Google Labs Aptitude Test

These are the questions asked to anyone interested in entering into Google Labs to work with the team. Have a look, you need some serious brains to tackle a few of these:

Solve this cryptic equation, realizing of course that values for M and E could be interchanged. No leading zeroes are allowed.
WWWDOT – GOOGLE = DOTCOM

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

What’s the next line?
1
1 1
2 1
1 2 1 1
1 1 1 2 2 1

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

What’s broken with Unix?

How would you fix it?

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.

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

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

What colors would you choose?

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

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?

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?

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

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

What will be the next great improvement in search technology?

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

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.)

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?

What’s the coolest hack you’ve ever written?

‘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.

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

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

[Hat tip James]