How to answer an insanely hard brain teaser interview question without seeming nervous

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"How much does a school bus weigh?"

"How many people are currently online in Germany?"

"How many windows are there in New York City?"

And, most importantly: "How the heck do you answer these crazy questions?"

If you're interviewing for a tech job, chances are you'll get thrown one of these brain teaser questions at some point during the selection process. And when you do, you don't want to stammer, "Um, I have no idea."

So to make sure that you're ready to handle just about anything, let me share nine steps that helped me earn offers at Apple, Amazon, Microsoft, LinkedIn, and VC-backed startups.

1. Understand what the interviewer wants

It's easy to get flustered if you assume that this is the same kind of question you might find on a multiple-choice test (i.e., there's one right answer and lots of wrong ones).

Instead, think about it from the interviewer's perspective. She needs to find someone who can succeed in this job — not someone who's great at counting windows. So what she really wants to know is whether you can handle the rigors of a crazy tech job, which include:

• Dealing with uncertainty
• Thinking analytically
• Communicating clearly

So, your first step is to take a deep breath and remember your goal is to demonstrate your curiosity, logical analysis, and clear communication — not come up with the exact, perfect calculations.

2. Clarify the question

To demonstrate your curiosity, start by asking some clarifying questions. For instance, if you've been asked how many windows are in New York (here's a list I've collected of other common tech brain teasers), you might respond by asking:

"When you say windows, do you only mean building windows or are you also thinking of subways, computers, and exhibits at the Bronx Zoo?"

This not only shows off your curiosity; it can also save you tons of agony. Because if it turns out that your interviewer only cares about building windows, this question just became a whole lot simpler.

3. Ask for time

Now, as tempting as it might be to dive right into calculations, resist that temptation. There are few people in the world who can write an essay and read it aloud simultaneously. But that's exactly what you end up doing when you try to answer the question immediately.

So instead, ask for a few minutes to gather your thoughts and then jot down a quick outline like this one:

Assumptions

• Only building windows
• Three main categories
• NYC: 10 million people
• Apartments: three windows/person

Categories

• Residential
• Retail
• Office

Calculations

• Residential: 10M x three windows/person
• Retail
• Office
• Total

That way, you get both the time to think analytically and the organization to communicate clearly. And no, interviewers aren't going to mark you down for taking a timeout. Because, again, they need someone who can do the job — and very few tech jobs involve answering brain teasers with answers, on a stage!

4. Give a roadmap

With your outline in-hand, it's time to give your interviewer a roadmap to your answer. That's because so many answers go off the rails when you think you're being clear but the interviewer is totally lost.

Say something like this:

"OK, so I'm going to solve this problem in three steps. First I'm going to name my assumptions. Next, I'm going to break the problem into relevant categories. And finally, I'm going to make calculations for each category."

Now, the interviewer can keep track of your progress at every step ("OK, she just laid out her assumptions. Check!"). And, as a bonus, you come across as way more organized and analytical.

5. State your assumptions

As I mentioned upfront, these questions rarely have one right answer. I mean, even the mayor of New York doesn't know exactly how many windows are in his city!

So instead of getting caught up in the search for an illusory truth, just make some logical assumptions. And then, most importantly, name and justify your assumptions.

For instance, you might say:

"When it comes to apartment windows, I'm going to assume that there are three windows per resident. That's because I've lived in a lot of two-person apartments that had six windows, on average. And so three per person feels about right."

While this might seem like relatively flimsy evidence, the critical word here is "because."Psychology research has shown that people are significantly more likely to accept something with a justification attached. And it makes you look more organized to boot!

6. Break the problem down

Now, these questions are often so massive that trying to solve them in one fell swoop can be downright ridiculous. So, instead, break them down into easy-to-digest parts.

In this case, you can offer an answer like this:

"OK, since buildings in New York are so different, I'm going to look at the three main categories of buildings separately: residential, retail, and office."

And now, the question that once looked freakishly scary has become quasi-reasonable—and you get to flex your analytical biceps!

7. Round your numbers

While knowing that there were 8.406 million people in New York in 2013 might help you win Trivia Night at the demographers' bar, trying to multiply 8.406 times anything is a recipe for disaster. So do yourself a big favor and round to the juiciest whole number you can think of:

"Alright, I'm going to say there are about 10 million people living in New York, give or take a million…"

Again, no one's testing your Rain Man skills. And this will pay off big time when you're ready to take the next step.

8. Calculate on paper

It might feel safer to do your calculations in your head so the interviewer can't see your crummy arithmetic skills. But that's just nuts—again, who can pull off 27 different mental calculations while simultaneously obeying the 95 rules of interview etiquette?

So skip the Math Olympiad stuff and show your work on paper or a whiteboard, step-by-step:

"OK, there are 10 million people in NYC. So I'm going to multiply that times three windows per person to get 30 million residential windows. Now let's move on to retail…"

Now, even if you do mess up, you have the visibility to stop yourself before your errors snowball into an avalanche.

9. Offer caveats

So you've finally reached an answer. However, you're actually not done yet.

Remember that these questions aren't about the answer: They're about the process. So before you drop the microphone, take one last chance to show off your full abilities by caveating your answer:

"So, that's my answer. But I'm not totally happy with it because I completely neglected development trends in the city. I basically assumed that every building was your typical old-school New York office or apartment, with relatively few windows. But all the new buildings are 100% glass, which suggests that this number is probably on the low side."

And now, at last, you're done. Which leaves you just enough time to figure out how much that school bus weighs after all.

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