## "How many cows are in Ireland", and other weird quesions

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Sabredog
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### Logically answering weird interview questions like this

Let's say you're asked to estimate something like this: how many cows (or fire hydrants, or golf balls) are there in Germany.

That's all you're asked to do. The actual "correct" answer is unimportant, what's important is the process of going about finding that answer. They want to see you state your assumptions and engage a question logically.

Assuming you couldn't just google it, but had to work out a little math, how would you begin?

Taking counting cows: The main headache in such a question is the lack of consistent dispersion of cows: you can't just plot out a square of land, count the cows, and then extrapolate to the rest of the country--some parts of Germany have heavier concentrations of cows than others.

So what would you do to get an answer?

Tirian
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### Re: Estimating tricky (or weird) parameters in statistics

You could work out cows from the other side. Estimate the amount of milk, cheese, and ice cream that the average German consumes in a week. Multiply by the population of Germany. Guess how much of that need is met by imports and how much is self-generated (and decide if Germany exports any significant amount of dairy products). That gives you the amount of milk produced in Germany per week, and then you can divide by the average milk output of the average cow to calculate the population of dairy cows. Repeat for beef consumption and add in a factor for German cows that are not kept for dairy or beef consumption (including bulls and calves).
Last edited by Tirian on Fri May 22, 2015 5:41 pm UTC, edited 1 time in total.

Twistar
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### Re: Estimating tricky (or weird) parameters in statistics

Fermi Problem

Not so much a statistics problem as much as an order of magnitudes problem.

Deva
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### Re: Logically answering weird interview questions like this

1. Begin with annual average beef consumption per person. Multiply by population.
2. Find the average beef yield per cow.
3. Adjust for imports and/or exports.
4. (Consumption +/- Exports/Imports) / Yield = Killed Cows per Year
5. Average cow's lifespan (on a farm) * Killed Cows per Year = Cows in country

Assumptions:
- Used all dead cows for beef.
- Consumed all beef produced.

Works similarly with dairy also. Recommends it as a check.
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ucim
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### Re: Logically answering weird interview questions like this

Sabredog wrote:...you can't just plot out a square of land, count the cows, and then extrapolate to the rest of the country.
Yes, actually you can do that. You'll of course need to make some assumptions; that's the kind of thinking that they are looking for. What fraction of Germany is cow-covered? (all farmland is probably an overestimate but it's a start...) What fraction is cow-free? (Probably the cities...) That lets you start to put bounds on the answer.

What kind of infrastructure does a cow need? (milk distribution, milk consumption, milking machinery, milk exports...) How much of that is there? How many milk trucks do you see on the highway? I'm only counting milk for now; some cows are raised for beef. (Probably most cows end up used for beef, dunno - why waste an old dairy cow?) Similar questions would apply. What's the population of Germany? How much beef do people eat? Is Germany a net importer or exporter of beef?

If you look at the question several different ways, you'll get several different answers, which will probably surround the "true" answer.

I don't want to give too much away; it's the thinking process that's important, but this should get you going.

I actually had to do just this not too long ago for theaters. Worked pretty well. (that is, answers from several methods were compatible, and jived with estimates I later found elsewhere).

Jose
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SPACKlick
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### Re: "How many cows are in Ireland", and other weird quesions

You could do a two step sampling. Sample n locations in ireland at random and see how many of them were fields (x) (with maps and aerial photos this can be a desktop study) sample m locations in fields and count how many cows are in the 100m2 around that point y. If total cows = C and total area of ireland is A

C = y*(x/n)*A

If you can't google A then you will struggle to come up with an absolute answer.

Tyndmyr
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### Re: Logically answering weird interview questions like this

Sabredog wrote:Let's say you're asked to estimate something like this: how many cows (or fire hydrants, or golf balls) are there in Germany.

That's all you're asked to do. The actual "correct" answer is unimportant, what's important is the process of going about finding that answer. They want to see you state your assumptions and engage a question logically.

Assuming you couldn't just google it, but had to work out a little math, how would you begin?

Taking counting cows: The main headache in such a question is the lack of consistent dispersion of cows: you can't just plot out a square of land, count the cows, and then extrapolate to the rest of the country--some parts of Germany have heavier concentrations of cows than others.

So what would you do to get an answer?

These questions are meant to gauge creativity, determination, etc, not math skills.

I'd take a gander at getting there indirectly. Estimate total population, percentage of population that would correspond to users, and average items/user. Easy enough, will probably suffice for a very rough estimate.

You do this in business all the time, and scientific precision is only rarely necessary.

Sabredog
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### Re: Logically answering weird interview questions like this

Deva wrote:1. Begin with annual average beef consumption per person. Multiply by population.
2. Find the average beef yield per cow.
3. Adjust for imports and/or exports.
4. (Consumption +/- Exports/Imports) / Yield = Killed Cows per Year
5. Average cow's lifespan (on a farm) * Killed Cows per Year = Cows in country

Assumptions:
- Used all dead cows for beef.
- Consumed all beef produced.

Works similarly with dairy also. Recommends it as a check.

That's great! My only issue with it would be that finding out annual beef consumption could be another complicated issue in itself. But the creativity of the answer is great
ucim wrote:
Sabredog wrote:...you can't just plot out a square of land, count the cows, and then extrapolate to the rest of the country.
Yes, actually you can do that. You'll of course need to make some assumptions; that's the kind of thinking that they are looking for. What fraction of Germany is cow-covered? (all farmland is probably an overestimate but it's a start...) What fraction is cow-free? (Probably the cities...) That lets you start to put bounds on the answer.

What kind of infrastructure does a cow need? (milk distribution, milk consumption, milking machinery, milk exports...) How much of that is there? How many milk trucks do you see on the highway? I'm only counting milk for now; some cows are raised for beef. (Probably most cows end up used for beef, dunno - why waste an old dairy cow?) Similar questions would apply. What's the population of Germany? How much beef do people eat? Is Germany a net importer or exporter of beef?

If you look at the question several different ways, you'll get several different answers, which will probably surround the "true" answer.

I don't want to give too much away; it's the thinking process that's important, but this should get you going.

I actually had to do just this not too long ago for theaters. Worked pretty well. (that is, answers from several methods were compatible, and jived with estimates I later found elsewhere).

Jose

Very good answer too. Now, you asked a lot of questions -- if you were answering this in an interview, you'd probably have to supply your own estimates for those questions to make the argument right? That's a hell of a lot of variables to juggle around in your head. At least it would be for me. The bounds you put on the question are themselves difficult to come up with--such as how much milk infrastructure there is.

In your theatre answer, did you come up with these assumptions and bounds, and apply them in real time to get a number? Or did you ask the questions open endedly
Tyndmyr wrote:
Sabredog wrote:Let's say you're asked to estimate something like this: how many cows (or fire hydrants, or golf balls) are there in Germany.

That's all you're asked to do. The actual "correct" answer is unimportant, what's important is the process of going about finding that answer. They want to see you state your assumptions and engage a question logically.

Assuming you couldn't just google it, but had to work out a little math, how would you begin?

Taking counting cows: The main headache in such a question is the lack of consistent dispersion of cows: you can't just plot out a square of land, count the cows, and then extrapolate to the rest of the country--some parts of Germany have heavier concentrations of cows than others.

So what would you do to get an answer?

These questions are meant to gauge creativity, determination, etc, not math skills.

I'd take a gander at getting there indirectly. Estimate total population, percentage of population that would correspond to users, and average items/user. Easy enough, will probably suffice for a very rough estimate.

You do this in business all the time, and scientific precision is only rarely necessary.

Good point. But how would you estimate the percentage of the population who correspond to users? (Presumably you mean using some product or service)

SecondTalon
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### Re: "How many cows are in Ireland", and other weird quesions

There is zero reason to post the same thing in multiple forums.
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Sabredog
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### Re: "How many cows are in Ireland", and other weird quesions

If it against forum rules, my bad

(The reason was more eyes, more input, how many people really come to "logical puzzles" regularly!)

ucim
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### Re: "How many cows are in Ireland", and other weird quesions

SecondTalon wrote:There is zero reason to post the same thing in multiple forums.

Where should future replies go?

Jose
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Sabredog
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### Re: "How many cows are in Ireland", and other weird quesions

Is this a case of bored mod looking for something to do?

I don't see any harm in posting across forums, but like I said, if it's against forum rules that's ok, I'll follow them. Silly rule though IMO.

ucim
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### Re: Logically answering weird interview questions like this

Sabredog wrote:Now, you asked a lot of questions -- if you were answering this in an interview, you'd probably have to supply your own estimates for those questions to make the argument right?
Depends on the actual question asked. "How many cows are there...." vs "How would you figure out...". Also depends on the context. I would not expect that they expect an answer off the top of my head. I'd think aloud, use pencil and paper to remember stuff if I needed to, and of course there are some things that have to be derived from stuff I already know (like how big a cow is compared to a person, which gives me an idea of its mass). Questions are not asked in a vacuum.

As to how much milk infrastructure there is, I have no idea. But I could just count milk trucks on a highway (or rely on my memory of how many I remember seeing) to get an idea to start with. Depends on what one is allowed to do, and how much time is allotted. Obviously in an office interview situation I can't even count the cows in a field (unless there's one outside the window). Instead I suppose I could picture in my mind the last few cow pastures I remember seeing (in magazines? Movies?)

I'm trying to not answer the questions for you, because you need to go through the process itself - that's the point of it. And these questions might not even be the best questions, but thinking along these lines should get you going. Try a different one. How many swimming pools are there? How much is an ad on Twitter worth? How much forest acerage does a house use up?

Sabredog wrote:In your theatre answer, did you come up with these assumptions and bounds, and apply them in real time to get a number? Or did you ask the questions open endedly
I needed to know how many theaters, authors, actors, crewpeople, etc there were in the country. I actually do some community theater myself, so I had a "local picture"; the question was how to extrapolate it and allow for overlap. There are ten-ish local community theaters in the area (~30 mile circle), which is suburbanish. I handwaved something about population density, audience travel times, theaters per state, actors per show, theaters per actor, how much of an exception NYC might be, and interestingly, these approaches all seemed to converge on a number. I settled on 3000 theaters in the country (could be as many as 10,000, depending on what you consider a "theater")
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SecondTalon
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### Re: "How many cows are in Ireland", and other weird quesions

Sabredog wrote:Thread as dead as a dodo.

Is this a case of bored mod looking for something to do?

I don't see any harm in posting across forums, but like I said, if it's against forum rules that's ok, I'll follow them. Silly rule though IMO.

If only there were a post, linked at the top of every forum, that explained the forum-wide rules and how to follow them.

Oh, wait, there is.

The harm is that forums that allow that sort of thing quickly become shotgun-post grounds, where people post the same thread in every single forum possible, obliterating legitimate discussion and making a multi-subforums site a fragmented, single forum site.

And that's beyond counterproductive.

Had you merely posted in general, no mod would have thought about where it should go, and it would have been left alone. Same is true for the other location you posted it. But you posted it in three spots, so I got to figure out where it actually belongs.

And since you aren't asking for an actual answer but a logical thought process - logic puzzles, where the process is more important than the answer.
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dimochka
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### Re: "How many cows are in Ireland", and other weird quesions

Welcome to management consulting and how a lot of management consulting interviews start - market sizing. The main point is not the answer but rather (a) the thought process and creativity of thought, and (2) fact checking that your answer makes sense. The cool thing is that after practicing a lot of these you begin estimating the most random things relatively precisely, just because of common sense.

Actual questions given at interviews include: estimate the number of people who would attend the next olympics (and subsequently estimate the revenues and profits received by the local government), estimate the demand for a new drug, etc.

The primary approaches are top-down (so for example for estimating the number of window washers in NYC you would estimate the number of buildings, then an average number of floors, extrapolate number of windows, estimate time to wash a window, hours worked by each window washer, etc) or bottom-up (to estimate number of people who want to use a new drug, estimate number of pharmacies and doctors, then estimate number of patients attendees for each, take a percentage of each that would be interested in your drug, etc).

Happy to talk in more detail if anyone is interested. Though as this may be irrelevant to this forum, feel free to PM me.
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Sabredog
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### Re: "How many cows are in Ireland", and other weird quesions

Excellent dimochka! Thank you. I may drop you a PM down the line, if you don't mind. Cheers

Sabredog
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### Re: "How many cows are in Ireland", and other weird quesions

And ucim, thank you for the great reply.

These types of questions tend to make me freeze in the high pressure environment of an interview, I want to be very prepared for them so I don't choke, for want of a better word

dimochka
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### Re: "How many cows are in Ireland", and other weird quesions

Definitely, feel free. Keep in mind that the purpose is NOT getting the right answers. The most important part is for them to understand how you think (logic and structure of thought)
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ucim
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### Re: "How many cows are in Ireland", and other weird quesions

Sabredog wrote:These types of questions tend to make me freeze in the high pressure environment of an interview, I want to be very prepared for them so I don't choke, for want of a better word
Two suggestions:

1: Ask yourself these kinds of questions routinely. Spend a few minutes each day answering them. You don't have to come up with the answer, just imagine ways you could get there, and start a few of the calculations. (How many subway train cars are there in NYC? How many busses are there in LA? How far apart are post offices, on average? How far apart are snowflakes or raindrops on average?) The more you do it, the more comfortable you'll get with thinking your way out of them.

2: Do some mock interviews. Make them casual at first, then ratchet up the intensity. Maybe videotape them (you don't even have to watch the tape; maybe just having a camera puts on the pressure).

Dunno if it will help; it's off the top of my head. But it would be interesting to hear back how you make out.

Jose
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Vytron
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### Re: "How many cows are in Ireland", and other weird quesions

dimochka wrote:Happy to talk in more detail if anyone is interested.

Would be interested to hear more about this, so if this is continues by PMs, I'd like them to be forwarded to me (or the contents of the PMs be posted on a spoiler or something.)

dimochka
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### Re: "How many cows are in Ireland", and other weird quesions

I haven't gotten any PMs, so feel free to start sending them or I'm happy to provide my email via PM as well.
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Vytron
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### Re: "How many cows are in Ireland", and other weird quesions

Well, I think that any kind of discussion related to this would be better posted on the thread.

Also, this is a very related xkcd:

Alt: I love how Google handles dimensional analysis. Stats are ballpark and vary wildly by time of day and whether your mom is in town.

So, it got me thinking. There's a sphere that can be drawn with me in the center, and the bigger the sphere, the more people having sex inside the sphere.

I can only wonder how this thread would have looked like with a title like "How many people are having sex within 1km radius", and other weird questions.

Wildcard
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### "How many people having sex within 1km" & other weird questi

Vytron wrote:I can only wonder how this thread would have looked like with a title like "How many people are having sex within 1km radius", and other weird questions.

I heartily second this. I think the thread title should be changed now. Although there's a character limit for thread titles; perhaps my modified subject line should be used.

...Aaaaand, some of the best (worst?) "approaches" to these types of questions are given in this highly amusing thread.

How many cows in Ireland? Count the cow hoofs in Ireland and divide by four, of course.
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Vytron
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### Re: "How many people having sex within 1km" & other weird qu

Wildcard wrote:How many cows in Ireland? Count the cow hoofs in Ireland and divide by four, of course.

Interesting. I guess a similar approach can be used for my question:

What is the distance of the couple having sex that it closest to me?

Approach the couple until you're with them, and the distance will be 0, of course.

Sableagle
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### Re: Logically answering weird interview questions like this

ucim wrote:(Probably most cows end up used for beef, dunno - why waste an old dairy cow?)
IWe have "beef" and "dairy" breeds, and the "beef" ones generally don't live to be 2 years old. Veal can be beef cattle or the male calves of dairy herds, which are a waste by-product if we don't eat veal. Veal is calves that didn't get to be 1 year old. Dairy cows used to live a lot longer than that, into double figures, but then we found out that grinding the old ones up and feeding them to the younger ones was spreading BSE, and had to stop. Found BSE in 1984, took action in 1996. Yay government! Now dairy cattle are all killed at age 5 to reduce their ability to "incubate" the disease. Then they're composted, because nobody wants such old beef!
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