Job interview questions for Google

How many piano tuners are there in the entire world?

Or how about?:

You are shrunk to the height of a nickel and your mass is proportionally reduced so as to maintain your original density. You are then thrown into an empty glass blender. The blades will start moving in 60 seconds. What do you do?

Here are many more, via Craig Newmark.  I gave a talk at Google on Friday (soon coming on YouTube), and yes they really do have toy stations and Lego blocks for everyone.  They also have the tastiest workplace cafeteria I’ve sampled.  Everyone is smart and beautiful, and I didn’t want to leave.

Comments

These questions are definitely not what Google asks for technical positions, at least not when I interviewed there. Most of them are standard management consulting questions. For a technical position, I got questions like: "How do you compute the nth digit of e without knowing digits 1..(n-1)?", and how to implement a tcp/ip header.

You see this sort of nonsense anywhere there are far, far too many people applying for entry level
jobs. Was endemic to investment banks back in the Gordon Gekko days when I was involved in it, and
assume it's been robust since. Works best if you have two interviewers, one asking straight questions
and the other interrupting the answers with this stuff to see how well the candidate can get back to
the first answer.

I generally found whether or not the candidate had researched any sort of arcane topic you had no knowlege
of, and could explain it to you and get you to understand and buy off on their thesis in 10 minutes, was
the best determinant.

These - the first is just a straight "can you estimate" question and the second, just lie down and wrap
yourself around the (non-rotating) bushing, where the wind will be least.

On another note: Do you think Google checks the Google history of the job candidates? :)

The first question is a so called Fermi question (a physicist famous for his ability to estimate).

http://en.wikipedia.org/wiki/Fermi_question

Jason, as I've seen that problem started, there is a time component as well:

http://www.math.temple.edu/~paulos/parable.html

[Immediately, every woman kills their husband]

no, the slaughter happens after 100 days, as each wife waits for the others to kill their husband (because she assumes that they all know that hers was faithful) and then realises that they haven't because they didn't because he wasn't.

I haven't interviewed at Google (nor do I plan on doing so) but the type of interview questions really depends on what position you are going after. So I always think its a bit silly when this type of topic comes up. Go back 5 (or 10) years and you will see the exact same type of issue around microsoft interview questions (e.g. the now infamous manhole cover question).

Well, if they are all pretty, then I clearly don't have to waste my time sending them my resume.

The queen is a bit of a distraction. If everyone becomes aware of 99 cheaters at the same time, that's when the clock starts ticking.

LN,

As long as the women don't share information, then the clock is stopped, it seems to me.

mkl,

I think you are correct.

And, if it could be proven that a man is guilty, then why would any man stick around. Or is this one of those PC questions that has the explicit assumption that men are a bunch of Homers.

All husbands should be saved according to the principle of cooperation in a repeated game!
I am already flat. No blade can cut me after I am flattered like a nickel!

Yancey,

Actually, I take it back, the queen does add information.

Go back to the 3-person case. Everyone knows that there are at least 2 cheaters, so it seems that the queen adds no information. But if your husband isn't cheating, that means that other women would see only 1 cheater. A woman who sees only 1 cheater assumes that the cheater's wife might not know if there are any cheaters at all. So the queen's announcement does carry some information in this case.

In the 4-person case, everyone sees 3 cheaters, and so they all know that everyone else sees at least 2 cheaters, and once again it's unclear what the queen adds. But... if a woman sees 2 cheaters, then she might think that these cheater's wives see only 1 cheater... and that the cheater's wife might not know if there are any cheaters at all.

Improbably, if there are 100 women, then you know everyone sees at least 98 cheaters. But other people might not know this; they might think that some women see only 97 cheaters. And women who see only 97 cheaters might think that other women see only 96 cheaters, and so on...

So the queen is actually crucial!

Game theory is the answer to every one of these questions.
Not John von Neumann's game theory.
But the "what game are you playing?" theory.
Because its all a game.
None of these questions will improve hiring.
John
SIMCGLACC
(Sitting in my chair grinning like a Cheshire cat.)

My brother-in-law is a chef on the Google campus and regularly regales us with tales of its magnificence. Apparently Google has bought into the whole local-vore movement and only buys food grown in the area.

Reading about this Google test reminds me of something in the book The Right Stuff. Astronaut candidates back during the Mercury program were subjected to a test in which they had to push buttons in response to flashing colored lights. As the test went on the lights began flashing faster and faster, eventually getting to the point at which it was completely impossible for anyone to follow. It was one of the most frustrating tests the candidates faced.

Which was the whole point of the test. It was not designed to test the candidates' reaction times, as they thought, but rather to see how they would hold up under extreme frustration.

And so it may be with the Google employment questions, or some of them. The interviewers may not really expect the applicants to be able to answer some, maybe most, of the questions, for example the one about piano tuners would be hopelessly obscure to most people. It all may be a way of seeing how people react under pressure.

LN,

I understand the logic of the backwards-working deduction, and I agree with it. However, once we reach the situation where every husband cheats, then every woman will be unsurprised that the queen's announcement results in no men dying after 100 days. The conclusion of every woman should be that there were no deaths because all the other women simply did not know that their husbands were cheating.

I just know I have to be wrong about this, but I just don't see a way around my conclusion.

I originally missed the part of the problem specifying that all of the husbands were in fact cheaters. Oops. But this part of my response stands:

What’s really interesting to me is that without having the decision points laid out discretely
(e.g. in days), it’s unlikely that any woman could reach the decision to kill her husband beyond the first couple of levels. Suppose the rule were that she must kill him as soon as she knows. If there were only one cheater, this would be straightforward. If there were two, well then I suppose it would be obvious enough to see that the one cheater’s wife you know about wasn’t acting immediately, and then know that yours is the second cheater. But beyond that, it becomes a complete mess. Basically, you have to determine that all of the other women are up to reasoning level n before you can move to level n+1. (While if someone has reached n+2 by that point, she has already incorrectly killed her old man.)

Heh, can anyone tell that I'm procrastinating?

*criticism... i have a low IQ...

If I were a husband in this game, I'd kill the Queen.

Isn't the problem assuming that all 100 women has perfect logic? And even if they all do, why would each of 100 women also assume that the other 99 women also have perfect logic? After all, the problem assumes that none of the women share information with one another.

The queen's proclamation is necessary for the 2-wife scenario (which all the others build off of). In the 2-wife scenario each wife can believe it is possible that the other cuckholdette assumes no one is cheating. She only has to believe it is possible.
Once the queen has spoken, that possibility is stripped and the game is on.

Oh, the hell with it! If I took the test, I would just answer that the men would kill all their wives the instant after the queen spoke. In self-defense, of course.

Yeah, ditto Jeff, it is very cool.

Fascinating that all of the women are just going to chill out for a bunch of days knowing that nothing is going to happen, but that waiting out those days is still crucial. And, as I mentioned, that if the decision stages aren't fixed to something outside the reasoning parties, the whole thing falls apart.

What the wives should do is replace days with something like marks on a board. ("Once you know you husband is a cheater, you need to declare that you're going to kill him before the next mark is made.") The whole thing could get solved pretty quick.

Does anyone here know if the people who think
tests like these reveal anything useful about
whom to hire are also the people who think the
Myers-Briggs test is useful for anything other
than enriching the testing company?

OK I now get it about iterating downwards. But how does the information of 1 cheater lead to killing. (These brain teasers kill me.) Lets do the A B C analogy. A thinks that B thinks that C thinks that there are zero cheaters. Queen arrives. No killing. A is confused as she knows B knows that C knew of no cheaters. Therefore no killing implies that C knows of a new cheater. And because C didn't kill, A thinks that B thinks that it must be A's husband because B is ignorant of her own husband. How does this lead to A killing her own husband?

LN, you miss my point. Is it not readily apparent that these reasoning questions seem test-like? Wouldn't it be more efficient and reliable a metric to give applicants a group of these questions in test form, with a time limit? However, companies cannot administer tests for avery obvious reason: certain groups will perform poorer on average than others opening that company up to the charge of discrimination law suits. That's why you have these reasoning problems in interview format. To avoid lawsuits.

http://en.wikipedia.org/wiki/Griggs_v._Duke_Power_Co.

"Griggs also held that the employer has the burden of producing and proving the business necessity of any testing."

Why there is no longer such pure reasoning testing when applying to elite companies such as Google, Goldman Sachs, etc. who as you said, attract the best and the brightest.

Instead, companies get around this by oral exams featuring questions like the one Tyler mentions...

"During that trip, I must have heard Mr. Gates mention ‘IQ’ a hundred times. The obsession with smarts is embedded deep in Mr. Gates's thinking and long ago was institutionalized at Microsoft. Apply for a job and you’ll face an oral grilling that probes for IQ. It is oral and informal because of Griggs v. Duke Power, the 1971 Supreme Court ruling that banished written IQ tests and ‘tests of an abstract nature’ from job applications. But Microsoft knows what it wants. It wants IQ. And Microsoft always has been savvy at getting what it wants."

- WSJ (http://online.wsj.com/article/SB109096908950675667.html?mod=todays_us_opinion)

Google is like a college campus, because they bought the campus that way from SGI! :-)

Seriously though, Google pressures its employees into ridiculous hours. Ridiculous to me that is. It's one reason they hire young people, because the young don't know any better.

Ridiculous hours, maybe, but the smart and beautiful part definitely beats working at a law firm or investment bank. As for it being like a college campus--college was great! Everything was taken care of for you and you were surrounded by attractive members of the opposite sex. What's not to like?

I don't understand. A wife must kill her husband if she can prove that he is unfaithful. But all we have is the Queen announcing that one husband has been unfaithful. How is that remotely anything like proof? Does anyone really believe that Queens never lie and never make mistakes? What happens if the Queen was deceived into thinking she had seen one husband being unfaithful, like Claudia was deceived into seeing Hero being unfaithful in Much Ado About Nothing?

This problem appears to assume that the wives in the village are rather ignorant about the history of monarchies.

Thanks, samson. I think what originally confused me about the problem (as originally stated) was that it wasn't clear which of the given facts the women also knew. i.e., Do they know other women also know about every other woman's knowledge of all other women?

Plus, I think a lot of people were secretly thinking, "Women can't follow a chain of logic that long!"

Most of those questions can be found in the book, "How Would You Move Mount Fuji?" The book is about how Microsoft and other companies have changed the way interviews are conducted and how to find creative thinkers.

I work at Google as an analyst (there are in fact business and financial analysts here) and our interview process eschews these brain ticklers, though I understand that Engineering still pulls them out from time to time in their interviews. Interviews for position in my department are relatively standard questions, aiming to discern whether or not the candidate understands Google's business model. If you were a mom and pop e-retailer selling golf clubs online, how would you determine how much to bid for your advertisement? How many daily Maps transactions do you think there are in Thailand?

It should also be said that while the degree varies from team to team, "Googliness" - how you interact with teammates, your niceness, your sense of humor - is a highly valued quality and a lack of it will get you bounced from consideration most groups, regardless of skills.

Yancey_Ward: I thought the puzzled relied on how women *did* know what other women know about other men?

(Dagnabbit, the story is making me talking like ELIZA.)

Can someone explain the problem again in order to make sense of it for me?

Here's my issue: each woman can assume that the other 99 women can see at least 98 or perhaps 99 cheaters (because each woman knows she sees 99, and isn't sure about her own husband). Therefore the information that there is (at least) one cheater won't be news to anyone.

Am I missing some restriction in the problem that explains this discrepancy?

Zubon,

The logical reaction of the men would be as I described above, kill every wife the instant the queen lets the cat out of the bag. Every man knows he has been unfaithful, knows the wife will eventually figure it out, either that day, or some n-days in the future.

Hopefully I can post a quick breakdown of the answer for those who can't get through all the confusing posts.

What's key to the answer is to know what would happen if the village only had 2 couples. The Queen tells every women at their nightly meeting that one husband may be cheating and it may be their husband. Before, they only knew about other women's husbands.

So, women 1 thinks that women 2 knows of no other cheaters, because women 1 thinks her husband isn't a cheater. Women 1 thinks that when women 2 hears the Queen's announcement, she immediately knows that it HAS to be her husband. This is because women know that they will always recognize each husband that's cheating except for their own.

When women 1 sees that women 2's husband is still there, she knows that could only happen if women 1's husband was also cheating. Women 1 (and Women 2) kill their husband.

For N=3, women 1 thinks that women 2 and 3 are in the N=2 case. So after 2 nights, when both husbands are still alive, women 1 knows that her husband had to have been cheating for both husbands to still be alive.

This goes on up for any N and all husbands will die after N days.

You have very nice and imagnative articles....Keep it up...Good work!

I think the point of these questions may simply be to generate interesting discussions that contain the word "Google"... self-propagating advertising.

That was an absolutely fascinating puzzle. And a very, very weird one for me. If the problem were asked using four couples, I would have constructed exactly the deductive argument outlined, and believed it completely, though I now know I would not have understood why the queen's statement was necessary. With one hundred couples, I simply could not get my mind around it even knowing that the number of couples was completely irrelevant to the validity of the logic. Why? I am not really sure.

For me, the "Aha!" moment came from LN's reply to Emily who had the same issues I had expressed earlier,

"each woman can assume that the other 99 women can see at least 98 or perhaps 99 cheaters (because each woman knows she sees 99, and isn't sure about her own husband). Therefore the information that there is (at least) one cheater won't be news to anyone

LN's reply was quite clear, at least to me:

Emily,
The information is not news to anyone. What is news is that this is not news to anyone

Hammers finally broke through the concrete that is my head.

Yancey: I was commenting on your penchant for a husbands' uprising. Clearly, I should hit refresh before posting a comment! I'm glad LN made it clear. His quip really does get to the heart of it.

I did my best to explain but it looks like it was actually Zubon was the person who really made it clear.

samson: Every wife knows that the queen is not lying. Remember that each one see 99 cheating husbands. Clearly each wife knows the queen is not lying that there exists at least one cheating husband.

But the queen's statement being new information depends on all the second and higher order knowledge affects, which only collapse if we don't merely know that the queen is not lying, but know that all other women will know that, and know that all other women know that, etc., etc.

So the queen's statement provides the new meta-information necessary only if we assume that all the women will believe her no matter what they see and expect others to do the same.

Thus Tracy W.'s point stands.

In my version of the answer to this, somewhere around the 98th day, all the women wake up and decide they need to have a big town meeting about this law.

I mean seriously, if they are smart enough to follow this chain of logic impeccably, and trust everyone else to be smart enough to do the same, then you'd think they'd also be able to figure out that killing all their husbands isn't going to be a good thing for the village.

Alternately, on the first night one of the women who really wants to be rid of her husband anyway guesses how this will play out and decides to make him the sacrificial goat.

I first saw this question (same logic anyway) in _Calculus_ by Spivak, where the story is of a department of math professors who live by a code of resigning if they ever make a mistake in published work, all know that every other professor has made a mistake, one day some wiseguy comes in and says, etc. etc. Like the statement of this problem, some of the particular assumptions necessary to make the problem work were not spelled out in detail (one of my peeves with many of these problems).

one crucial bit being that if there is not a determined time for the resignation, you have to assume not only that everyone can follow the chain of logic, but will almost assume that everyone else follows the chain *exactly as fast*.

Most math profs being among the most arrogant people I've ever known, I took that to be an extraordinarily unreasonable assumption. If I am an arrogant prick and I know that every one of my colleagues has made an error, and until today I believe that I have *not* made an error, is it likely that I'll assume that every last one of them can follow this contorted chain of logic exactly as fast as I can and that *I* also made an error?

Bwahahaha.

First, note that this problem is more commonly given in other forms, either "blue-eyed monks" or "muddy children".

Second, everyone is posting elaborate explanations of why the queen must be providing new information but I don't think anyone has said what that information actually *is*.
In other words, what's some fact that the wives didn't know before the queen's announcement that they do know after?

In the case of one couple it's easy: Fact known only after queen's announcement: There exist unfaithful husbands.

Case 2:
BEFORE: Does not know that the other wife knows of infidelity.
AFTER: Knows that the other wife knows.

Case 3:
BEFORE: Knows that everyone knows of infidelity but does not know that everyone knows that everyone knows. (Wife 2 thinks Wife 3 is oblivious, as far as Wife 1 knows. Ie, Wife 1 thinks 2&3 are in Case 2.)
AFTER: Knows that everyone knows that everyone knows.

Case N:
BEFORE: Doesn't know X.
AFTER: Knows X.
where X is "Everyone knows that ... (N-1 times) ... that everyone knows of infidelity."

That's what it means to say that infidelity becomes "common knowledge".

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