coverOK, here is the first puzzle of 2013.  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.

There exists a grassy field that contains no other food.  11 goats could last there for 7 days before they run out of food.  10 goats could last 8 days there.  How long could 3 goats survive there?

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle (UKhere and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.

59 comments

    1. The puzzle is vague enough to allow even more than two answers. For example, it could be that the grass is growing enough in a day to explain the capacity difference. Still, best to solve it for the simple case(s) for now and save the major whining for Monday.

    2. Stop being a silly person. Yes, the answers will all be between 0 and infinity; it doesn’t take a genius to state the obvious. The point is that context is important to narrow down the range, and all the “variables” that actually apply to the puzzle can only be assumed if they are not explicitly stated.

    1. Having now plugged in all the biologically unrealistic, but mathematically convenient assumptions the algebra comes out with the answer I suspected. Very neatly too.

  1. Took about 5 minutes.
    Trying to understand the apparent inconsistency in the question took me longer than getting the precise solution.
    Best puzzle for a long time Richard.

  2. An excellent puzzle.
    3 mins imagining the complexity of the problem and 30 seconds realising how simple it was ! The answer confirmed what I had instinctively guessed before I started any calculations.

  3. Tool me 30 seconds of calculating to arrive at one solution, then another 30 seconds of thinking to arrive at another, which I assume will be the correct one. One assumption needed, but it helped that the first solution seemed unnecessarily imprecise.

  4. About 5 mins. As someone else found, my (pleasantly simple) mathematical solution confirmed what I suspected originally.

    I did have to invent the new unit of a “goat-day-of-food” though.

  5. I wrote a one line computer program to do it and I’m sure I got the right answer and I bet it will be different from the “official” answer.

  6. Simple linear algebra (which is pretty rusty for me). I’m interested in some people’s so-called “intuitive” solution, because I still can’t see how I could have got the answer without some maths.

    1. When you see the answer on monday (if I have the right one, but it falls so nicely on a very specific case that I am pretty sure it is the case), you’ll see why it is funny to say you got it +/- 1 !
      Rounding is not important, the problem can be solved using only integers.

  7. Assuming it’s not mid-winter:
    As with Drew, I intuitively I got an answer in a few seconds. Then 2 mins with Excel to confirm it was logical. However, having read some others’ comments I am wondering if I have missed something!

    1. No calculations of a complexity sufficient to require excel spread-sheets, one-line computer programs, integration, linear algebra, simultaneous equations or the like are required to solve this problem.

      I spent a minute thinking I was going to have to do solve some simultaneous differential equations or something. Then I spotted the answer without the necessity of any difficult calculations. Drew’s comments make clear he has the same solution.

  8. Which is it? 7 days for 11 goats, or 8 days for 10 goats? Each gives a different solution for 3 goats. Though it’s only a 1 day difference.

  9. Had to use some pen and paper for this one. But after coming across the same route as Drew I’m pretty confident I have it correct.
    As Yat has already said, there’s no need for fractions, or rounding, or rather you always round down, you can’t have half a goat.
    Although I suppose you can have so many days plus a few hours.

    1. I should add that the 8 days and 4 hours is made up ad not reflected in the puzzle, in case I though anyone off.

  10. Richard is very crafty! The puzzle starts off by talking about the goats running out of food and then asking how long they will survive. That is two different things! A normal person would not assume the goats simply die the first day they run out of food. How long the goat lives without food must be factored in!
    Plus what if they started out with 11 goats and 8 of them died immediately. The 3 remaining goats could be eating the carcasses before moving onto the grass. This is another variable you must account for!

  11. Good one, Richard. I went hoofing off in the direction of those old school problems that started “If if takes three men five days to dig a ditch. . . .” But that led to a contradiction. So I put it down and got on with the turmoil of the day. It wasn’t until an hour later, over a second coffee that the answer struck me. Change my name to dumbastheycome.

  12. This is a great puzzle. The answer was unexpected to me, and I’m sure I got it right. Took me a while to reconcile the apparent inconsistency in the given info, but it lead directly to the answer.

  13. I took the approach of determining the difference between how fast 11 goats can eat the whole field in 7 days (the group eats 1/7 of the field per day) versus how fast 10 goats can eat the field in 8 days (the group eats 1/8) of the field per day. Based upon that, one goat eats 1/56 of the field per day, so how long would it take 3 of them to eat the whole field……
    Really liked the comment indicating that perhaps the grass grows back, in which case one would also have to know how fast it does so.
    Then again, I could be fullasht

  14. You could go for the max/min approach but I have a horrible feeling I know what the answer is ‘meant’ to be, but I think some information has been left out.

    Looking forward to Monday!

  15. I have an answer, which I think is great. It only uses the information given, but it calculates a couple of complicated things and produces an answer I really love.

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