Last week I described how Albert made a terrible mistake whilst creating a clock. Well, this week we are sticking with Albert as he continues to work in a clock factory…..

Albert has noticed that his favourite clock in the factory takes 7seconds to strike 7 o’clock. How long will the same clock take to strike 10 o’clock?

Update: I have had loads of emails about this arguing that it is impossible to solve! So, here is the new question ‘Albert thinks that they answer will definitely be 10 seconds. Is he right?’ 10 points for anyone who gets the right answer to that, and 100 points for anyone who tries to work out an answer to the original question!

The answer to this puzzle, and 100 others,  can be found in a new kindle ebook called PUZZLED, and is available in the UK here and USA here.

1. Took me about 30 seconds to get past the seeming-initially-obvious to the realisation. But now I’m thinking seven seconds for seven o’clock seems a little short?

2. CybrgnX says:

Way too easy. about 30 secs to figure out how.
I’m slow so 5min to get the actual answer.

3. I easily spotted the gotcha right away as I’ve seen similar traps on math tests. Only took me a few seconds since I already knew how to deal with something like that.

4. Michael Kingsford Gray says:

There is not enough information to make an accurate determination.
(For instance, are the gaps as long as the rings?)
I spent at least 30 seconds deciding what was a minimum set of reasonable assumptions.
From then, it took about a minute with a pencil and paper, but I cannot imagine anyone being able to solve the 2 simultaneous equations in their head. At least not quickly.
The answer that I arrived at is not pretty, not intuitively obvious.

Perhaps my assumptions were incorrect?

5. I think it’s easy, maybe I was wrong…

6. Dently says:

If the question is how long between strike number 7 at 7 o’clock and strike 10 at 10 o’clock, then it’s simple.

7. …Are we discussing the grandfather clock in the photo? And, is it wind-up or battery operated?

8. Carl says:

This question has several built-in assumptions, not all of which are reasonable, IMHO.

But, thinking of it in the simplest terms, it’s reasonably easy (and no, not 10 seconds), but does require a calculator.

9. Took me about 10 minutes. I knew it would be simple to work out, and I had the right idea, but one tiny error kept throwing me off. Once I saw my error it took only a couple of seconds.

@Michael Kingsford Gray: If your answer is “not pretty”, then I think your assumptions may be incorrect.

@Carl: I did not need a calculator to work out my answer.

@Dently:Very nice take on the problem. If that’s the answer then mine is incorrect.

10. Carl says:

@Michael Kingsford Gray: You’re right, there’s not enough info – we’d need to know how long the rings last. Which is why I made the assumption that we’re only counting the time between the start of the strikes – and ended up with an ugly fractional answer. Is there another approach that I’m missing?

11. I think I see the gotcha, but I’m not sure. There is two different ways to take this problem.

12. To give the answer Richard probably wants you have to make an assumption which must be false. Without that assumption you can only hope for a range within which the actual answer will fall. You could give a precise answer if you knew the exact time it takes to strike some other hour.

13. Carl says:

Doh! Just realised I had my ratios back to front – so it is a fractional answer, but not an ‘ugly’ one. Yes, now I realise I could have done it without a calculator, but it was only when I saw the answer that my calculator gave me that I realised this to be so. What can I say – I’m lazy.

@Michael Kingsford Gray: A more interesting (IMHO, in that it’s realistic) question could be: “It takes 7 seconds to strike 7, 10 seconds to strike 10, – how long to strike 12?” Then you could solve simultaneously and allow for the ring decay time.

14. Kevin says:

There are a lot of assumptions.

Assuming that the 10th bong rings for the same amount of time as it takes me to make a roast then it should take 4 hours to finish chiming.

15. Richard says:

That one’s easy… took me about 0.1 nanoseconds to get the answer (first time I was confronted with a similar question was when I was 10)

16. @PURPLEXED says:

hi there – first answer too easy – no time at all. Second answer 1 minute + 3 minutes looking 4 a pen. Still easy though. Cheers.

17. Nick Sharratt says:

If I make the assumption that a clock has finished ringing when the sound has decayed (rather than the instant of the last strike) then the answer is trivial as each ‘strike’ then has a duration of one second. Of course if you define the finish as the instant of the 7th strike then the answer is different with first strike at zero seconds and 7th at 7 secs etc but it’s still fairly simple maths.

I can only assume other posts refering to simultaneous equations etc are red herrings or spotting further assumptions I haven’t thought of – would be interesting to see what they are 🙂

18. Easy! Same when dividing something: You always need an extra milestone.
Hope I’m right.

19. Hilary says:

If I’m right I got the unpretty answer with the aid of a calculator in about 10 seconds.

20. I may be over-thinking it, but I think the answer is “given this information, you can’t tell”. Is there a preamble to the ring (Westminster chimes, birdy song, whatever)? How do we measure the end (what if it is a big bell and the decay is 5s)?

21. Anonymous says:

I have an approximate answer, no calculators or equations or anything! I don’t know how right it is but it’s the assumption I’ve made that’s the important bit to me, not the actual X number of seconds I get. We shall see.

22. Mark says:

I didn’t like that it’s effectively necessary firstly to define what striking the hour means, such that it’s solvable and [hopefully] not too inelegant. Assuming that, I knew the McGuffin already, and just had to do a bit of writing down and staring: ten seconds or so.

23. Dyson says:

Is there a different between strike and chime? (@sean)
Assuming we are talking about the clock’s frame of reference (is “Albert” a clue?) then the duration of the decay of the sound of the bell is not relevant. Then again a clock like the one in the picture will start the process of striking the hour before the observer hears any bells. I am not talking about the speed of sound but the fact that the mechanism will engage a short while before sounding the bell. I hope there is more to this one than the “how many posts in a fence” question we all appear to know so well.

24. Michael Kingsford Gray says:

Some unknown variables that affect the answer in a notably material way:
1) How exactly is duration of a ‘strike’ measured?
Is it from the beginning of the first chime to the “end” of the last chime,
or the beginning of the first chime to the beginning of the last chime?

2) What is the ratio of time for each chime, relative to time of the intervening silence? (Assuming a constant ratio: another realistic variable, given my experience with such mechanical marvels.)

3) Is: “…clock in the factory takes 7seconds to strike 7 o’clock. How long will the same clock take to strike 10 o’clock?” a trick question, implying a determination of the implied temporal gap between ‘striking’ 7 & 10?
(If so, a subsidiary question arises regarding AM/PMness of both targets.)

I feel frustratingly hamstrung in explaining my meaning by virtue of the non-disclosure protocol!

In any of these cases, (bar an unrealistic one), the answer is “not pretty”, as far as I can determine.
Please do the simultaneous equations for each reasonable combination of the above scenarios to get a feeling for my meaning…

I am quite willing to be embarrassed by a logical response, but do not in fact expect it to happen.
As I, and others have said, there is no where near enough information with which to provide a definitive reply.

25. Benjamin says:

I honestly think that all the people who claim to have solved the problem in “0.1 nanoseconds” are lying.
Every time I read the comments to Friday’s puzzle is always saying how easy the question is and how unbelievably quickly they solved it, but then when the answer comes out on Monday, the comments are always flooded with complaints.

Though, maybe I’m just dumb for not being able to work it out.

26. I Think too many of you are thinking to deep for this question….

Either that or im way out west with my answer 🙂

27. ScreamingGreenConure says:

I’m really awful at puzzles. I think I can get this one, though. Can’t wait until Monday to find out!

28. Marktech says:

[Changing my handle from my post of 8.45]

@Michael Kingsford Gray: This puzzle must surely exist, as most do, in a puzzle universe, where mechanisms may be assumed to be regular, and definitions of events must be assumed to be unrealistically simple: the matchstick-and-triangle puzzles of a few weeks ago wouldn’t have worked if we had worried about the physical imperfections of matchsticks. As to the definitions of events [what is a chime, and how long does it take?], if we make similarly abstract puzzle-universe assumptions about the correct definitions of our terms, there’s a simple and elegant answer. Since this is presented as a puzzle, and not as a problem of physics, I think it’s fair to select the definitions which lead to the elegant answer.

@Benjamin: I had to write it down and visualise it, but [making the assumptions about what the question means] there’s a neat way of working out the answer which can be *seen* pretty much instantly, and expressed in a single sentence.

Updated question: noooo, Albert would definitely be wrong to think it’s ten seconds!

29. Victor Meldrew says:

I was not going to post as it was IMHO blindingly obvious what the trap is. Now I have seen the updated question, I decided to post after all. I got the answer in 10 secs with the aid of a calculator (hint!). I am willing to eat humble pie on Monday if I am wrong…………

30. Garrett says:

I believe that the only piece of information that you need to solve the first problem that isn’t given is the length of the last ring.

Although you could take the word “strike” to mean the instant the last chime starts in which case it is easily solvable as the chime length doesn’t matter, only the interval at which each one starts.

In any event, I’ve worked out the answer assuming strike means the instant the last chime starts, and I’ve also worked out a formula where you enter the length of the last chime and the hour, and it returns the amount of time it takes the clock to ring.

Have a good weekend! I expect my 110 points on Monday 😉

31. I enjoyed that. Reminds me of when I wrote some 6502 code to read EAN13 barcodes – the ones with 666 in the middle (almost).

@Dently has a good point.

32. Richard says:

@Benjamin wrote :

> I honestly think that all the people who claim
> to have solved the problem in “0.1 nanoseconds”
> are lying.

Thank you Benjamin for this nice statement. No, I am NOT lying. As soon as one has realised where the “trap” of this question lies (the milestone problem as cited by Esther) it is OBVIOUS that you solved the puzzle.

Perhaps you wanted to state something like “I honestly think that not all people who claim to have solved the problem in 0.1 nanoseconds have actually found the correct answer”… I could live with that statement, it makes complete sense, but the statement you gave however is actually pretty insulting.

Richard

33. I have a very simple answer…hope its right.

34. Sally says:

Think that I have an answer to the original question.

35. Ok I have an answer for the initial question and one for the subsequent question. They are different. Looking forward to the answer!

36. Janine says:

I have two answers depending upon how you look at it! Hopefully one of them will turn out to be right! 😀

37. Janine says:

Oops I forgot to say how long it took, 5 minutes thinking about it to come up with both answers.

38. Janine says:

Actually, bizarrely I have a third answer now! 😀

39. I’m thinking this is a trick question. It took me but a moment to come up with and answer, which was ridiculous and no doubt wrong.

40. phiend says:

I think it’s kind of important to know if the clock uses a passing strike or not.

41. liz says:

Thought I’d solved it really quickly but now I’m not so sure can’t wait to see the answer

42. I got it in seconds, but only because it took Windows that long to pull up the calculator…

43. Michael Kingsford Gray says:

Albert thinks that they answer will definitely be 10 seconds. Is he right?

Ah… I came up a definite answer to that question in under a second.
Verified it algebraically with 4 lines of scribble in 10 seconds.
(2 lines for two assumptions)

and 100 points for anyone who tries to work out an answer to the original question!

An instant 100 points. Yay! 🙂
(Workings are available on request, but only after the non-disclosure period has expired.)

44. Kerstin says:

I described how Albert made a terrible mistake whilst creating a clock

Is it really a mistake? The 4 on our clock is also written IV. I thought that was the correct way. Well, you’re never to old to learn. Thank you for your Friday puzzles, I love them.

45. ram says:

easy it will take 10.5 Seconds