How to answer 11 fiendishly hard interview questions posed by Google, Microsoft, and Dropbox

Suggested answer:

"Determine the volume of the room. For example if the room is 10ftx10ftx10ft the volume would be 1000ft cubed. The average mens' basketball has a diameter of 25cm. There are approximately 30cm in a foot. Therefore you could fit one inflated basketball in a 1 foot cubed space. Therefore you could fit 1000 inflated basketballs inside a room with a volume of 1000 ft cubed.

If we can deflate the basketballs and flatten them down to one inch thick, this would allow us to place 12 flattened basketballs in a 1 foot cubed space. Therefore you could fit 12,000 basketballs in a room with a volume of 1000 ft cubed.

It would be more complicated depending on the shape of the room but the process for figuring out the solution would be the same."

(People analyst)

Suggested answers:

"First 0 degree. Second 90 degree. Now I have 4 have equal parts. Third From the Centre height wise. (Z-axis)
Now I have 8 equal parts."

"It depends on the shape of the cake."

(Program manager)

Suggested answers:

"Since there are only 90 seconds left, removing bomb via bottom floor or roof is not possible since there is not enough time. Place bomb in corner of building so that at least half of blast is going out building away from personnel."

"Break a window, and throw it out?"

(Technical support engineer)

Suggested answer:

"About 60 percent of adults (18+) Americans have a Facebook account. But we're talking San Francisco here--the Valhalla of Nerdery and all things internet--so lets bump that up to 80 percent (this 30 percent increase is justified by the fact that SF is 30 percent geekier than anywhere else...).

For purposes of the question, let's limit this explicitly to the city of San Francisco--not the entire Bay Area. At night, SF is about 800,000 people strong. Let's assume a little over 20 percent of that population is either too old or young to use Facebook (it would be higher if mothers hadn't taken off FB...). Let's say that leaves 600,000 people (note: working with round numbers is better for these sorts of things). But then we have to take into account the fact people commute to and from SF! Nerds pour out into the South Bay, suits (e.g., bankers) come in from the East. I suspect the city population swells by 50 percent. If we toss in tourists and conference goers and everything else, 1 million people are in San Francisco at 2:30pm on a Friday. Eighty percent of those people use Facebook, so we have 800,000 possible Facebook users at that time.

The final step is to figure out what percent of the 800,000 are using Facebook at 2:30pm. It's later in the day so I suspect it will be higher than at 11:00am. But I don't really have a good baseline to judge. When I walk around my office, roughly 10 to 20 percent of screens I see as around the office are on some non-work related thing at any time. Let's call that 15 percent and assume that all non-work related surfing by FB users includes some sort of use of FB. That means 120,000 people are using FB at 2:30pm on Friday in San Francisco."

(Vendor relations manager)

Suggested answers:

"Depends on the position one is applying for - who do you want to be directly responsible for it and who will have oversight and authority to implement the plan? the owner of the fridge? Then establish a system to prompt the owner to check milk level and process for him/her to obtain the milk. the interviewee? Take direct responsibility to check and obtain or delegate the responsibility to an appropriate person, e.g. set up automatic delivery schedules...."

"Have a slot for a gallon or half gallon of milk that measures the weight of the container. One the milk runs low the refridgerator could light up a light, order milk online, text the owner, etc. The control scheme would have to take into account the possibility that the milk was removed for use or discard. An adjustable time delay with a default of 2 hours would work. Greater than 2 hours and the indicator/message is tripped/sent."

(Microsoft Explorer)

Suggested answers:

"25%. Paths never cross if ants go the same way: 2 ways to go * 1/2 ant goes one way*1/2 second ant goes same way*1/2 third ant goes same way = 2/8 = 1/4."

"There are 2*2*2=8 total possible ways there ants will go. Ants will not run into each other only when they are all in right direction or all in left direction, which is 2. So the answer is 2/8=0.25."

(User operations)

Suggested answer:

"First determine the number of houses.

• Clarify, are we talking stand-alone residential housing only or including things such as high rises? Assuming it is stand-alone residential
• Also clarify whether we are talking just exterior painting or interior painting; assume exterior for now
• 300 M people in US
• About 3 people per household, or 100 M households in US
• Assume 40% live in condos/high-rises, leaving 60 M households living in stand-alone residential housing
• Assume 1 household living in 1 house (simplifying assumption)
• So we have total of 60 M houses in US; we need to paint a 1/3 of them or 20 M houses
• Assume a house is 2000 sq ft on average (you can also make it more complicated by doing 25% being 1500 sq ft, 25% being 2000 sq, 25% being 2500, and 25% being 3000+)
• Assume a gallon of paint covers 100 sq ft
• Thus painting the outside will take 20 gallons on average

Now do the math: 20 M houses X 20 gallons = 40 M gallons of paint."

(AdWords associate)

Suggested answers:

"Switch doors. When you chose door #1, there was a 66% chance that the prize was not behind that door. When the host revealed the coal, there was still a 66% chance the prize was not behind the door you chose. Thus, you have doubled the odds of getting the prize by switching to door #2. The key to this puzzle is that the host knew which door has the prize."

"Your choice splits the doors in two sets. Set A contains the door you selected, and the probability that is a prize behind this door is 1/3. The set B contains all remaining doors, and the probability that the winning door is somewhere in there is 2/3. By removing one door, which all have the success probability of zero because there's coal behind them, from set B, only one door remains in B, but the overall probability for success in set B is still 2/3. Therefore you must switch."

(Program manager)

Suggested answer:

"If you could somehow measure the type of words in the emails, such as whether or not some are considered angry words or something, then you could answer the ones with more angry words first.

You could also rank them in the order of stuff that only you, due to your specialized skill set, can answer, and also the number of emails from the same person, perhaps also showing or highlighting frustration, and therefore should be addressed first."

(Rotation program)

Suggested answer:

"[1] Fact: 1% of the population has the disease (given)

[2] Data: Test is only 80% accurate, and 20% inaccurate (given):

Assume, Population = 10,000 people
1% have the disease = 100 people
99% do not have the disease = 9,900 people

Of the 1% who have the disease 80% tested +ve = 80
Of the 99% who don't have the disease 20 tested +ve = 1980

[3] Question: How likely is it that you have the disease?

To identify that you have the disease you have to test +ve and actually have the disease = 80 / (80+1980) = 80 / 2060 = 3.88%"

(Finance operations analyst)

Suggested answers:

"Using the dice you can count to a maximum of 66 combined. When the plane flies by on the 1st month's 30th day, each day after that at the same approximate time in the day you can increase the value of the dice by 1. For example plain flies by on 30th day of 1st month. the next day you wake up and assuming plane flew by at dawn you place the side with the 1 facing up. Each dawn after that you increase to 2, 3, 4, 5, 6-- after six you would use both die, and make some indication to your self saying that 1+6= 7, 2+6=8... and so on after you reach the 4+6=10th day it would be easier to use the die to show "1""1"-> 11th day, etc. That way eventually, you can make a calendar that tells you the day of the month."

"Dice 1: each pip equals 1 day: 1 pip =1 day, 2 pips = 2 days, etc.
Dice 2 each pip equals 5 days: 1 pip = 5 days, 2 pips = 10 days 3 pips = 15 days etc.
Die 2 is always to the left of Die 1.
For days less than or equal to 5 use 1 die.
When counting a day that is a multiple of 5 (days 5,10,15 etc.) count day by putting Die to 5 pips and Die 2 to the remaining number of days."

(Program manager)

Google: “How many cows are in Canada?”

Google: “How would you determine if someone has won a game of tic-tac-toe on a board of any size?”

Microsoft: "Why is a manhole cover round?"

Microsoft: "How to come out of a maze given that you can move one step at a time and you cannot turn left.”

Dropbox: “There are two children, 5 and 6 year olds who understand addition and subtraction. They do not understand multiplication or division. How would you explain the concept of prime numbers to them?”

Dropbox: “If we were being attacked by zombies what would be the first thing you would do?”

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