Google Labs Aptitude Test (GLAT)

Joe Kraus has a new typepad about entrepreneurship, and one of his first posts is about Hiring -- No False Positives, a great subject. It's important to remember that there's no one who's great in every environment, so great candidates need to be interviewed as much for cultural fit as they do for skillset. Joe writes:

Any hiring process should focus on never letting in a bad fit. Even if that means accidentally rejecting a lot of people that would be good fits. Said another way, it optimizes for no false positives, even at the expense of false negatives.

The Google hiring process is notoriously long and complicated. Internally, it's kind of a Liberum veto thing - a single no-vote of the hiring committee means you're not in. Why? Because they put the principle of 'no false positives' to work. They assume that there is a huge talent pool of great people and that they can afford to pass on people that would be great fits in order to make sure they never let someone through who doesn't fit.

Trust me. It's so hard to do. Especially in a startup where you've got much more to do than you have people to do it. But, slip up, even once and it's trouble fast.

I totally agree with Joe on this, and have been burned when I didn't listen to this advice. I would rather be understaffed, with everyone productive, than hire someone who does nothing (zero productivity) or -- worse -- takes away from the productivity of others (negative productivity).

So I was flipping through Dr. Dobb's Journal for October 2004 that came in the mail this week, and discovered after page 28 the Google Labs Aptitude Test, test code WR-426F: "How much aptitude do you have for the sort of mind-bending engineering problems encountered each day at Google Labs? Take the GLAT and find out. Simply answer all questions to the best of your abilities (cheaters will answer to the karma police) [and send it to: Google Labs Jobs, 1600 Amphitheatre Parkway, Mountain View, VA 94043-1351]. Score high enough and we'll be in touch. Good luck."

A few comments before I list the test.

• Philosophically, I have a slight problem with their desire for people not to cheat. One set of skills is the raw talent to answer the questions oneself, derived from first principles and creativity, and I guess this test is meant to probe that. On the other hand, another set of skills that is also useful is having the perseverance, the searching skills (uh, hello, this is the friggin' Google Labs Aptitude Test, and the sheer willpower to find the answers by any means necessary shows a lot about a candidate). I'd like to think that the best candidate is someone who's smart and creative enough to answer some questions, and who's tenacious enough to glean the answers to some other questions, and who's ethical enough to tell me when they went for additional help. I believe the answers to most of life's (and a company's) questions do not come from within; they come from constructively collaborating with others; that is why a team is often greater than the sum of its parts.

• That said, I think this test is awesome. I love the idea, and I enjoyed noodling on some of the problems just for the fun of it. Kudos to Google for taking the first 10-digit prime found in consecutive digits of e billboard up a notch. By the way, finding the answer to that question is not brain surgery, but it sure does make one feel smart for solving it because for a moment you think to yourself, "yeah, I'm smart enough to work at Google", before going back to whatever it was you were doing before you fell down that rathole.

• Wouldn't it be cool if there were also a Google Labs Attitude Test? :)

If, after reading the following questions, you decide you're Google Caliber, by all means apply for a Google job, because heaven knows that with only 2200 employees they'll need to do more recruiting before they can be "the biggest and most important company in the world in 5-8 years".

Google Labs Aptitude Test:

1. Solve this cryptic equation, realizing of course that values for M and E could be interchanged. No leading zeroes are allowed.

   WWWDOT - GOOGLE = DOTCOM

2. Write a haiku describing possible methods for predicting search traffic seasonality.

3. What's the next line?

   1
   1 1
   2 1
   1 2 1 1
   1 1 1 2 2 1

4. You are in a maze of twisty little passages, all alike. There is a dusty laptop here with a weak wireless connection. There are dull, lifeless gnomes strolling about. What dost thou do?

   A) Wander aimlessly, bumping into obstacles until you are eaten by a grue.
   B) Use the laptop as a digging device to tunnel to the next level.
   C) Play MPoRPG until the battery dies along with your hopes.
   D) Use the computer to map the nodes of the maze and discover an exit path.
   E) Email your resume to Google, tell the lead gnome you quit and find yourself in a whole different world

   (editor's note: I always thought the acronym was MMoRPG, not MPoRPG?)

5. What's broken with Unix?

   (editor's note: I would love to hear Allan's answer to this question...)

   How would you fix it?

   (editor's note: Allan's pontification parable rave about this question is far better than an actual answer to this question...)

6. On your first day at Google, you discover that your cubicle mate wrote the textbook you used as a primary resource in your first year of graduate school. Do you:

   A) Fawn obsequiously and ask if you can have an autograph.
   B) Sit perfectly still and use only soft keystrokes to avoid disturbing her concentration
   C) Leave her daily offerings of granola and English toffee from the food bins.
   D) Quote your favorite formula from the textbook and explain how it's now your mantra.
   E) Show her how example 17b could have been solved with 34 fewer lines of code.

7. Which of the following expresses Google's over-arching philosophy?

   A) "I'm feeling lucky"
   B) "Don't be evil"
   C) "Oh, I already fixed that"
   D) "You should never be more than 50 feet from food"
   E) All of the above

8. How many different ways can you color an icosahedron with one of three colors on each face?

   (editor's note: "An icosahedron is not-necessarily a regular 20-faced polyhedron! Examples include the regular icosahedron, Jessen's orthogonal icosahedron, rhombic icosahedron, 18-sided prism, 19-sided pyramid, or 10-sided dipyramid..." Jiminy crickets, am I a geek...)

   What colors would you choose?

9. This space is intentionally blank. Please fill it with something that improves upon emptiness.
   
   

10. On an infinite, two-dimensional, rectangular lattice of 1-ohm resistors, what is the resistance between two nodes that are a knight's move away?

11. It's 2pm on a sunny Sunday afternoon in the Bay Area. You're minutes from the Pacific Ocean, redwood forest hiking trails and world class cultural attractions. What do you do?

    (editor's note: I should stop interrupting this test with editor's notes, but I cannot help but ask myself if there's any possible answer to this question better than do some laundry....)

12. In your opinion, what is the most beautiful math equation ever derived?

13. Which of the following is NOT an actual interest group formed by Google employees?

    A) Women's basketball
    B) Buffy fans
    C) Cricketeers
    D) Nobel winners
    E) Wine club

14. What will be the next great improvement in search technology?

    (editor's note: It's gotta be Fisher, right? Gotta get me a pocket Fisher, man...)

15. What is the optimal size of a project team, above which additional members do not contribute productivity equivalent to the percentage increase in the staff size?

    A) 1
    B) 3
    C) 5
    D) 11
    E) 24

16. Given a triangle ABC, how would you use only a compass and straight edge to find a point P such that triangles ABP, ACP, and BCP have equal perimeters? (Assume that ABC is constructed so that a solution does exist.)

17. Consider a function which, for a given whole number n, returns the number of ones required when writing out all numbers between 0 and n. For example, f(13) = 6. Notice that f(1) = 1. What is the next largest n such that f(n) = n?

18. What's the coolest hack you've ever written?

19. 'Tis known in refined company, that choosing K things out of N can be done in ways as many as choosing N minus K from N: I pick K, you the remaining.

    Find though a cooler bijection, where you show a knack uncanny, of making your choices contain all K of mine. Oh, for pedantry: let K be no more than half N.

20. What number comes next in the sequence: 10, 9, 60, 90, 70, 66, ?

    A) 96
    B) 10 to the 100th power
    C) Either of the above
    D) None of the above

21. In 29 words or fewer, describe what you would strive to accomplish if you worked at Google Labs.

    (final editor's note: I still have 23 words left over after scribbling "don't be evil; do some laundry"... any suggestions?)
    

Note that cruftbox has a scan of the GLAT in stylish green-and-white jpg's. (Spoiler alert: some of the test's questions are answered in the comments of that post.)

I wonder how they'd feel if I submitted the form completely written in collage-style, cutting and pasting passages from newspapers and magazines. Or if I answered all the questions in crayon.

By the way, you can find at least two answers on Dion's blog. And I do agree with Mark Szpakowski's answer to the most beautiful equation ever derived:

Most beautiful equation ever derived? It's gotta be:

(e**(i*pi)) + 1 = 0

Brings together e (the Google [IPO offering] valuation :-), pi, i, 1 and 0, not to mention equality, addition and multiplication/exponentiation. What more can you ask for?

I try to grok this in fullness.

Euler, you magnificent bastard, all I can say is, Amen, brother. And remember, kids, don't drink and derive...

Comments

[Timboy]

Howard, I don't work at Google either ... how about Yahoo! Search though? Post the answer to GLAT #19, and then let's talk... (This goes for anyone, actually :)

[Howard Robbins]

GLAT Problem: Given a triangle ABC, how would you use only a compass and straight edge to find a point P such that triangles ABP, ACP, and BCP have equal perimeters? (Assume that ABC is constructed so that a solution does exist.)

Amended answer: I should have explained more clearly. Simple algebra gives AP - BC = BP - AC = CP - AB. Call this quantity Q. Then AP = BC+Q, BP = AC+Q, and CP = AB+Q. But these three equations have a simple geometric interpretation:

A circle of radius |Q|, centered at P, is tangent to circles of radii BC, AC, and AB, centered at the vertices A, B, and C. This is the classic 3-circles problem, with the additional requirement that the tangencies must be all external (Q>0) or all internal (Q<0).

[The Duke]

Question #19 really is the key, isn't it?

I believe I have the (or at least one) answer, but there's no way Google would hire me.

Anyway, it took me a month, but I solved every one except #10. I did use an Excel spreadsheet to calculate #17, is that "cheating"?

Not bad for a high-school education!

Regards,
The Duke

[i never use Google - I use altavista]

How about I give you (10) engineering questions and if you get at least (6) right MAYBE I might work for you (out of my home)

[Timboy]

Heh. Post the questions, that's always fun. But working from home is a lose IMHO.

btw, If you're using Altavista, then you're using Yahoo Search. Thank you for your support.

[Hew]

I think I have a nice solution to problem #19: take a look at

http://www.hewwolff.org/GoogleProof/proof.html

Google does not seem to be interested in this. :-( But maybe someone else will be....

[Adam]

Ok, I'm impressed, Hew. Nicely done. They should definitely hire you -- and if not them, maybe you're right that someone else will be interested.

Also, thanks for the link to some of the Mathematica solutions. Now that the cat's out of the bag, I guess we can look forward to

GLAT II: Judgment Day

*wink*

[John Woods]

Question 16 - Triangle ABC

B\
| C
A/

For ABP, ACP, BCP to have equal perimeters the point P must be in the centre of the equilateral triangle. This point is located by aligning the triangle so that the line A-B is pointing due north. Draw a straight line west from C and another NNE from point A. P is located at the intersection of these lines. And result - no circles.

[melena]

The answer for the first Q is :9O-4.5O=4.5O

[melena]

The answer for Q3 is:212112211

[melena]

The answer for Q8 :6
i will choose black, white,and red

[melena]

How i could contact with you ?
you should make a new glat

[cymer]

can i ask everybody about the kinds of "aptitude test"?please help me im a student..come from the phillippines..

[Preetha]

I recently attended google interviews.. it was like 3 screening interviews and 6 onsite interviews.. I believe that I did great job in all my interviews.. answered all their logical and analytical problems ... infact all interviewers appreciated me when they left.... I was confident that I will get selected... It took them atleast one month to give me the interview results.. I was not selected.. the reson I guess is, I am not from stanford or MIT or Carnegie Mellon University or IIT or BITS.. BUT MY QUESTION IS THIS .. IN THAT CASE, WHY DID THEY SELECT ME IN THE SCREENING INTERVIEWS ???... WHY DID THEY CALL ME FOR AN INTERVIEW ?? .. I wasted atleast one month refreshing all those stuffs I learnt in my undergrad and grad.. the whole process took me abt 2 months.. .. I believe its useless now.. atleast I know I must not apply for this company if I am not from the mentioned universities.

-Preetha

[Ram]

yes I agree with preetha... and also you must have atleast presented or published a research paper..

[Aravind]

A very amateurish program for solving Question 17 which takes 2.5 hours to arrive at the answer on my system :)

#include
int function(int n)
{
int i=0;
int j=0;
int k=0;
int m=0;
for(i=0;i<=n;++i)
{
m=i;
while(m)
{
k=m%10;
m=m/10;
if(k==1)
j++;
}
}
return j;
}
main()
{
int n=2;
int b;
while(n)
{
b=function(n);
if(b == n)
{
printf("\nYeah Baby the number: %d\n" , b );
exit(0);
}
n++ ;
}
}

[Aravind]

A much better program.. sack the old one :-)

#include
#include
int function(int n)
{
int a=0;
int b=0;
while(n)
{
a=n%10;
n=n/10;
if(a==1)
{
b++;
}
}
return b;
}
main()
{
static int k=1;
int i=2;
while(i)
{
k=k+function(i);
if(k==i)
{
printf("\nYeah Found:%d\n",k);
exit(0);
}
i++;
}
}

[aditya sen singh]

mail the GLAT questions

[dating]

That's so cool. I wish more teachers possessed that kind of enlightenment.

[gbolcer]

The correct answer for 9 is:

src="http://pagead2.googlesyndication.com/pagead/show_ads.js">

[MMO]

I dont think i could even answer one of those questions lol