It’s the Friday Puzzle!

100

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 on “It’s the Friday Puzzle!”

1. Rob says:

Easy peasy. Clever though. I think I must have seen something like this before.

• Rob says:

Also, I only missed on my Blue guess by 0.16%. That’s within rounding error, right?

• M says:

LOL, Nice try.

2. saoili says:

Solved it in about a minute, but I’d’ve heard very similar ones before.

3. Anders says:

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

4. Anders says:

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

• Julia says:

I’d like to know which film Richard chose in the end too.

• Anders says:

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

5. Paul Brandon says:

Full of cold today, but got this straight away. Lurgy has somehow boosted my cognitive powers.

6. suraj says:

3 seconds to solve. 🙂

7. dcmonk79 says:

Yes I can!

8. Anonymous says:

Got it! only a couple of minutes to make sure

9. KRai says:

Easy. You don’t even need the scales. It’s the one that smells like chocolate!

10. M says:

Seen this one before.

11. Pete says:

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.

12. Rusty says:

Yes, eventually. Took about 4 minutes even though it seemed vaguely familiar.

Solved under a minute.

14. Nigel Alexander says:

Solved in about 15 seconds. It can also be done with 9 coins.

• tomviner says:

It’s no coincidence that n / 3^2 <= 1 even for 9.

• One Eyed Jack says:

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.

15. Julie says:

I got stage 1 very quickly. Stage 2 took another 5 minutes.

16. Anon says:

10 seconds to solve, but several hours looking for “ambiguities” in the question.

17. repton says:

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!”

18. Paul Creevey says:

For once… Easy peesey!
Work for 7,8 or 9 coins either

😉

• M says:

It even works for 1 coin!

19. JimC says:

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.

• 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.

• JimC says:

You’re quite right, Peter. My supposed solution was incorrect.

20. ritesh says:

56 seconds (including time to read the question)

21. John says:

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

22. Ian says:

An old one. As people have said – can be done with 9.

23. Paul Durrant says:

Ten seconds or so. It’s an easy one compared to similar problems I’ve come across before.

24. Noam says:

This time around I had the answer before I even finished scrolling down. This one was a lot easier than any others…

25. Olaf Bühler says:

A minute.

26. Charles Sullivan says:

Took at least 3 minutes, but I had to tend the cooker.

27. Drew says:

Not long, about 30 seconds. Like this one 🙂

28. Tony says:

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..!

29. Al says:

Got it pretty quickly, but I have seen another variation of this one before.

30. Mick says:

Got it in seconds.

31. Richard says:

This was quite easy but quite fun and satisfying to solve too. I guess it took me around a minute or maybe two.

32. A minute or so. Nice one.

33. Yat says:

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.

• Nice bonus variant – even that works with 9 also!

• Yat says:

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

• One Eyed Jack says:

I like it.

34. Kristian says:

5 minutes or so. Had to fully falsify my first approach before going in a new direction.

35. Paul says:

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.

36. Rayne says:

If my solution is right, then I got it right away.

37. Steve Jones says:

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?

38. Yes indeed a few seconds and I had an answer. Don’t think I’ll be getting Yat’s bonus point without using JimC’s definition of use.

39. About a minute – Also like Yat’s bonus puzzle (see 9:42am above).
Love this type of problem much more than anything wordy and nice to have a problem devoid of ambiguities!

40. mittfh says:

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).

41. AMWhy says:

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…

42. Lazy T says:

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.

• Lazy T says:

Incidentally, how many people ‘picked a colour’ yeserday?

43. Lazy T says:

+t

44. Reminds me of Bulls and Cows. 2 minutes.

45. Solved it, took about 3 minutes.

46. Mikael says:

Since this is a classic, I agree with the “the 10 s to solve, several hours to check for ambiguities” reply…

47. Matt Sydes says:

Got a solution. Took under a minute.

48. Anonymous says:

0.000325636363 seconds. Weigh too easy this week

49. eowyn says:

Had no idea, then saw the hint from TomViner, and got it within 10 seconds.

50. Anonymous says:

Yep, pretty easy I thought

51. Duncan says:

Solved almost immediately. I think I might have done this one before.

52. Carlz says:

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?

53. Jerry says:

About a minute to write down the possibilities and be 100% sure.

54. samusfairchild says:

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

55. Anonymous says:

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.

56. Phil Boswell says:

About 10 seconds, but it was more a matter of remembering where I’ve heard this one before…yay for a memory which works even sometimes 😉

57. Nelis says:

30 seconds to solve as well.

58. Eddie (@edzeteito) says:

Didn’t think there’d be too much chat on this one.

59. RobHes says:

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

• Eddie says:

Well done!

60. physicalist says:

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

61. Nick says:

I got it immediately for once! 🙂

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

62. Got it: as they say – leave it out 🙂

63. Curnir says:

Yes.

64. really quick, next time use Piers Anthony as the source for a harder variation

65. livedman says:

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

66. Tim Greenwood says:

This was an easy one. Just took a minutes thought.

67. Mickey D says:

68. This puzzle was on an episode of Columbo! 🙂

69. Anonymous says:

10 seconds… 🙂

70. SamC says:

71. Chris says:

I haven’t got a Scooby Doo.

72. Gail Hatton says:

solved it in under a minute, found this one easy, but been practising with mensa puzzles, still good though.

• Chris says:

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?

73. Zach says:

Approx. 20 seconds

74. John Loony says:

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.

75. John Loony says:

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.

76. Carl says:

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%

Well, I reckon I must’ve spent 30mins pondering this until it clicked? One of these days I’ll get it quickly!

78. Jerry says:

I’m amazed. I got this one almost immediately. I did not even use a pencil and paper.

79. Kathy says:

80. Mike Torr says:

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…

81. Anders says:

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?