OK, 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.

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I found a ‘logic ‘ answer straight away.

Impossible to calculate the answer without knowing at least one other variable which is not given.

not true. there are two answers (a minimum and a maximum).

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.

that variable will still give you a minimum and a maximum.

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.

not true

but there is one correct answer

Impossibily Stupid not a Genius then!

Nice one!

It initially took me longer than it should have with a little algebra. In retrospect, there is a more intuitive solution.

I can calculate it to a small range, but not get an exact answer.

Knowing it’s obtuse intellectual laziness, I won’t even try. My math skills, even at 47, are so lacking, any attempt to figure this one out would raise my systolic.

Disregarding weather, sessions, age and health of goats, the answer is simple.

More than the average number of assumptions required to answer this one…

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

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.

If one of the goats were my brother-in-law, you would run out of food and beer in 3 hours.

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.

A superbly deceptive puzzle, with an astonishingly simple answer… 10 mins thinking time and 5 mins of maths.

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.

i expect a solution after a few seconds, however i still have to proove it…

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.

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.

I think I have it…

Depends on the variety of grass species. Different growth rates, nutritional value and digestability.

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.

Got it+/-1. How important is rounding? One variable is nicely hidden

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.

I saw the nature of the problem right away, but the answer did not cross my mind before I actually did the math.

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!

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.

there’s one answer, I believe. It took a min of mental math.

I won’t let the grass grow under my feet on this one…

Just pooped my pants

Just pooped someone else’s pants – but it’s hardly relevant to the question

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.

You have missed something.

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.

About a minute.

Anon, Richard’s only counting full days. For example, 10 goats may be able to survive for 8 days and 4 hours.

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.

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!

evidently, most of us are not normal.

goat it, 572 nanny seconds

Indeed more that 1 answer. If the numbers for 3 goats and 8 goats had been given, the answer for 7 goats would have been unique.

Are goats carnivorous?

Possibly, but that would not necessarily make them cannibals

I got it in 1/8 of second.

Richard Wiseman’s New Year’s resolution: No more lame puzzles. We’ll see how long it lasts.

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.

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.

I guessed the answer in seconds, and then spent a minute proving it.

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

………..and that would be 56/3 or about 18 and 2/3rds days.

Oh, was that out loud?

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!

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.

Best puzzle ever on RW’s blog.

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