Please do NOT post your answer, but do say if you think you have solved the puzzle and how long it took. Solution on Monday.

Yesterday my friend and I started to walk down a road.  We began our walk at the same time, from the same point, and headed in the same direction. I walk at 5 km/h and my friend walks at 6 km/h. Throughout the walk a dog ran between the two of us again and again, with a constant speed of 10 km/h. How far did the dog travel in 1 hour?

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.


    1. I’m thinking it would be many times, even in the first second. However, since they all start at the same time and the dog is travelling fastest, it is not between the two people, so my calculations break down….

  1. The dog cannot be maintaining a constant speed of 10mph as it is changing direction repeatedly. That must mean it’s average speed goes from some maximum (say 11mph) to zero and back each time it turns around.

    For that average to average out to 10mph we must need to know how often the dog has reversed direction in the hour. This means we really do need to sum the series rather than just reflect on how far a dog travelling at 10mph for an hour travels.

    I think a number of early posters have fallen for the trap set by Richard and done the simple yet wrong calculation.

    That is the hallmark of a good puzzle. Watch as everyone thinks it is the same as the fly and locomotives they learned at school and then fall flat on their faces when it isn’t.

    Nitpickers could argue that the dog is moving in an ellipse with a constant angular speed. But that cannot be the case if you read the original wording as it is written.

    Good puzzle! Time for the early posters to have a second thought.

    1. I think Barry is overthinking it. If Richard’s puzzles have a simple answer, that’s usually it (often regardless of more complicated maths that may mean it’s wrong).

    2. Barry, or Garry the usual troublemaker. You were caught this time! Speed was km/h not mph.

    3. You have assumed that the dog takes a non-zero amount of time to change direction. That would be true in reality, but this is a hypothetical puzzle. It clearly states that the dog travels at a constant speed of 10kph, therefore it does. It follows then, that it must also change direction in zero time. Your assumption is incorrect.

    4. A more challenging question (not the simple item being asked) would have been what is the dogs average velocity (not speed). The average velocity would be between 5 and 6 km/hr. But it wasn’t obvious to me how to calculate it (after about 1 min of thinking).

    5. Thank you @the eight people above who have taken the time to write in and support my viewpoint.

      Puzzles need to be clear about whether real rules of physics apply to them or not. Last week the issue was presented as a MYTHICAL family when it transpired the answer was about a real family. This causes confusions and makes it hard to discuss the finer matters of the issue.

      This week it is clear that it is not possible for a dog to do what the puzzle says the dog does. We are therefore challenged to look deeper. To go beyond what is called in literature “an unreliable narrator” and find the deeper reality within. My years of experience with star charts make this second nature (or second nurture) for me.

      I believe I have solved the puzzle within that deeper reality and my solution is more satisfying and accurate and longlasting and meaningful than solutions that are of the sort that posit (to use a traditional example) “that a horse is a perfect sphere moving in a vacuum”.

      Solving puzzles in the.real world is practice for solving real world puzzles, Please try this. It will benefit us all.

  2. Like many others, I was starting to think the puzzle was incredibly complicated, but then had a lightbulb moment which lead to an instant solve.

    If Richard had asked us how many laps the dog makes, on the other hand…

  3. the best part about this puzzle is that it presents a neat disproof of zeno’s paradox. at least the classic form of this puzzle does; i’m not sure about this particular one since the endpoints of the dog’s paths are diverging, not converging.

  4. Why post (what you think is) the solution, when we are specifically asked not to? This is supposed to be for fun, so no spoilers!

  5. and the fleas on the dog ran up and down it’s 50cm back at 2 metres per hour, how long
    did it take for the dog to stop and scratch them off?

  6. I think the puzzle wants gross distance. But consider this: What is the dog’s net distance? That is, how far away from the starting point is the dog after 1 hour?

  7. 0.2 seconds to calculate the answer, 3 seconds to wonder why such an easy and obvious question had been asked, and then the rest of the time realising that it’s yet another of Richard’s obvious questions.

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