Problem solver. Creative. Works well under pressure.

These are key personality traits employers will be seeking no matter what position they’re hiring for—and chances are, your resume probably already showcases them in some way. But these days, hiring managers from some firms aren’t content to take job seekers at their word—they want to see it to believe it.

And that’s why some companies have turned the interview process on its head. Instead of the traditional questions you might expect in an interview, they’re giving candidates problems to solve—problems which, at first glance, might seem totally random. Google, for example, has been known to ask, “How many people are using Facebook in San Francisco at 2:30 PM on a Friday?” Hewlett-Packard asks, “If Germans were the tallest people in the world, how would you prove it?”

What? Where do you even begin?

Here’s the secret (yes, there’s a secret): Your interviewer isn’t necessarily looking for a right answer. He wants to determine how quickly you can think on your feet, how you’ll approach a difficult situation, and, most importantly, whether you can remain positive and proactive and make progress in the face of a challenge.

So, if one of these “problem-solving” questions gets thrown your way—relax, be yourself, and tackle it calmly. Talk the interviewer through your internal thought process, so he can gain insight into the way you think and analyze information. Below are some of the toughest types of questions employers are known to ask—and your guide for how to ace them.

1. Design an evacuation plan for this office building.

(Inspired by Google)

As with any complex on-the-job challenge, the first step to answering a question like this is to clearly identify the problem. If designing an evacuation plan was really your task on the job, you definitely wouldn’t be able to solve it in an hour-long meeting—you’d need a lot more information. So, when an employer asks these types of questions, the idea is actually to see if you can pinpoint and explain the key challenges involved.

For example, in the question of an evacuation plan, you’ll have to know the nature of the disaster before you can answer it. A fire would have a different plan than a hurricane or earthquake, right? You’d also need to know how many staircases, elevators, and people are in the building.

When you’re presented with a complicated question like this, don’t be afraid to answer it with more questions. What the interviewer is really looking for is that you can think through the information you’ll need to reach a solution, and then ask for it—or explain how you’d seek it out—in a structured, logical way.

2. How many tennis balls can you fit into a limousine?

(Inspired by Monitor Group)

1,000? 10,000? 100,000? In these types of questions, the interviewer doesn’t necessarily want an exact number—he wants to make sure that you understand what’s being asked of you, and that you can set into motion a systematic and logical way to respond.

So, just take a deep breath, and start thinking through the math. (Yes, it’s OK to ask for a pen and paper!) For example, start by estimating the cubic inches of a limo and the volume of a tennis ball (also in cubic inches). Pretend the limo is a box to simplify things for yourself, and just make a note out loud that you’re approximating. Divide one into the other, make allowances for the seats in the limo, and move from there. Even if you don’t know the exact measurements, the real goal is to impress your potential employers with your ability to get to the heart of the problem quickly and with purpose.

3. How much should you charge to wash all the windows in Montana?

(Inspired by Google)

Remember that not all questions must have a complicated answer. As a matter of fact, with a question like this, most candidates don’t even provide a correct answer. Employers are simply asking the question because it is difficult to prepare for, and they want to see firsthand how quickly you can think on your feet.

Prepared responses may cut it for open-ended questions such as “Tell me about yourself,” or “What are your strengths and weaknesses?” But, employers want to see that you remain calm when you feel uncertain—and that you are able to think outside of the box if they take you “off-script.”

Yes, this question is especially broad—but you could get around that by naming what you consider to be a fair price per window rather trying to figure out the number of windows in the area. Talk it out. You both know that there’s not enough information to get a completely accurate answer, so relax and see where your mind goes.

4. Explain the Internet to an 8-year old in three sentences.

(Inspired by Microsoft)

The point of questions like this is to test your ability to communicate complex ideas in simple language.

Whether you describe the Internet as a “complex series of tubes” or as “the cloud,” the key here is to back up your explanation with easy-to-understand logic and facts. What you say doesn’t matter as much as how you can clarify and defend it by answering the most important questions that the employer is looking for: What? How? Why? For example, try this:

What? Use your first sentence to establish a basic premise: “The Internet is a series of tubes.”

How? Your second sentence can describe the first: “The tubes connect information that is stored on computers throughout the world.”

Why? Finally, close by summing up the purpose of the Internet: “It helps people to access global information quickly and easily.”

Yes, interview questions like these four can be more than a little intimidating. But, they can also give you a chance to show an employer who you are, how you think, and if your work style is a match for the position.