This wasn't an interview, it was a test. I had a similar experience with a startup. I was interviewing for a Marketing Communications Manager position. Essentially PR.
One of the unofficial interviewers (at 24 year old MIT engineer working as an email marketer) challenged me with the question "How many barbers are in San Francisco?" We proceeded to map it out the analytical process on the whiteboard. He wanted to see formulas to understand how I would arrive at the answer.
It was a stupid, impossible question. In a similar way to this girl's experience, he jabbed repeatedly critiquing my logic.
He wrote me later to explain that he posed the same question to his girlfriend, an MIT engineer herself, and she couldn't come up with an answer. Neither could he.
They offered me the job and I declined solely based on this guy and his misguided, silly behavior. I would have hated to work with him.
When a company misguidedly challenges potential employees in this way it hurts the quality of its hires. Sure, Google can afford to be picky but does it really need an engineer in a Product Marketing role? Perhaps for dev-facing apps but such an interview process is overall misguided and immature.
I don't think this is such a terrible thing, although clearly this adversarial approach to testing ideas isn't for you, or everyone. Enrico Fermi used to challenge grad students with similar questions, the famous example being 'how many piano tuners in Chicago?'.
I don't think it's a stupid or impossible question, but one that seeks to establish how you go about estimating tricky things and thus identifying fruitful territory for more rigorous research. Let's walk through it, with the awareness that we're trying to refine our techniques of estimation rather than caring about the actual number of barbers.
'Barber' implies haircuts for men. This is good, because the number of hairstylists that cater to women depends on fashion, which is hard to quantify. On the other hand, hair cutting is more related to hair growth. There's about 3/4 of a million people in San Francisco. Roughly half of them are men, so we have 375,000 potential customers. Most men wear their hair short, off the ears. Of course some wear their hair long and have it cut very infrequently, while others like it much shorter, eg with a buzz cut and have it cut more often...but some of them may cut their own hair, since a buzz-cut isn't too challenging. I'm going to assume the number of hippies cancels out the number of close-cutters because San Francisco has a bit of a hippy reputation. So much for hairstyling.
OK, so I've postulated 375,000 men who average out to a 'regular hairstyle'. And I've postulated that a regular hairstyle means not having your ears covered, ie the old 'short back and sides'. While it's growing, you could comb it out of the way or let it cover the tops of your ears, but once it gets half-way down then you're either growing it out or it's time to visit the barber. How much hair is that? My ears are about 2 inches high, but I have small ears. 3 inches sounds pretty big though...I'll guess the average is 2.5 inches, so half of that is 1.25 inches. That's already pretty fluffy though...let's round it down to 1 inch. OK, so 375,000 men get a haircut whenever their hair has grown by more than an inch.
How long does that take? Hair grows at about 4 inches a year, so let's say 3 months. Which gives us 1.5 million male haircuts a year for the whole city. (we could have started calling the population p and the rate of hair growth g[h] and so on, but why bother, it's a chain of reasoning we're concerned with here). A haircut takes, what, 20 minutes? it could be faster, then again some want a more difficult style. So let's guess that there's half a million hours of actual hair cutting (including the bit with the sheet and the sweeping up etc) going on in a year in SF.
Now we're getting somewhere. How much does a barber work? I'd say 45 hours a week. Some barbershops open early for the business crowd, but then they're closed on Saturdays. Monday-Saturday seems reasonable, as does 2 weeks' holiday. So one barber could spend a maximum of 2500 hours per year cutting hair. Only, that seems a bit high. Sometimes you wait in line, but I don't usually think of barbers as busy flat-out most of the time. 30 hours of cutting and 15 hours a week of of waiting for a customer seems more realistic. So 1500 hours of haircutting per barber (edit: 1650, but who cares). And dividing that into half a million hours of cuttable male hair per year gives me 333, the number of people needed to cut all that hair.
At this point you can start arguing about whether someone that caters to both men and women is truly a barber, or whether women can be said to be barbers even if they only cut men's hair. If your answers to those questions are no and no, and we go with the stereotype of a barber as a man who only cuts other men's hair, then I'd halve these numbers and guess that the number of 'pure' barbers in SF is 75-100.
OK, so this is 10 minutes of my life I won't get back, but if I was going to market something specific to barbers then I now have a decent guess at the number of potential customers in my local metro area.
Of course, you could have just said 'pass me a copy of the Yellow Pages and I'll tell you'. So having done the above, I went and looked that up and got 131 results at http://www.superpages.com/yellowpages/C-Barbers/S-CA/T-San+F... ...with 2 or 3 cutters at each shop, that would suggest somewhere in the 3-400 range, but some of these entries are for Salons and some are in Daly city or Sausalito, not quite in San Francisco. Still not definitive, but not too far off either. Sure, there's a lot of guessing and hand-waving here...but the important thing is that I arrived at an estimate that roughly correlates with reality. In this case I was able to check that reality (by looking up the number of self-identified barbering businesses) but once you become adept at this technique you can use it for anything, and then get on with solving the problem instead of feeling stuck by a lack of information.
Maybe it's the traditionally educated engineering in me (I was trained as a mechanical engineer), but I don't see a point in this purely theoretical hand-wavy math. There are established ways for us to get good estimates of a great deal of information - including your hairdresser problem - that involve seeking out real data. Sitting in a void of zero knowledge and postulating wildly, even if it gets you in the ballpark, is wildly inefficient and I'd hate to be involved in it as part of a professional company.
A number out of your ass - regardless of how soundly backed with logic - is at the end of the day a number out of your ass. This isn't to say that all inference or estimation is bad - but rather that estimations done in a complete void of background data is practically useless.
A more concrete example: estimate the number of users our chief competitor has. I can go through this like a logic puzzle and come up with a number that has zero verifiability... or I can go look up relevant data (their page rank on Google, other available metrics on their site, etc) and arrive at a far better conclusion.
I agree with the GP that these exercises are pointless and unrelated to the job for which you are interviewing. As a traditionally educated engineer, my training teaches me not to guess whenever facts are available. Don't try to memorize and infer numbers - keep your references within reach at all times. An engineer who makes few assumptions about his data is one who makes fewer mistakes and costs less money in damage.
I don't disagree. If you actually asked me for informational purposes, I'd have started with the Yellow Pages and then go look for a trade association or something.
On the other hand, that's not always practical. Sometimes the facts aren't readily to hand or you have to make some decision that's time sensitive. For example, working in film production it's not so unusual to have to eyeball something and estimate your needs for time or material - you try to anticipate as much of that as possible in advance, but say you come to the set one day and the lead actor has fallen ill, so now you have to rearrange your shooting schedule on the fly...in which case it's not uncommon for a few key crew members to huddle, deliberate, and then split the difference rather than obsess over further optimization.
This isn't to say one should rely heavily on gut decisions, since that's likely to be self-defeating; on the other hand, you don't use a slide rule and protractor to drive.
"As a traditionally educated engineer, my training teaches me not to guess whenever facts are available."
Ah, but the most lucrative questions are about products not yet invented, for which there are few facts. They are lucrative because there is not yet any competition. If there were lots of facts available, ripe for the picking, then by definition the net margins would be terrible.
For instance, suppose you were a grad student at the MIT Media Lab in 1995. Does it make financial sense to join the work on an electronic ink product? The answer to that question could only have been derived from a series of guesses and wild deductions. You cannot just look up how efficient planar electroluminescent backlights are going to be in 10 years. Or how expensive and power-hungry non-volatile memory devices are going to be in 10 years.
For a research organization to invent and capture a new market, they have to be good at making and using wild guesses about the future. (Looking up answers is valuable too, but for different reasons.)
I think you're badly mistaking what I'm talking about with "looking up answers" - what I'm talking about is considerably more than that.
How efficient will planar electroluminescent backlights be in 10 years? That's a good question - and one we can make an educated stab at given the right historical data, the right experience in forecasting, and a little bit of plain luck. Heck, you're now talking about an entire field of mathematics and engineering in and of itself!
Compare this to the Google interview though - where they expect you to pull a number out of your ass, with no opportunity to consult historical data, no field experts to interview... no due diligence done at all. It is either an extremely poor approximation of real-life problem solving skills, or everyone at Google is recklessly cowboy and trying to deduce every decision ever by sheer will of logic alone.
Your logic is flawed (as is nearly every "solution" to one of these problems I've seen). The question wasn't "How many barbers should there be?" It was "How many barbers are there?" This is an important distinction as your approach shows the appropriate number of barber shops that can reasonably be operated and have no shortage of customers due to hair growth speeds. I would approach the problem from the opposite direction. How many distinct professions are there in San Francisco? What is the current population? What are the percentage breakdowns of those professions? At that point, you can easily get the number of people employed as barbers. Now, did they want individual barbers, or the number of barber shops? You then only need to infer the number of barbers per shop, rather than estimating a lot of data that isn't readily available.
You know, the University of Chicago still sounds like it.
The best answer would be, there are 14 haircutting places within the shopping disctructs of the U of C, and it is currently overzoned for hair currently, accroding to the maroon. Only two are true barbershops. It consists of three long blocks. Lets take the U of C landscape to be somewhat abnormal, and that there should really only be 7, of which 1 is a barbershop. There are about 24 neighborhoods in chicago. There should be 24 barbershops...ect ect....
There are a lot of ways to do this type of problem.
Say, 375,000 men and 25% of them men get a hair cut every 2 weeks taking 30 min, most men get far fewer haircuts but they bring the average down to about once a month.
Av workweek = 40 hours * 4 weeks = 160 men per barber sounds low call it 200.
The "how many X are in Y" is also known as a "case study question." From what I understand it's a standard practice in interviews for consulting companies, such as Bain or McKinsey. I've never seen one in an interview, but friends of mine who took that route obsessed over them.
As your interviewer said, these questions are asked just to see how you will come up with an answer. The actual number hardly matters, so long as you can sell it to the interviewer. Pushing you is part of the process, as well, to see how you hold up "under pressure."
If you want to be uncharitable, this is much like what a management consultant does -- come in, get some problem from a troubled company ("How can we improve sales by 20% in six months?"), develop a strategy, and then convince the client that they should do it. The interview technique makes sense for that context because it selects for people who can pull this off.
Actually, for a PR role I don't think this question is such a bad fit. You will have to think quickly on your feet, answer hostile people, and come up with diplomatic, plausible answers to crazy questions ("why does your product not work with Slackware?"). The precise answer is of course important, since if you're wrong you will be caught, but how you react is more important.
Maybe you forgot to mention it, but how did you go from "discussing an intentionally impossible problem" to "misguided, silly behavior"? If your ego makes it upsetting to work with people who "jab repeatedly, critiquing [your] logic", or find it upsetting not being able to answer a question, that says quite a lot about what kind of work environment you'd be a good fit for.
mmmmm....yes and no. if you perceives critique negatively, that's a problem with your attitude. you'll never find a good place to work because you'll react poorly to natural differences and disagreements. if others are aggressive or negative that's a problem with them, especially if they're not interested in self-analyzing and learning to be mindful.
I disagree. I actually think the questions in both your example and google's was good in seeing how you approach a problem. The point is not the answer. It is the approach.
I can think back to meetings where questions of similar nature have popped up. You have guys that want the precise numbers and refuse to make any assumption of any sort. You have guys that throw stupid guesses and just want to move forward. You have guys that do a little bit of thinking to come to a quick but critically thought out answer. This seems like a good way to identify which category you fall in and whether your approach is a good fit for the job.
Isn't the sizing of markets something of marketers need to do, all day long? You can't blow $20k for a Gartner report every time you imagine a new market. You need to be able to make some ballpark estimates.
(Barbers cut the hair of half the population (the male half) around every two months. The population of San Francisco is about 750k. A haircut takes about 30 minutes, and about 50% of the time a barber is cutting hair. This gives about 8 cuts per day, or about 60x8 = 480 haircuts per every two months. So to service 750k/2 of the population you need about 750k / (2 x 480)) = about 781 barbers. Or roughly one out of a thousand people is a barber.)
Comments
This wasn't an interview, it was a test. I had a similar experience with a startup. I was interviewing for a Marketing Communications Manager position. Essentially PR.
One of the unofficial interviewers (at 24 year old MIT engineer working as an email marketer) challenged me with the question "How many barbers are in San Francisco?" We proceeded to map it out the analytical process on the whiteboard. He wanted to see formulas to understand how I would arrive at the answer.
It was a stupid, impossible question. In a similar way to this girl's experience, he jabbed repeatedly critiquing my logic.
He wrote me later to explain that he posed the same question to his girlfriend, an MIT engineer herself, and she couldn't come up with an answer. Neither could he.
They offered me the job and I declined solely based on this guy and his misguided, silly behavior. I would have hated to work with him.
When a company misguidedly challenges potential employees in this way it hurts the quality of its hires. Sure, Google can afford to be picky but does it really need an engineer in a Product Marketing role? Perhaps for dev-facing apps but such an interview process is overall misguided and immature.
I don't think this is such a terrible thing, although clearly this adversarial approach to testing ideas isn't for you, or everyone. Enrico Fermi used to challenge grad students with similar questions, the famous example being 'how many piano tuners in Chicago?'.
I don't think it's a stupid or impossible question, but one that seeks to establish how you go about estimating tricky things and thus identifying fruitful territory for more rigorous research. Let's walk through it, with the awareness that we're trying to refine our techniques of estimation rather than caring about the actual number of barbers.
'Barber' implies haircuts for men. This is good, because the number of hairstylists that cater to women depends on fashion, which is hard to quantify. On the other hand, hair cutting is more related to hair growth. There's about 3/4 of a million people in San Francisco. Roughly half of them are men, so we have 375,000 potential customers. Most men wear their hair short, off the ears. Of course some wear their hair long and have it cut very infrequently, while others like it much shorter, eg with a buzz cut and have it cut more often...but some of them may cut their own hair, since a buzz-cut isn't too challenging. I'm going to assume the number of hippies cancels out the number of close-cutters because San Francisco has a bit of a hippy reputation. So much for hairstyling.
OK, so I've postulated 375,000 men who average out to a 'regular hairstyle'. And I've postulated that a regular hairstyle means not having your ears covered, ie the old 'short back and sides'. While it's growing, you could comb it out of the way or let it cover the tops of your ears, but once it gets half-way down then you're either growing it out or it's time to visit the barber. How much hair is that? My ears are about 2 inches high, but I have small ears. 3 inches sounds pretty big though...I'll guess the average is 2.5 inches, so half of that is 1.25 inches. That's already pretty fluffy though...let's round it down to 1 inch. OK, so 375,000 men get a haircut whenever their hair has grown by more than an inch.
How long does that take? Hair grows at about 4 inches a year, so let's say 3 months. Which gives us 1.5 million male haircuts a year for the whole city. (we could have started calling the population p and the rate of hair growth g[h] and so on, but why bother, it's a chain of reasoning we're concerned with here). A haircut takes, what, 20 minutes? it could be faster, then again some want a more difficult style. So let's guess that there's half a million hours of actual hair cutting (including the bit with the sheet and the sweeping up etc) going on in a year in SF.
Now we're getting somewhere. How much does a barber work? I'd say 45 hours a week. Some barbershops open early for the business crowd, but then they're closed on Saturdays. Monday-Saturday seems reasonable, as does 2 weeks' holiday. So one barber could spend a maximum of 2500 hours per year cutting hair. Only, that seems a bit high. Sometimes you wait in line, but I don't usually think of barbers as busy flat-out most of the time. 30 hours of cutting and 15 hours a week of of waiting for a customer seems more realistic. So 1500 hours of haircutting per barber (edit: 1650, but who cares). And dividing that into half a million hours of cuttable male hair per year gives me 333, the number of people needed to cut all that hair.
At this point you can start arguing about whether someone that caters to both men and women is truly a barber, or whether women can be said to be barbers even if they only cut men's hair. If your answers to those questions are no and no, and we go with the stereotype of a barber as a man who only cuts other men's hair, then I'd halve these numbers and guess that the number of 'pure' barbers in SF is 75-100.
OK, so this is 10 minutes of my life I won't get back, but if I was going to market something specific to barbers then I now have a decent guess at the number of potential customers in my local metro area.
Of course, you could have just said 'pass me a copy of the Yellow Pages and I'll tell you'. So having done the above, I went and looked that up and got 131 results at http://www.superpages.com/yellowpages/C-Barbers/S-CA/T-San+F... ...with 2 or 3 cutters at each shop, that would suggest somewhere in the 3-400 range, but some of these entries are for Salons and some are in Daly city or Sausalito, not quite in San Francisco. Still not definitive, but not too far off either. Sure, there's a lot of guessing and hand-waving here...but the important thing is that I arrived at an estimate that roughly correlates with reality. In this case I was able to check that reality (by looking up the number of self-identified barbering businesses) but once you become adept at this technique you can use it for anything, and then get on with solving the problem instead of feeling stuck by a lack of information.
Maybe it's the traditionally educated engineering in me (I was trained as a mechanical engineer), but I don't see a point in this purely theoretical hand-wavy math. There are established ways for us to get good estimates of a great deal of information - including your hairdresser problem - that involve seeking out real data. Sitting in a void of zero knowledge and postulating wildly, even if it gets you in the ballpark, is wildly inefficient and I'd hate to be involved in it as part of a professional company.
A number out of your ass - regardless of how soundly backed with logic - is at the end of the day a number out of your ass. This isn't to say that all inference or estimation is bad - but rather that estimations done in a complete void of background data is practically useless.
A more concrete example: estimate the number of users our chief competitor has. I can go through this like a logic puzzle and come up with a number that has zero verifiability... or I can go look up relevant data (their page rank on Google, other available metrics on their site, etc) and arrive at a far better conclusion.
I agree with the GP that these exercises are pointless and unrelated to the job for which you are interviewing. As a traditionally educated engineer, my training teaches me not to guess whenever facts are available. Don't try to memorize and infer numbers - keep your references within reach at all times. An engineer who makes few assumptions about his data is one who makes fewer mistakes and costs less money in damage.
I don't disagree. If you actually asked me for informational purposes, I'd have started with the Yellow Pages and then go look for a trade association or something.
On the other hand, that's not always practical. Sometimes the facts aren't readily to hand or you have to make some decision that's time sensitive. For example, working in film production it's not so unusual to have to eyeball something and estimate your needs for time or material - you try to anticipate as much of that as possible in advance, but say you come to the set one day and the lead actor has fallen ill, so now you have to rearrange your shooting schedule on the fly...in which case it's not uncommon for a few key crew members to huddle, deliberate, and then split the difference rather than obsess over further optimization.
This isn't to say one should rely heavily on gut decisions, since that's likely to be self-defeating; on the other hand, you don't use a slide rule and protractor to drive.
"As a traditionally educated engineer, my training teaches me not to guess whenever facts are available."
Ah, but the most lucrative questions are about products not yet invented, for which there are few facts. They are lucrative because there is not yet any competition. If there were lots of facts available, ripe for the picking, then by definition the net margins would be terrible.
For instance, suppose you were a grad student at the MIT Media Lab in 1995. Does it make financial sense to join the work on an electronic ink product? The answer to that question could only have been derived from a series of guesses and wild deductions. You cannot just look up how efficient planar electroluminescent backlights are going to be in 10 years. Or how expensive and power-hungry non-volatile memory devices are going to be in 10 years.
For a research organization to invent and capture a new market, they have to be good at making and using wild guesses about the future. (Looking up answers is valuable too, but for different reasons.)
I think you're badly mistaking what I'm talking about with "looking up answers" - what I'm talking about is considerably more than that.
How efficient will planar electroluminescent backlights be in 10 years? That's a good question - and one we can make an educated stab at given the right historical data, the right experience in forecasting, and a little bit of plain luck. Heck, you're now talking about an entire field of mathematics and engineering in and of itself!
Compare this to the Google interview though - where they expect you to pull a number out of your ass, with no opportunity to consult historical data, no field experts to interview... no due diligence done at all. It is either an extremely poor approximation of real-life problem solving skills, or everyone at Google is recklessly cowboy and trying to deduce every decision ever by sheer will of logic alone.
Your logic is flawed (as is nearly every "solution" to one of these problems I've seen). The question wasn't "How many barbers should there be?" It was "How many barbers are there?" This is an important distinction as your approach shows the appropriate number of barber shops that can reasonably be operated and have no shortage of customers due to hair growth speeds. I would approach the problem from the opposite direction. How many distinct professions are there in San Francisco? What is the current population? What are the percentage breakdowns of those professions? At that point, you can easily get the number of people employed as barbers. Now, did they want individual barbers, or the number of barber shops? You then only need to infer the number of barbers per shop, rather than estimating a lot of data that isn't readily available.
You know, the University of Chicago still sounds like it.
The best answer would be, there are 14 haircutting places within the shopping disctructs of the U of C, and it is currently overzoned for hair currently, accroding to the maroon. Only two are true barbershops. It consists of three long blocks. Lets take the U of C landscape to be somewhat abnormal, and that there should really only be 7, of which 1 is a barbershop. There are about 24 neighborhoods in chicago. There should be 24 barbershops...ect ect....
Just for the record...
Wow. That was cool. Thanks for walking through the logic/reasoning.
There are a lot of ways to do this type of problem.
Say, 375,000 men and 25% of them men get a hair cut every 2 weeks taking 30 min, most men get far fewer haircuts but they bring the average down to about once a month.
Av workweek = 40 hours * 4 weeks = 160 men per barber sounds low call it 200.
375,000 / 200 is less than 2,000.
The "how many X are in Y" is also known as a "case study question." From what I understand it's a standard practice in interviews for consulting companies, such as Bain or McKinsey. I've never seen one in an interview, but friends of mine who took that route obsessed over them.
As your interviewer said, these questions are asked just to see how you will come up with an answer. The actual number hardly matters, so long as you can sell it to the interviewer. Pushing you is part of the process, as well, to see how you hold up "under pressure."
If you want to be uncharitable, this is much like what a management consultant does -- come in, get some problem from a troubled company ("How can we improve sales by 20% in six months?"), develop a strategy, and then convince the client that they should do it. The interview technique makes sense for that context because it selects for people who can pull this off.
Actually, for a PR role I don't think this question is such a bad fit. You will have to think quickly on your feet, answer hostile people, and come up with diplomatic, plausible answers to crazy questions ("why does your product not work with Slackware?"). The precise answer is of course important, since if you're wrong you will be caught, but how you react is more important.
Maybe you forgot to mention it, but how did you go from "discussing an intentionally impossible problem" to "misguided, silly behavior"? If your ego makes it upsetting to work with people who "jab repeatedly, critiquing [your] logic", or find it upsetting not being able to answer a question, that says quite a lot about what kind of work environment you'd be a good fit for.
mmmmm....yes and no. if you perceives critique negatively, that's a problem with your attitude. you'll never find a good place to work because you'll react poorly to natural differences and disagreements. if others are aggressive or negative that's a problem with them, especially if they're not interested in self-analyzing and learning to be mindful.
we don't know the situation in this case.
I disagree. I actually think the questions in both your example and google's was good in seeing how you approach a problem. The point is not the answer. It is the approach.
I can think back to meetings where questions of similar nature have popped up. You have guys that want the precise numbers and refuse to make any assumption of any sort. You have guys that throw stupid guesses and just want to move forward. You have guys that do a little bit of thinking to come to a quick but critically thought out answer. This seems like a good way to identify which category you fall in and whether your approach is a good fit for the job.
Isn't the sizing of markets something of marketers need to do, all day long? You can't blow $20k for a Gartner report every time you imagine a new market. You need to be able to make some ballpark estimates.
These 'stupid impossible questions' have a long history. http://en.wikipedia.org/wiki/Fermi_problem
(Barbers cut the hair of half the population (the male half) around every two months. The population of San Francisco is about 750k. A haircut takes about 30 minutes, and about 50% of the time a barber is cutting hair. This gives about 8 cuts per day, or about 60x8 = 480 haircuts per every two months. So to service 750k/2 of the population you need about 750k / (2 x 480)) = about 781 barbers. Or roughly one out of a thousand people is a barber.)