Erica and John are standing in the same cattle field at the same time. Erica can see the same number of bulls and cows in the field. However, John can see twice as many cows as bulls. How can this be and how many cows and bulls are there in the field?

As ever, please do NOT post your answer but feel free to say if you have solved it and how long it took. Solution on Monday!

Oh, and here is a photo of my good self helping to launch the Edinburgh International Science Festival yesterday, with Festival Director Simon Gage.


  1. I quickly thought of both a straightforward solution that doesn’t put any bounds on the number of cows and bulls, and one which makes the answer very precise (and low).

    1. I think I have the same two (types of) solution as well – one involving topography (note the photo), the other onomastics.

      Took about a minute.

    2. I have at least two solutions.
      However, if we are looking for the minimum number of beasts that could be seen, then there is only one solution that fits…..

    3. Come on, this need some recognition – Richard B: “Yes, a number of cows often low.”


  2. Solved with two different solutions. The solution with a higher number of bulls and cows is the one I believe you wanted.

    1. A little better wording could certainly make only the intended answer work, as it is there are certainly many possibilities.

    2. Yeah, i’m pretty sure i have richard’s intended answer, but i can think of numerous other solutions that are equally valid based on the wording… And i don’t think i’m being very tricky.

    3. There are three answers with one based on the solution that Richard almost certainly has in mind. The other two are slight variations and equally valid, each based on a half-way house version.

      I think that any other solution would require making unwarranted assumptions – the way the land lies, odd shaped fields, visitors from Mars…

      I’ll be interest to see what he comes up with. If it’s what I think it is, then I’d like to see how he could defend it as the only valid answer.

    4. The simplest way to cut away most of the spurious solutions would be to add “From wherever they stand in the field, looking in all directions”. Then i think the answer richard wants falls out as the most straightforward.

  3. Zero seconds… the answer occurred to me before I finished reading the question, and was confirmed when I got to the end and there was no sudden twist.

    1. Minus 14 hours. The answer occurred to me the night before I read the question, I’m just that good.

  4. The question reminded me of the story of the father and son being involved in an accident and they are rushed to the hospital and the son is prepared for surgery however the surgeon seeing the patient says “I cannot operate as he is my son”.
    This and your story depend on assumptions and there are assumptions we are being asked to make in the puzzle. You can challenge the assumption in two ways I could see straight away – but there may be more.

    1. I refer people to that tale all the time. The answer really makes you think about the way you assume details without even realising it.

  5. I think this is a twist on an old puzzle, and I have an answer, but I don’t think it’s the one you are after… The answer I immediately had in my head was wrong, so I had to challenge some assumptions (both the assumptions most people might make, and then the assumptions that this was the standard old puzzle). So it took a couple of minutes of scribbling and crossing out. I’ll be interested to see the “actual” answer on Monday.

  6. Why are there cows and bulls in the same field? Tiz not how you would normally keep them. And you certainly can’t keep bulls together.

    Anyways. It didn’t take long to work out your answer. 😛

  7. Three seconds for me. I hope these livestock win the Nobel Prize because they are out standing in their field.

  8. I’m sure I was helped by John’s story of the doctor and his son, but whether I was or wasn’t, it took me about two minutes.

    On the subject of the time taken… Just a query. Does anyone actually time how it long it takes to do these? I’m sure in some previous puzzles it has said things like ’42 seconds’ or whatever. Now, that’s pretty precise! Maybe I’m not taking it seriously enough. 🙂

  9. I’m assuming they are both looking into the same field – John could be looking at a different field. Anyway I’ve got it, a minute or two

  10. I got two solutions as I was reading it (plus a few seconds to work out the numbers), one with a small number of cattle, the other unlimited, then a couple of minutes later a third solution came to me, also with an unlimited number of cattle.

  11. There’s a very simple non-maths answer to this.

    Moreover, standing in a field with more than one bull would a) never happen in the real world as it’s one bull per herd and b) be a very silly thing to do.

  12. I’ve got a question for the Friday Puzzle solving community.

    Six months ago, I emailed Richard a scanned page from a puzzle book, containing what I thought would make a good future Friday Puzzle. Richard’s reply, dated 22 August 2010, said: “That’s lovely and will def use and credit!“. I replied with a scan of the solution from the same book, which I assume Richard received.

    Saved in the draft folder of my blog, ready to be published at a moment’s notice, is a blog post discussing the puzzle and (in some detail) how I personally went about solving it. I planned to wait for it to show up in this series and then publish that post shortly after Richard gives us his version of the solution.

    I didn’t expect to still be waiting six months later. So my question to you all is: how much longer should I wait before I reveal to the world what the puzzle was, and, after a suitable delay, publish my explanatory blog post?

    The puzzle is neither particularly well-known nor particularly rare. There’s a reasonable chance puzzle connoiseurs have seen a version before, but everyone else probably hasn’t. (There is an extremely famous puzzle in the same class, but it’s different.) It’s an excellent Friday Puzzle candidate because it involves people getting killed if the puzzle is not solved.

    1. sooner the better to submit your link & maybe post the solution 7 days later. I have been waiting to hear what it is since you first mentioned it. I guess Richard doesn’t read these replies on a routine basis or he might reply to the many direct & indirect questions here. Shame, but business is business.

  13. I have several solutions. One is the answer you are probably looking for. The others have smaller numbers. (Took two minutes on these). By the time it took to write this, I had an explanation for the answer zero.

  14. Er…Practical restrictions would be the size of the field and how far our protagonists can see but to the problem as stated theoretically aren’t there infinitely many solutions?
    In fact as for how many cows in the field I think you can make a sound case for any number from 0 up.
    Either I’ve misunderstood (always possible) or this is a weak puzzle.

  15. I have several solutions at the moment, but the only one that fulfills all requirements of the puzzle is kind of a let down.

    1. Fortunately I solved it before reading the comments (a couple of minutes to work out the permutations), or I too would have had it spoiled by the comment you refer to. There’s always someone who has to drop unsubtle clues to demonstrate how clever they are, even after all these months of “no hints” requests.

  16. I can think of two solutions – the minimum number of bovines in each is significantly under a dozen. Both solutions depend on some beasts being hidden from view of the observer, but the mechanism is different in each solution.

  17. Solved it in less that 1 minute – just a few seconds I think but wasn’t accurately timing it. I love reading all the comments – that alone is worth the puzzle. Thanks!

  18. I came with several lame answers in seconds. I now have a bit better answer in 2 minutes. But I am not sure if I got the right answer.

  19. I’ve got an answer and I got it quite quickly, however I’m now confused because people have written about working out the number of cows and bulls. I haven’t done any maths and have no ideas about the number of beasts in the field.
    I think I will stick to my answer and see what Monday brings!!

    1. Just re-read question and realise I missed the bit about the number of beasts.
      Oh well got other stuff to do now will have to wait until Monday now to see what the correct answer is.

  20. There are actually three answers to this problem. There’s the one the problem setter will almost have certainly intended, but there are two more, equally valid answers.

    I think the problem setter has fallen into his/her own version of the same trap set for the rest of us…

  21. I got the answer I belive is the inteded one in about 30 seconds or so.
    Of course, there could be other solutions, and probably an infinite number of numbers would fit.

  22. Oh, wait. Got it. Obvious, once you figure it out. It was one of my solutions (mainly derived out of knowledge about cattle behaviour), I just hadn’t worked the wording of the puzzle into it, so I didn’t know how to GET to that solution.

  23. I think this is pretty easy, an old trick. Of course the real world solution makes it impossible to know the number of cattle, but easy to explain the discrepancy.

  24. I knew the first answer before I was done reading the question, but the second answer just occurred to me while I was writing this response.

  25. First solution: 30 sec, second solution 2 minutes. Think i got it. Nice puzzle ! Dont watch to the photo, open your mind and think: less is more !

  26. I got one solution immediately and one after reading Michael’s comment re “onomastics” to fluffy’s post. Oh, you Brits!

  27. There are different ways the two can see different numbers of cows and bulls, but the question of the actual numbers can’t be answered unless the “how” answer proposed matches the intended. This sort of riddle annoys me.

  28. I figured out the twist pretty quickly, then it was just a simple simultaneous equation, leading to only one answer.

    I assumed that Erica and John can see the entire field, it’s not some trick of placement or perspective.

    1. There are two other answers besides the one you have. That’s because, without giving it away, you don’t have to make (or not make) the same assumptions about both Erica and John.

      Try that, and you get two more sets of simultaneous equations to solve.

  29. Pretty well, honestly it is kind of confusing, but while “i” will be sleeping “i” will replace counting sheep with counting cows and bulls lol and might get to an answer lol, but regarding John, he might like to reduce drinking a bit lol so that he can be able to see better, which sometimes it isn’t recommended to see lol, the more you see the more you get confused, in religion it says that “blindness is a grace” lol, so you might like to think of those whom they do live inside churches, they chose to be kind of blinds but yet in the after life they’ll be the people’s guide lol

  30. Yep, got the answer I’m sure is intended, as well as a “solution” that works without a limit on the number of cows/bulls which clearly isn’t what is intended since the question asks for a specific number.

    However, I also “see” an issue with the right solution based on the physical abilities of cows/bulls and what it means to see something which I’ll save until Monday.

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