambiguities. Something must be wrong.

  23. FWIW, I don’t think the crowd-sourced average of 44.58% is particularly good, considering the actual value was 38.3%. It less accurate than the expected random average of 33.33%

  24. I’ve seen this type of thing before, so I got it in seconds. I think it’s a slightly strange variation on the puzzle, unless I’ve missed something…

  25. If there are 10 coins, what is the optimum strategy, and what is the average number of weighs needed to reach an answer? I believe the answer is 2.8, but I’m not sure if it’s optimal.

    Generalized, for n coins, what is the best strategy, and is there a general formula for the average weighs needed?

  26. Took half a minute. My solution works also for 9 coins, so in fact having the “simpler” problem with only 8 coins even distracted me for a moment and tends to lead one on a false path.

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