In an interview setting, even the most basic questions can feel nerve-racking. If you’ve ever drawn a blank when asked to talk about your hobbies, just imagine having to calculate the number of piano tuners in all of Chicago under that same kind of pressure.
Some competitive tech companies are notorious for asking hard-to-answer questions like this one. The interviewers who use them aren’t always looking for concrete figures, but rather they’re trying to gauge the candidates’ creativity and problem-solving skills. And while you may not know the exact number of piano tuners in Chicago off the top of your head, there is a “correct” line of thinking you can follow to find out.
These baffling brainteasers are becoming less common in the interview process (Google, one of the worst offenders, banned them a few years ago), but if you ever find yourself faced with one, here’s how to answer like you know what you’re talking about.
1. HOW MANY GOLF BALLS CAN FIT INSIDE A SCHOOL BUS?
Here’s an example of a question where the interviewer isn’t expecting you to blurt out a specific figure with no context. There are lots of variables at play here, and the more questions you ask the better picture you’ll paint of your problem-solving process. “Is this a standard school bus?” “How large are the golf balls?” “Is this accounting for the seats inside?”
Once you figure out the dimensions of the school bus, you can calculate its volume into cubic inches then divide that number by the volume of a golf ball (2.5 cubic inches). The result would be the number of golf balls you could fit into the space when it’s completely empty (ignoring any gaps between the golf balls). To account for seats and other equipment, you have to estimate what percentage of the space is actually empty and multiply that by your original golf ball figure.
If a standard school bus is 8 feet wide, 6 feet high, and 20 feet long, and 75 percent of the interior is unoccupied, then it could theoretically fit 495,000 golf balls (though if you're taking into account the gaps between the golf balls, it would be closer to 350,000). If you care more about being right than actually getting the job, feel free to shout out this number with no explanation.
2. WHY ARE MANHOLE COVERS ROUND?
This may seem like an open-ended question designed to evaluate the answerer’s personality, but the reasoning behind the manhole cover’s design is surprisingly straightforward. As we’ve explained here before, round covers are incapable of falling through manholes no matter how you position them. The ‘lip’ lining the rim of the opening ensures that the cover is always wider than the hole. Covers that are square, rectangular or oval in shape risk falling through if they’re inserted diagonally. Answering the question with these facts to back you up shows that you’re a logical thinker—or that you’ve spent too much time pondering your city's infrastructure.
3. HOW MUCH SHOULD YOU CHARGE TO WASH ALL THE WINDOWS IN SEATTLE?
Like the golf ball question, this problem can only be solved by making an educated guess at several variables. If Seattle consists of 10,000 city blocks with 600 windows per block, and the window washer spends five minutes per window while being paid a rate of $20 per hour, the answer would be approximately $10 million. On the other hand, the ability to keep things simple can sometimes be just as valuable as on-the-fly math skills. In that case, an answer like "$10 per window" (and you’d get paid 6 times as much!) would also suffice.
4. HOW MANY PIANO TUNERS ARE THERE IN THE CITY OF CHICAGO?
If you were asked this question in a job interview, your natural response may be to laugh, cry, or perhaps flee the building as fast as possible. But with the help of some neat math tricks, you can actually come up with a pretty close approximation of the number using what little data’s available.
This type of question is known as a Fermi Problem, and it can be solved by slightly overestimating and underestimating the figures using powers of ten with the assumption that they'll balance each other out in the end. To start you need to figure out the number of people living in Chicago. Instead of coming up with an exact number you can use 10 to the sixth, which equates to 1 million, to represent the population (the actual population of Chicago is just under 3 million, but we’re estimating!). Next, you need to estimate what portion of the population owns a piano. If it’s one out of every 100 people, that’s represented by 10 to the power of negative two, which when multiplied by ten to the sixth equals ten to the fourth (this may be starting to look complicated, but using the power of ten is actually how mathematicians are able to keep big numbers manageable).
Ten to the fourth is the same as saying 10,000 pianos. To figure out the number of piano tuners based on that figure, you can assume that piano tuners are able to tune ten squared pianos each year. By dividing the number of pianos by the numbers of pianos tuned each year, you come up with the answer that there are ten squared, or 100 piano tuners in Chicago.
Thanks to all the overestimations and underestimations cancelling each other out, you can count on ending up with a number that falls within one order of magnitude of the correct answer. Of course if you already have a Chicago phone book on hand, you could just count the number of piano tuners manually and find that there are actually around 81—but then you’d be missing out on all that fun math.
See Also: 8 Illegal Interview Questions
5. HOW MANY TIMES DO A CLOCK’S HANDS OVERLAP IN A DAY?
Without giving the question much thought, you might automatically assume the answer to be 24, one overlap for each hour of the day. But, this being a list of tricky job interview questions, you can probably guess that this answer is wrong.
The only time the minute and the hour hand come together perfectly on the hour is at 12 o’ clock. After that the overlap occurs slightly after 1:05, then slightly after 2:10, etc. By the time the minute hand catches up to the hour hand the eleventh time, the hour hand has had enough of a head start that they don’t cross paths until 12 o’ clock, thus beginning the second twelve-hour cycle of the day. This means that there are only 11 times the two hands overlap every 12 hours, so they come together a total of 22 times during one day.
Now try explaining all that coherently to a prospective employer while maintaining eye contact and an upbeat attitude.
6. AN APPLE COSTS 40 CENTS, AN ORANGE COSTS 60 CENTS AND A GRAPEFRUIT COSTS 80 CENTS. HOW MUCH IS A PEAR?
There are several ways to tackle this question. One way is to look at the letters in the words themselves. If each vowel is worth 20 cents, then you can conclude that a pear would cost 40. If you were being read this question out loud as opposed to reading it, you might choose to interpret “pear” as “pair.” In that case a clever answer would be 80 cents for two apples, $1.20 for two oranges and $1.60 for two grapefruits.
7. HOW MANY TRAFFIC LIGHTS ARE IN MANHATTAN?
Initially this question sounds similar to the piano tuner problem in that it can only be solved using the power of ten. While that’s probably the type of thinking interviewers are looking for, you could always take the easy route and pull up New York City’s Department of Transportation webpage (as of June 30, 2011, there were 2820 traffic signals in Manhattan).
8. HOW MANY BASKETBALLS CAN FIT IN THIS ROOM?
This is similar to the golf balls in a school bus problem, but this time the interviewee has the added advantage of being able to visually estimate the dimensions of the space that's being filled. You can go about solving it using the same straightforward math equations, or you can show off your creative thinking skills by asking some out-of-the-box questions first. A question like "Are the balls inflated or can I deflate them first?” demonstrates that you approach problems in a thoughtful way and are able to come up with smart solutions to achieve the best results.
9. WHAT DO WOOD AND ALCOHOL HAVE IN COMMON?
The way you answer this question shows potential employers how you’d go about finding common ground between two seemingly unrelated concepts. For this particular example, acceptable answers could include that both materials are flammable, or that methanol, a type of alcohol, is traditionally made from wood.
10. HOW DO YOU MEASURE THE WEIGHT OF A BABY ELEPHANT WITHOUT A SCALE?
Being stuck with a baby elephant and no scale to weigh it with is quite a predicament, but the problem can be solved using a resourceful trick you may have learned about in high school. You can fill a large cylindrical glass vat with water not quite to the top, place a boat in the water and mark the water level. Then you put the elephant in the boat (which is probably harder than just buying a scale) and mark the new water level. Measure the difference between the two marks and with a little math you can easily calculate the weight of the elephant. Let’s hope that literally having to do this isn't part of the job description.