Subaru_WRC_Rally_CarI normally post these on Friday, but the happiness project has taken over my life, and so I decided to post the puzzle today.

I try to vary the puzzles as much as possible, both in terms of how hard they are and the skills needed to solve them.  This one is from my colleague Mike, and is a tad trickier than most…..

As part of a rather odd driving challenge you are required to complete two laps of a racetrack at an overall average speed of 80mph.  At the instant you finish the first lap, you are informed that your average speed over that first lap was
only  40mph.  How fast do you need to travel over the second lap to get your
overall average speed up to the target value of 80mph?

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. Think I’ve got this figured. 🙂

    Just signed up for the happiness project – feeling pretty happy about it.

    1. Exactly. It stumped Einstein’s friend “Bucky” when they sat together and calculated this … so they are in good company.

  2. fairly easy – the trickier puzzle would be one where there is a fixed distance, but then it took x minutes to complete the course, how much faster for the remainder to meet the overall average speed…

  3. Fairly straightforward algerbra. Took around 30 seconds, plus another minute checking there wasn’t a trick in the wording.

    1. After dismissing the obvious answer as too easy, that’s exactly where I went next. As I’m sure you realise, I now have an exploded brain. I was going to assume that the answer would remain the same regardless of track length, but your comment makes me think otherwise.

  4. Beleive it or not I was taught this in primary school about 58 years ago. Even today I find most people I ask get it wrong.

  5. Took a guess after 30 sec that proved wrong. Took about a minute to do the algebra and got an answer that initially confused me thinking I’d messed up, about another minute to throw in some numbers to understand the question, then another 2 minutes to re-do the algebra on a slightly different basis which gave the same answer which then seems obvious as the right answer. Much longer than usual to feel sure I’ve got the right answer but feel like it took me much longer than it should have now.

  6. 30 seconds for the simple calculation. But another minute to think through as many of the reasons for it to be wrong: e.g, by the time the communication was made you have already progressed on part of the lap at around 40; what the limits of G-force on the body mean – instantaneous acceleration from 40 to N would kill you – but is the need for a live driver at the end part of the puzzle?

  7. I think I got this in moments but like all of these puzzles I have self-doubt. Still, I’m in a happy mood anyway for some reason.

    1. Wondering if we move the experiment into space, and use gravity wells and the speed of light we can invoke some relativistic effect?

  8. Thought I had it right, read the comments, re-read the question, now I have it right and I was wrong the first time.

  9. I went for the obvious answer first but re-checked and got a different answer. I was worried that I’d made a horrible mistake but from the comments of others I think I may have the right answer.

    It took me just over a minute to get what I think is the right answer.

  10. Got it. My initial guess was way off, but a minute or so later, and a different approach, got me to the truth.

  11. Took me about 5 seconds. These are the sort of SAT questions (well, they wouldnt actually put a trick question on there like this) that people waste their time on.
    Very simple algebra.

  12. Well, I got an answer in about 20 seconds, not sure if I was on the right track though *groan*

    Came across you in twitter re the happiness experiment, glad to be part of it, though I am generally happy most days 🙂

  13. I’m still waiting to find out what the happiness experimetn is really about. I’m skeptical of the claims made about it’s true purpose. ;^)

  14. I arried at an answer in about 1 min by thinking about an eg lap of 80 miles. Answer seemed a bit odd so thought about it for another 2 or 3 mins, but sticking with original answer.

  15. I’m with Jamie. Seems straight forward to me, although I can imagine an answer that many might jump to first, then realize a mistake.
    I’m going to stick with the answer I came up with almost immediately.

  16. AAAGHH!!! Yeah that’s a horrible one. Got the right answer now, but I had a helping hand. I can see a lot of people getting this wrong (me included :]).

  17. Bit confused by this. 20 minutes and a spreadsheet later and I’m with the ‘answer’ I got after 30 seconds, but think I still must be missing a trick….

  18. Nice puzzle you’ve got here Richard. Initially I was worried about the answer I’d got, but I keep checking it and I’m sure there’s nothing wrong with my thinking.

  19. Got an intial answer in about 20 seconds, realised that I was probably wrong given that it’s supposed to be ‘a tad trickier than most’, so thought it through with a pen and paper. It took me a minute or two but I think I’ve got the correct answer now.

  20. I’ve come up with an answer almost instantly, but I’m almost certain it’s wrong!! I’ll keep thinking about it and see if I can work out the correct answer!

  21. OK, I’ve thought about it a bit more, and I’m almost certain I have the right answer. When I first worked out this answer I thought it had to be wrong, just because it seems so, well, weird, but I did a few more scribblings and that was enough to convince me it was right. This is a really interesting puzzle, the answer was so unexpected, and counterintuitive even.

  22. I wrote the equation and ground it out using high school algebra. Took about 30 seconds or so. I suppose there is a trick to get it immediately, but I haven’t figured that out yet.


  23. I got it extremely quickly, but by “it” I mean the wrong answer. I’m still not quite sure how to get the right answer so put me down for a long, long time.

  24. I got it really quickly as well, but I have a feeling I may have gotten it wrong, as it is supposed to trickier than usual…

  25. Took about a minute to interpret algebraically and solve. Then another two minutes to interpret the answer physically and accept its truthiness.

  26. I’m having a slow brain day, so I had to take it back to my old friend distance = rate x time. Once I got the answer, I remembered having seen this problem before.

  27. If i’ve worked it out right, it’s brilliant…if I’ve worked it out wrong, it’s brilliant!

    It’s made me think, though…what if I am driving my car, and (forgetting speed limits- I’m on the Autobahn!) I need to average 80 mph to get to my destination on time. Then I find, when I’m halfway there, that I’ve only averaged 40 mph…wouldn’t anyone put their foot down?

  28. About a minute using logic to confirm my intuition (which occurred to me in ‘ flash’, as it were), and a further 30 seconds to verify it using algebra.

  29. I got stuck. Let it simmer for about ten minutes while I did something else. Came back and worked out an answer in about 30 sec.

  30. An answer came to me before I’d finished reading, almost as intuition, but I’m not convinced that Mr Wiseman would post such a simple algebraic problem… not solved it yet (well, not to the point I’M convinced I’m right).

  31. I got my answer instantly as I read it, although I started to doubt it and looked at an alternative for a few mins. I couldn’t find one so stuck with first one.

  32. Richard it might be handy to have all these puzzles tagged or categorised under puzzle so we can easily go look through the old ones.

    I enjoyed this one and now want more.

  33. Hi, This is Vinay from India.
    Though i am weak in these things but i want to enhance my logical skills and so i joined this forum. i hope my desire will get fulfilled.

  34. An fascinating discussion is price comment. I believe that it’s best to write more on this topic, it might not be a taboo subject but generally individuals are not sufficient to talk on such topics. To the next. Cheers

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )


Connecting to %s