Google used to ask job applicants ridiculously hard brainteaser interview questions.
Recently, we posted 15 of these questions to show just how hard they were.
Now, we've got the answers.
How many golf balls can fit in a school bus?
Job: Product Manager
Answer: This is one of those questions Google asks just to see if the applicant can explain the key challenge to solving the problem.
Reader Matt Beuchamp came up with a dandy answer, writing:
I figure a standard school bus is about 8ft wide by 6ft high by 20 feet long  this is just a guess based on the thousands of hours I have been trapped behind school buses while traffic in all directions is stopped.
That means 960 cubic feet and since there are 1728 cubic inches in a cubit foot, that means about 1.6 million cubic inches.
I calculate the volume of a golf ball to be about 2.5 cubic inches (4/3 * pi * .85) as .85 inches is the radius of a golf ball.
Divide that 2.5 cubic inches into 1.6 million and you come up with 660,000 golf balls. However, since there are seats and crap in there taking up space and also since the spherical shape of a golf ball means there will be considerable empty space between them when stacked, I'll round down to 500,000 golf balls.
Which sounds ludicrous. I would have spitballed no more than 100k. But I stand by my math.
Of course, if we are talking about the kind of bus that George Bush went to school on or Barney Frank rides to work every day, it would be half that ... or 250,000 golf balls.
How much should you charge to wash all the windows in Seattle?
Job: Product Manager
Answer: This is one of those questions where the trick is to come up with an easier answer than the one that's seemingly being called for. We'd say. "$10 per window."
In a country in which people only want boys …
... every family continues to have children until they have a boy. If they have a girl, they have another child. If they have a boy, they stop. What is the proportion of boys to girls in the country?
Job: Product Manager
Answer: This one caused quite the debate, but we figured it out following these steps:
 1. Imagine you have 10 couples who have 10 babies: 5 will be girls, 5 will be boys. (Total babies made: 10, with 5 boys and 5 girls.)
 2. The 5 couples who had girls will have 5 babies. Half (2.5) will be girls. Half (2.5) will be boys. Add 2.5 boys to the 5 already born and 2.5 girls to the 5 already born. (Total babies made: 15, with 7.5 boys and 7.5 girls.)
 3. The 2.5 couples that had girls will have 2.5 babies. Half (1.25) will be boys and half (1.25) will be girls. Add 1.25 boys to the 7.5 boys already born and 1.25 girls to the 7.5 already born. (Total babies: 17.5 with 8.75 boys and 8.75 girls.)
 4. And so on, maintaining a 5050 population.

How many piano tuners are there in the entire world?

Job: Product Manager

Answer: We'd answer "However many the market dictates. If pianos need tuning once a week, and it takes an hour to tune a piano and a piano tuner works 8 hours a day for 5 days a week 40 pianos need tuning each week. We'd answer one for every 40 pianos."
 On Wikipedia, they call this a Fermi problem.

The classic Fermi problem, generally attributed to Fermi, [2] is "How many piano tuners are there in Chicago?" A typical solution to this problem would involve multiplying together a series of estimates that would yield the correct answer if the estimates were correct. For example, we might make the following assumptions:
 1. There are about 5,000,000 people living in Chicago.
 2. On average, there are two persons in each household in Chicago.
3. Roughly one household in 20 has a piano that is tuned regularly.
4. Pianos that are tuned regularly are tuned on average about once a year.
5. It takes a piano tuner about two hours to tune a piano, including travel time.6. Each piano tuner works eight hours in a day, five days in a week, and 50 weeks in a year.

From these assumptions we can compute that the number of piano tunings in a single year in Chicago is:
(5,000,000 persons in Chicago) / (2 persons/household) × (1 piano/20 households) × (1 piano tuning per piano per year) = 125,000 piano tunings per year in Chicago.
And we can similarly calculate that the average piano tuner performs:
(50 weeks/year)×(5 days/week)×(8 hours/day)×(1 piano tuning per 2 hours per piano tuner) = 1000 piano tunings per year per piano tuner.
Dividing gives:
(125,000 piano tuning per year in Chicago) / (1000 piano tunings per year per piano tuner) = 125 piano tuners in Chicago.
A famous example of a Fermiproblemlike estimate is the Drake equation, which seeks to estimate the number of intelligent civilizations in the galaxy. The basic question of why, if there are a significant number of such civilizations, ours has never encountered any others is called the Fermi paradox.
Why are manhole covers round?
Job: Software Engineer
Answer: So it doesn't fall through the manhole (when the plane, ordinarily flush with the plane of the street, goes perpendicular to the street).
Design an evacuation plan for San Francisco
Job: Product Manager
Answer: Again, this one is all about the interviewer seeing how the interviewee would attack the problem. We'd start our answer by asking, "What kind of disaster are we planning for?"
How many times a day do a clock’s hands overlap?
Job: Product Manager
Answer: 22 times. From WikiAnswers:
AM
12:00
1:05
2:11
3:16
4:22
5:27
6:33
7:38
8:44
9:49
10:55
PM
12:00
1:05
2:11
3:16
4:22
5:27
6:33
7:38
8:44
9:49
10:55
Explain the significance of "dead beef"
Job: Software Engineer
Our (wrong) answer: Beef is always dead. Calling something "dead beef" is redundant — a nono for coders.
The actual answer, from a reader:
DEADBEEF is a hexadecimal value that was used in debugging back in the mainframe/assembly days because it was easy to see when marking and finding specific memory in pages of hex dumps. Most computer science graduates have seen this at least in their assembly language classes in college and that's why they expect software engineers to know it. From wikipedia:
"0xDEADBEEF ("dead beef") is used by IBM RS/6000 systems, Mac OS on 32bit PowerPC processors and the Commodore Amiga as a magic debug value. On Sun Microsystems' Solaris, it marks freed kernel memory. On OpenVMS running on Alpha processors, DEAD_BEEF can be seen by pressing CTRLT.[3]"
A man pushed his car to a hotel and lost his fortune. What happened?
Job: Software Engineer
Answer: He landed on Boardwalk. (Painful, right?)
You need to check that your friend Bob has your correct phone number…
… but you cannot ask him directly. You must write the question on a card and give it to Eve who will take the card to Bob and return the answer to you. What must you write on the card, besides the question, to ensure Bob can encode the message so that Eve cannot read your phone number?
Job: Software Engineer
Answer: Since you are just "checking," you ask him to call you at a certain time. If he doesn't, he doesn't have your number.
Too simple? A reader suggested: "In that case you need a checksum. Have Bob add all the digits of your phone number together, write down the total, and pass that back to you."
You're the captain of a pirate ship …
… and your crew gets to vote on how the gold is divided up. If fewer than half of the pirates agree with you, you die. How do you recommend apportioning the gold in such a way that you get a good share of the booty but still survive?
Job: Engineering Manager
Answer: You divide the booty evenly between the top 51% of the crew.
You have eight balls all of the same size …
Seven of them weigh the same, and one of them weighs slightly more. How can you find the ball that is heavier by using a balance and only two weighings?
Job: Product Manager
Answer: Reader Hyloka nailed this one first:
Take 6 of the 8 balls and put 3 on each side of the scale. If the heavy ball isn't in the group of 6, you know it's one of the remaining 2 and so you put those two in the scale and determine which one. If the heavy ball is in the 6, you have narrowed it down to 3. Of those 3, pick any 2 and put them on the scale. If the heavy ball is in that group of 2, you know which one it is. If both balls are of equal weight, then the heavy ball is the one you sat to the side.
You are given some eggs …
You have access to a 100story building. Eggs can be very hard or very fragile, meaning they may break if dropped from the first floor or may not even break if dropped from 100th floor. Both eggs are identical in appearance. You need to figure out the highest floor of a 100story building an egg can be dropped without breaking. The question is, how many drops you need to make? You are allowed to break two eggs.
Job: Product Manager
Answer: The maximum egg drops for this method is 14 times.
Instead of partitioning the floors by 10, start at the 14th floor, and then go up 13 floors, then 12, then 11, then 10, 9, 8, 7, 6, 5, 4 until you get to the 99th floor, then here. If the egg were to break at the 100th floor, it would take 12 drops (or 11 if you assume that it would break at the 100th floor). Say, for example, that the 49th floor was the highest floor, the number of drops would be the 14th, 27th, 39th, 50th (the egg would break on the 50th floor), plus the 40, 41,42,43,44,45,46,47,48, and 49th floor for a total of 14 drops.
Explain a database in three sentences to your 8yearold nephew.
Job: Product Manager
Answer: The point here is to test the applicant's ability to communicate complex ideas in simple language. Here's our attempt: "A database is a machine that remembers lots of information about lots of things. People use them to help remember that information. Go play outside."
You are shrunk to the height of a nickel …
And your mass is proportionally reduced 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?
Job: Product Manager
Answer: This one is all about the judging interviewee's creativity. We'd try to break the electric motor.