ôô

Find out how math can be your ticket to a career at one of the top web companies.

By
Jason Marshall, PhD,
May 24, 2014
Episode #078

Congratulations, new college graduate! What does finishing college really mean? Well, it can mean lots of things. But mostly it means that all of that hard work you’ve put in over the years to fill up your brain to its maximum capacity is about to finally pay off…assuming you can rock that interview and land your dream job. Surely you’re now free to forget all that math you learned and focus on preparing for “more important” types of interview skills, right? Well, not so fast!

SPONSOR: http://stitcher.com/math. Use the code MATH to be entered to win \$1000.

## The Modern Job Interview

Imagine yourself walking into an office at Google, Apple, or Facebook. You’re dressed well—better than usual, at least—because you want to impress. You sit down, the woman across the table introduces herself, and then says:

“How can you use an infinite supply of water, a 5 gallon bucket, and a 3 gallon bucket, to measure out exactly 4 gallons?”

Umm…feeling stumped? Unfortunately, your troubles aren’t over yet because after stumbling through a few thoughts leading pretty much nowhere, someone else at the table says:

“How many times a day do the minute and hour hands of a normal 12-hour clock overlap?”

Now you’re sweating profusely, and the answers just aren’t coming. Before you know it, another question comes at you:

“How many points are there on a sphere where after walking one mile south, then one mile east, and finally one mile north, you end up back at the place where you started?”

## What Math Means in the Real World

Does this all sound like a bad dream? Well, maybe it does—but these are all real interview questions that job candidates at Google and Microsoft have been asked. Were the interviewers just being mean? Or were they insane? Well, no. In fact, they were asking questions that do a fantastic job at testing whether or not a person can think on their feet…which is something a college transcript doesn’t tell you. The ability to think critically and reason out problems—especially those you haven’t seen before—is one of the most valuable skills you can develop and one of the most desirable things you can offer a company.

And, as you’ll notice, all of these problems use math. Why? Because math provides a great way to test this sort of thing—they’re all questions about logic, and math is very logical. The good news is that the math isn’t usually complicated, you just have to get used to the idea of thinking through and solving this type of problem. To get you started, here’s how to work out the first two questions:

## Brain Teaser Interview Question #1

The first question in your imaginary interview was: “How can you use an infinite supply of water, a 5 gallon bucket, and a 3 gallon bucket, to measure out exactly 4 gallons?” Before I give the answer, I encourage you to stop for a minute and think about how to solve this puzzle. Once you’re ready, here’s how I’d do it:

First, fill the large 5 gallon bucket. Then fill the small 3 gallon bucket with water from the large bucket, leaving you with 2 gallons in the large bucket. Now dump out the water in the small bucket and pour the 2 gallons of water from the large bucket into the small bucket. We now have an empty 5 gallon bucket and a 3 gallon bucket with 2 gallons of water in it. Next, completely fill the empty 5 gallon bucket. Now, finish filling the 3 gallon bucket using water from the 5 gallon bucket. Remember, the 3 gallon bucket already contained 2 gallons of water, which means that we’ll end up with a total of 5 – 1 = 4 gallons of water in the large bucket—exactly what we need!

## Brain Teaser Interview Question #2

The second question in your imaginary interview was: “How many times a day do the minute and hour hands of a normal 12-hour clock overlap?”

Again, go ahead and think about it and try to reason out the answer. Remember that if this was an actual interview, the final answer you give is actually not as important as the process you work through to reach it. Your interviewers want to know that you can think on your feet about new problems, not necessarily that you can instantaneously answer every problem they ever throw at you.

So, did you come up with the answer that the hands of a clock overlap 24 times per day? Let’s see if that’s right: If we start at midnight, the hour and minute hand are both pointed straight up (so that’s once). A little over an hour later—sometime between 1 AM and 2 AM—the hands must cross again (so that’s twice), and the same thing happens each subsequent hour. Sometime between 10 AM and 11 AM the hands cross again (which is the eleventh time), and then between 11 AM and noon…actually, the two hands don’t cross between those two hours—they don’t end up crossing again until noon itself! Which means that the two hands actually line up a total of 11 times every 12 hours, or 22 times every day.

## Brain Teaser Interview Question #3

Of course, there’s no absolutely right or wrong way to work out any of these questions. As long as your line of reasoning and logic are sound, you’re sure to impress your interviewers.

And as for that last brain teaser question—the one asking: “How many points are there on a sphere where after walking one mile south, then one mile east, and finally one mile north, you end up back at the place where you started?”—I’m going to let you try to reason out the answer to that. If you want to check your logic, you can find my answer next week on The Quick and Dirty blog.

## Number of the Week

Before we finish up, it’s time for this week’s featured number from my post on QDT’s blog, The Quick and Dirty. The number is 1.6. Why? Well, if you ever need to convert from miles to kilometers or vice versa, the number 1.6 is the key. To convert a distance from miles to kilometers (or a speed from miles per hour to kilometers per hour), just multiply the number of miles by 1.6. And to convert a distance from kilometers to miles (or a speed from kilometers per hour to miles per hour), just divide the number of kilometers by 1.6. That’s all you need to remember!

## Wrap Up

And that’s all the math we have time for today. Remember to become a fan of the Math Dude on Facebook where you’ll find a new number of the day and math puzzle posted each and every weekday. And if you’re on Twitter, please follow me there too. Finally, if you have math questions, feel free to send them my way via Facebook, Twitter, or by email at mathdude@quickanddirtytips.com.

Also, are you ready to break free of bad habits and enjoy your road to success? Check out Get-It-Done Guy’s new e-book 3 Bad Habits Successful People Break.

Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!

Clock image from Shutterstock

• Audio
• Audio
• Audio
• Audio