How To Ace The Brainteaser Part 3

REAL-WORLD REASONING PUZZLES

Sometimes the most common artifacts of our lives are the most puzzling. How well do candidates observe the world in which they live? How curious are they about the phenomena, both natural and artificial, that fill the corners of our daily lives? How easily can they manipulate the tools and concepts that allow people to display the kind of intelligence people still call “common sense”? These puzzles test all kinds of skills— curiosity, observation, pattern recognition, for example—useful in business. Interviewers believe that asking candidates puzzles like the ones in this chapter provide a glimpse into how candidates engage the world around them. And it’s a bonus that many of these problems are just plain fun.

1 MANHOLE COVERS

“Why are manhole covers round?” This is the mother of all job interview brainteasers. Actually, the puzzle should be more precisely phrased as “why are manhole covers circular?” This is the puzzle that may have started the recent trend of routinely using brainteasers in job interviews. One of the founding myths of Microsoft is that CEO Steve Ballmer was jog- ging with another Microsoft executive when he stepped on a manhole cover. It was round, and it occurred to him that every manhole cover he had ever seen had a similar shape. “Why are manhole covers round?” Ballmer asked himself. Within a few hundred yards, Ballmer had worked out three reasons. “Hmmm, that would be a good question to ask in interviews.”

Why are manhole covers circular?

For years in the early 1980s, job candidates coming for their job inter- views would yell upon arriving on the Microsoft campus, “Because they won’t fall into the hole!” And the puzzle still shows up because it’s a classic. Interviewers get good clues about the candidate even if he or she has studied the classic responses. Here are the classic responses, in order of their popularity:
1. Circularcoversaretheonlygeometricshapethatwon’tfallinto the manhole shaft they cover.
2. Circular manhole covers don’t need to be aligned or oriented with the manhole shaft.
3. Circularmanholecoversmakeiteasiertolift,carry,orevenroll the heavy items.
4. Themanufactureofcircularmanholecoversischeaperbecause it requires less metal than the manufacture of covers of any other shape.
5. Because manholes are circular!

The puzzle really extends beyond just picking an answer. A candi- date is expected to pick one or two responses and then defend them. A Microsoft recruiter found the following response perfectly reason- able for its grounding in moral values. It’s always good to remind the interviewer that these real-world problems are focused on preserving human safety:
A circular cover is the only geometric shape that won’t fall into the hole and possibly injure someone below or create a hazard for someone above. The slight lip on the manhole cover shaft prevents the cover from ever falling in, no matter how it’s held. A square manhole cover just wouldn’t work as well. That’s because the diag- onal of a square is the square root of 2 times its side. Should a square manhole cover be held near-vertically and turned just a little, it would fall easily into the shaft. The same is true with triangular shapes. Circular shapes alone, because a circle has the same diam- eter in all directions, have the property we are looking for.

If you want to go with another response, fine. All these responses can work, so pick one and be prepared for the objections and conversation. This puzzle is not about your engineering skills. It’s about evaluating your ability to make a decision, communicate your reasoning, and defend it.
Avoid the temptation to be a smart aleck. Yes, there are other shapes besides circular that satisfy the condition that the cover be unable to fall into the shaft. But bringing the class of shapes referred to as Reuleaux polygons into the conversation will not advance your chances unless you’re applying for a topology position.
Extra credit: The reality is that not all manhole covers are circular. Dan Heller is a photographer who maintains a Web page of dozens of photos of manhole covers (many with his shoes visible in the photo) that he takes on his assignments around the world (http://www.danheller.com/ manholes.html). While most of the manhole covers are indeed circular, clearly some municipalities prefer square and rectangular covers.

2 ELIMINATE A STATE

This is one of the most popular questions still asked at Microsoft. I’ve talked to dozens of people who have been asked this question. In each case the interviewer seems to have a different “correct” answer in mind.
If you had to eliminate one of the 50 U.S. states, which one would you select? Be prepared to give specific reasons why you chose the state you did.
Don’t get hung up looking for a “correct” answer.” There is no correct answer, unless you’re applying for a job with Microsoft, in which case Washington State is definitely a nonstarter. The best course is to reframe the question in some compelling way. Another idea: Don’t start with the name of a state, but build some suspense by walking the interviewer through your logic and seeing where you end up together. Humor always helps. There are dozens of creative answers. Here are three of them.
1. Well,Idon’twanttoberesponsibleforeliminatingactualpeople. So I’d eliminate the political entity of a state by ceding it to

Canada, perhaps a state that shares a border with Canada, such as North Dakota or Vermont. Would I still be able to visit?
2. Asimilarapproachcallsforeliminatingastatebyactuallycom- bining it with one of its neighbors. For example, Connecticut can annex Rhode Island. Or North and South Dakota can be combined to form the state of Dakota.
3. I’d eliminate Wyoming [you get points for knowing that Wyoming is the least populous state], but only if the people and natural attributes can be relocated to a theme park on the Las Vegas strip.
Candidates should be aware that some interviewers have an agenda when asking this question and want candidates to come to a certain con- clusion. One candidate reports that when he was asked this question, the interviewer indicated the “correct” answer was to divide a square state (like Colorado or Wyoming) into several parts (presumably rectangular) and merge them with the neighbor states. It turns out that the interviewer had Colorado in mind as the ideal response. Listen to how angry the candidate was:
I thought I had covered every realistic possibility, but it boiled down to the interviewer being totally arbitrary. At the end, it was more like “but what about splitting a state into multiple regions and combining with all the neighbors” and “Colorado is rectangular and easy to divide” and so forth. She had no comment either way about my other solutions and was totally stuck on dividing Colorado. I wasn’t sure if she wanted me to go into depth about satellite photography and how it isn’t that tough with modern technology to divide an irregularly shaped state into equal parts, or admit that dividing a state into multiple parts is a valid method that I skipped. She was very hung up on dividing equally area wise, as if population densities or other considerations didn’t matter. We talked for a long time, as a portion of the interview, about why I thought involving more states made it less likely for success, and she always seemed to ignore this reasoning and return to dividing Colorado equally. So maybe the interviewer had some grudge against the state of Colorado,

was fascinated with that state’s rectangular shape or fascinated with easy geometric constructions (divide a rectangle into equal areas). Or was just being difficult for the sake of being difficult.
Of course, the interviewer might have been testing how the candidate reacted if she pushed back on the candidate’s solution.

3 A QUESTION OF BALANCE

This may seem like a trivial question, but Ed Milano, vice president of marketing and program development at Design Continuum (www.dcontinuum.com), a product design consulting firm with offices in Boston, Milan, and Seoul, finds it can be revealing.
There are two people who want to balance on a seesaw. The first person weighs 125 pounds. The second person weighs 150 pounds. How do they have to arrange themselves so the seesaw is balanced horizontally? (See Figure 3.1.)
For Milano to make a job offer, he has to see how the candidate thinks under stressful conditions, the environment that often describes life at a consultancy that assists clients with make-or-break strategic design programs. “We never solve the same problem twice; every engagement is unique,” Milano says. “So we’re looking for people who think about new things in a new way, eager to move past established limits, and are confident enough to push their teammates over their respective boundaries.”

What kind of response is Milano looking for? “At a minimum, the candidate needs to communicate that the heavier person must sit closer to the pivot point than the lighter person. If the candidate gets up to draw the configuration on the whiteboard, I see evidence that the candidate conceptualizes in images,” he says. For a designer, that’s good.
For a more elaborate seesaw puzzle, see puzzle 93. Solution: The heavier person must sit closer to the fulcrum.

4 SALT AND PEPPER

This is a charming puzzle reminiscent of junior high school physics experiments. Some recruiters like to use it during lunch interviews.
Imagine that we sprinkle some salt on a piece of white paper. Then we sprinkle some pepper over the salt. Now, using only a plastic comb, how would you separate the salt from the pepper? Hint: The answer will shock you.
Pull the comb through your hair several times. This will create static electricity and attach a negative charge to the comb. Now wave the comb over the salt-pepper combination and the pepper, being much lighter, will attach itself to the comb. The salt crystals, being much heavier, will be left behind.

5 ROPE LADDER, RISING TIDE

This puzzle is almost too much of a trick question, but some interviewers find it a good way to start an interview. Here, the interviewer is looking for a candidate who can “picture” a problem and thereby find the solu- tion obvious.
A rope ladder hangs over the side of a ship. The rungs are 1 foot apart, and the ladder is 12 feet long. The tide is rising at 4 inches an hour. How long will it take before the first four rungs of the ladder are under water?

Candidates must be wary of problems that sound too easy. There’s always a trap. No interviewer would offer a problem that requires such trivial math, so the issue becomes a meta-problem: what’s the unstated puzzle? In this case, the real puzzle is to realize that the frame of reference is inclusive. The ship and the rope ladder act as a unit. The rope ladder, being attached to the ship, rises with the rising water, and if it is not submerged now, it will never be submerged no matter how high the water rises.
Solution: Forever. 

6 COCONUTS

This is also a trick question, but its solution calls for a mind that is flexi- ble in its scaling and unbound by a deep-seated assumption that trips up almost everyone confronting this puzzle. There’s a cute preferred an- swer, but the resulting conversation can go in any number of interest- ing places. That’s what a good puzzle is intended to do.
A businessman devises a business plan for buying and selling coconuts. He calculates that by buying coconuts for $5 a dozen and selling them for $3 a dozen, that in less than a year he will be a millionaire. His business plan and calculations are accurate. How is this possible?
Hint: Starting conditions.
When we hear puzzles like this, most of us start thinking in dot-com terms: elaborate rationalizations of why losing money is a sound business proposition. Some candidates respond by suggesting the businessman is building market share by giving away product at below cost. Or that his strategy is to drive his competitor out of business so that he can then control the coconut market. All well and good, but these responses always assume a starting condition that the businessman has more money at the end of the experiment than before. Perhaps the most elegant answer is to conclude that the guy is perpetually going to lose money with this scheme, so that if he ends up a millionaire, he had to have started out as a billionaire.
Solution: The businessman started out as a billionaire.

7 HOLE IN THE IRON WASHER

This is a good warm-up question for a job interview. Some candidates shoot themselves in the foot by making the question more complicated than it is. There’s something about the concept of holes that confuses people.
What happens to the hole in an iron washer when the washer is heated? Does the size of the hole decrease, increase, or stay the same?
Hint: What happens when metal is heated?
When a piece of metal is heated or cooled, it expands or contracts uniformly. The effect is just the same as if the whole thing were scaled up or scaled down. The iron washer would expand when heated, as would the hole in it.
Solution: The hole gets larger. 

8 SIX WATER GLASSES

Another puzzle for interviewers who like puzzles that involve manipu- latables. It can be presented using Figure 3.2 or using actual glasses of water or, as in this example, orange juice.
Here are six glasses. Three of these glasses contain orange juice (or water). Moving only one glass, can you arrange the glasses such that those containing the orange juice (or water) are next to each together, without any empty glasses in between?

Solution: Pick up glass 2 (from left to right) and empty its contents into the empty glass 5.

9 EAST COAST, WEST COAST

This puzzle has a satisfying solution, but should be restricted to candidates who are expected to be familiar with the geography of the United States and the fact that East Coast and West Coast states are separated by two time zones—Central and Mountain Time—and when it is noon in, say, New York, it is 9 a.m. in, say, California.
Two people are talking long distance on the phone; one is
physically in an East Coast state of the United States, the other
is in a West Coast state of the United States. That is, the East
Coast state borders the Atlantic Ocean; the West Coast state
borders the Pacific Ocean. The first person asks the other, “What
time is it?” When he hears the answer, he says, “That’s funny.
I’m only one hour earlier than you.” How is that possible?
Hint: East is East and West is West and never the twain shall meet. But they come closer than you think.
As far as I can tell, there’s only one reasonable solution to this puzzle. One of the people is in eastern Oregon (a West Coast state that borders the Pacific, yet whose eastern portion is in Mountain Time). The other per- son is in western Florida (an East Coast state that borders the Atlantic, yet whose western portion is in Central Time). The difference between Mountain and Central Time is one hour.
Solution: One person is in eastern Oregon; the other is in western Florida.
Extra credit: The puzzle can be made even more challenging by mak- ing the time for each person the same. This is possible if it happens to be at the exact moment when daylight savings changes at 2:00 a.m.

10 HEADS-UP COINS

To some people, this puzzle is trivial; to others, its solution is hard to fathom even after it is explained. Most interviewers prefer to present

this puzzle as an abstract word problem, but it can also be presented with coins or playing cards. The blindfolding is definitely not recom- mended.
You are blindfolded and are presented with a collection of coins on a table. You are told that exactly 26 coins show heads. How can you divide all the coins into two sets, with the same number of coins showing heads in each set? You cannot distinguish, by sight or by touch, which coins are showing heads or tails.
Hint: The two piles don’t have to have the same number of coins.
Solution: Select 26 coins at random to be one pile (or in general, se- lect a number equal to the number of coins specified showing heads), and simply turn the coins in that pile over. Call all remaining coins the second pile. The two piles now have the same number of coins show- ing heads. Many people doubt that the solution is this simple. One can- didate explained it this way:
Let’s assume there are 50 coins in total. We know only 26 coins of the 50 show heads. Now, the first pile will have 26 coins; the second pile will have 24 coins. Let’s assume that, by pure chance, the 26 coins I selected are all showing heads. When I reverse the pile, there will be zero coins showing heads in either pile. Take another case. Assume that the first pile includes 26 coins of which 10 coins show heads and 16 coins show tails. By reversing the first pile, I end up with 10 coins showing tails and 16 coins showing heads. In this case, the other pile of 24 coins has 16 coins show- ing heads plus 8 coins showing tails. Both piles have 16 coins showing heads.

11 HOTEL HOT WATER

Most businesspeople are well acquainted with hotels for which this question is true. One recruiter often uses this question this way: He starts by asking, “Is your hotel comfortable?” The candidate will gen- erally say yes, and then the interviewer says . . .

Why is it that, when you turn on the hot water in most hotels, you don’t have to wait for the water to warm up like you do at home? That is, why is the water that comes out of the faucet instantly hot?
Hint: Recirculate the question.

The interviewer really doesn’t care if you know the engineering that makes this little miracle possible. Rather, the interviewer is looking for you to make analogies, brainstorm, reach for metaphors, and articulate a reasonable conclusion. The answer doesn’t have to be technically cor- rect, just reasonable or reasonably creative. One candidate responded:

Let’s see. In my apartment building, I have to let the hot water run a few minutes before it gets warm. That’s because the water heater is a long way from the hot-water taps and the water in the pipes cools down when no water is flowing. Let me brainstorm a couple of reasons why hot-water faucets in hotels instantly dispense hot water. One is that the pipes are heated. Another is that each bath- room has an on-demand water heater.

By this point, most interviewers would be quite satisfied and ready to move on. These responses are totally acceptable even though they happen to be wrong. No matter. Unless you are applying for a job in hotel plant maintenance, the interviewer doesn’t care. The candidate has demonstrated a fluency of thinking, creative responses grounded in an understanding of elementary physics, and the capacity to analogize new solutions from familiar experiences. One word of caution: If you tell the interviewer that you are going to brainstorm, do so and avoid evaluating the suggestions.
If you knew or could reason out the correct answer, so much the better. Here’s the real reason: Hotels feature a hot-water recirculating system. This system consists of a pump attached to an extra water line that con- nects the farthest hot-water tap directly to the hot-water heater. The pump slowly circulates hot water through the hot-water lines so that there is never standing water that cools down. Thus when you turn on the hot water, the line water is already warmed up.
Solution: Hotels exploit a hot-water recirculating system.

12 CAR BALLOONS

Everyone can easily imagine this puzzle as a thought experiment. Yet almost everyone gets it wrong. The trick here is to realize that the behavior of gases is not always the same as the behavior of solids.
You are in a stopped car with a helium balloon floating in the passenger compartment. All the windows are closed. The car accelerates forward. With respect to the passenger compartment, does the balloon move forward, move backward, or stay stationary?

Hint: The air moves, too.

The obvious answer is that the balloon has a tendency to move backward in the passenger compartment, as do all the CDs on the dashboard. In fact, the balloon will move forward in the passenger compartment because inertia forces the air molecules back, creating low pressure up front into which the balloon moves. Try it.
Solution: The balloon will move forward. 

13 BEER ACROSS THE BORDER

This is almost a cross between a logic puzzle and a business case. It calls for an understanding of the value created by commercial transactions.
Consider a point in time when the Canadian and U.S. dollars are discounted by 10 cents on each side of the border (i.e., a Canadian dollar is worth 90 U.S. cents in the United States, and a U.S. dollar is worth 90 Canadian cents in Canada). A man walks into a bar on the U.S. side of the border, orders 10 U.S. cents’ worth of beer, pays with a U.S. dollar, and receives a Canadian dollar in change. He then walks across the border to Canada, orders 10 Canadian cents’ worth of beer, pays with a Canadian dollar, and receives a U.S. dollar in change. He continues going back and forth across the border buying beer

and at the end of the day ends up dead drunk with the original dollar in his pocket. The question is, 

Who pays for all the beer the man drinks?

Hint: What value or work does the man provide?

The first task is to decide if any economic work has been accomplished? In fact, there has. As he transported Canadian dollars into Canada and U.S. dollars into the United States, the man performed “economic work” by moving currency to a location where it was in greater demand (and thus valued higher). The earnings from this work were spent on the drinks.

Solution: The simplest answer is that the man pays for all the beer he consumes. So how does he end up with the same amount of money? Because he did economic work for which he received payment in the form of beer. A more economically technical answer is that the beer was paid for by whoever was holding the dollars when they were devalued from $1.00 to $.90. If the bills are devalued by crossing the border, then the above answer is certainly correct. But this second, more general for- mulation also covers the case where the dollars were simply devalued suddenly, creating a loss for each person holding the “wrong” country’s dollar. For example, a U.S. citizen with U.S. $1 in his pocket can buy 10 beers in the United States. If he crosses the border, where the money is discounted by 10 percent, he suddenly can buy only 9 beers. For each dollar he takes across the border, he loses a beer. When the man takes that dollar back to its country of origin, he is drinking the beer that citizen lost.

Extra credit: Note that the man can continue to do this “work” only until the Canadian bar runs out of U.S. dollars or the United States bar runs out of Canadian dollars. At that point, he runs out of “work” to do.

14 REVERSING MIRRORS

This is a puzzle favorite at Microsoft, and so it is included here, although I don’t recommend using it except in the most specific circumstances. It is infernally slippery to discuss, and some very specific language is required if there is to be a deep discussion of the physics involved. Few interviewers have the understanding or patience that this puzzle requires.

There are more direct puzzles that test the deep insights this puzzle is supposed to expose.

Why do mirrors reverse right and left but not up and down?

Hint: Challenge the assumption. Mirrors may not really reverse right and left after all.

This puzzle continues to totally flummox some very bright people, some of whom have actually studied the question. That’s because a mirror is an everyday object we think we understand. Actually, most of us don’t. Another problem is that this brainteaser is in a class by itself. You can’t solve it with ordinary math. Not even logic can dent it. A solution even evades common sense. It requires the candidate to let go of all assump- tions, and that’s what makes the puzzle so revealing. The interviewer wants to see how you react to a puzzle that really throws you.

There are some very ingenious wrong answers. Here is, perhaps, the most creative: “The mirror does reverse top to bottom, but our brains recognize that the shape should be right-side-up, and flips it for us.” Very smart, but why don’t our brains also “correct” left to right reversing?

The critical insight to solving the reflection problem is to realize that the statement of the problem leads to hopeless confusion. Some candidates never recover because they try to answer the question as stated. Besides, normal language doesn’t provide the tools to properly analyze this ques- tion. The best response may be to challenge the statement of the question: A mirror doesn’t necessarily reverse left and right or up and down. The puzzle really tests a willingness to reflect independent thinking, even to the point of challenging assumptions posed by the interviewer. One candidate responded to the mirror puzzle like this:

I don’t think the problem is stated quite right. Mirrors don’t reverse left and right; they reverse front and back. Stated another way, mirrors invert front to back, not left to right. An easy way to prove this is to stand facing north with a mirror in front of you. Wave your left (west) hand. The image in the mirror waves its west hand too, so there is no left-right reversal. The popular misconception of the inversion is caused by the fact that when person A looks at another person B,

person A expects person B to face him or her. But when person A faces himself (in the mirror), he sees an uninverted person A.

Books have been written about this subject. Resist the temptation to summarize their points.
Extra credit: But if you have to quote someone, quote from Martin Gardner, the patron saint of mathematical diversions. Here’s Gardner’s take on the mirror puzzle: “Human beings are superficially and grossly bilaterally symmetrical, but subjectively and behaviorally they are rela- tively asymmetrical. The very fact that we can distinguish our right from our left side implies an asymmetry of the perceiving system. We are thus, to a certain extent, an asymmetrical mind dwelling in a bilaterally symmetrical body, at least with respect to a casual visual inspection of our external form.” (From Hexaflexagons and Other Mathematical Diversions, University of Chicago Press, 1988, page 170.) On second thought, don’t.

15 SHOWER CURTAIN

Almost all people have experienced this experiment. How observant are they? And if they haven’t really paid attention, can they reason out the physics to find a solution?

When you turn on the water spray in a shower stall with a shower curtain, which way does the bottom of the shower curtain move? Does the bottom of the shower curtain get pushed out of the stall, remain stationary, or get pulled into the stall? Assume that the shower curtain is hanging without friction and that the water spray does not directly hit the curtain.

The obvious solution (wrong, naturally) is that the spray of the water pushes air out of the shower stall, forcing the shower curtain to be pushed out. If that happens, it’s because the pressure of the water is directly moving the curtain. When the water does not hit the shower curtain, air is pushed out of the shower stall, but the air escapes from the top of the enclosure (especially if it is a hot shower). The resulting low pressure

at the bottom of the shower stall forces air in, the movement of which flutters the shower curtain toward the enclosure. A candidate who was posed this question, and failed to answer it correctly—and wasn’t offered the job—says he will never take another shower without being reminded of this job interview.
Solution: The shower curtain is pulled into the shower stall. 

16 CAR KEY TURNING

This favorite puzzler at Microsoft is less about eliciting one answer or another, but rather about getting you to give a well-considered reason for your answer. Despite the wording of the problem, the number of possible reasons for which way to turn a car key is more than a binary solution. In fact, the domain of possible reasons is the real solution space for the puzzle. On the other hand, the increasing popularity of the remote locking system makes the puzzle much less immediate.
Which way should the key turn in a car door to unlock it? Clockwise or counterclockwise?
Hint: What’s the predominant handedness of people?

Reportedly, this vintage puzzle still pops up from time to time at Microsoft. That’s because it is so Zenlike. Right or left. Most inter- viewers say the answer really doesn’t matter as long as candidates defend their decision. What they are looking for are candidates who can make an essentially arbitrary decision and defend it without getting hung up about it. This puzzle actually tests a viable skill, since most of the busi- ness decisions we are called on to defend are equally arbitrary.

For some reason no one has been able to fathom, the question never asks in what direction the key should turn to lock the car. It’s always to unlock it. But there may be a clue in this (see extra credit).
If the distribution of right- and left-handed people in the world were equal, it probably really wouldn’t matter. But since most people are right-handed, a good case can be made for designing car locks to unlock by turning right. Here’s why, as explained and dramatized by a candi- date, now working at Microsoft, who fielded this puzzle in the early

1990s. The candidate actually stood up, pulled put his car key, and acted out the motions:

I assume that most automobile buyers, like most people in the world, are right-handed, so let’s design this car to meet the needs of the majority of consumers. I extend my right hand, holding a car key like this, with the key between my thumb and pointer finger. Now, I turn my hand clockwise as far as it can turn without dis- comfort. I can probably turn my wrist a full 180 degrees. Now let’s try the motion counterclockwise. There is much less range of motion, maybe less than 90 degrees. I also seem to have less strength near the limit of the turn. The design of the hand, wrist, and arm thus makes it easier for a right-handed person to turn a key clockwise (that is, to the right). This analysis suggests that because it’s easier for right-handed people to turn the key clock- wise, turning the key to the right is the preferred design.

If you think about it for a moment, there’s a Zen paradox here. Since the frequency of locking a car is the same as the frequency of unlocking a car, one of these motions is going to be “easy” and the other will be “awkward.” On what basis should we decide to make the act of unlock- ing the car the easy motion? Is it as arbitrary as it appears? Perhaps not.

Extra credit: It makes sense to assign the easy motion to unlocking or opening the car door. There are life-and-death situations that call for being given every advantage to unlock the car. A mugger might be stalking you in the parking lot. An extra second may be the difference between being victimized and escaping. People with arthritis need every advantage to open locks. Even people with full strength in their wrists sometimes have trouble unlocking car doors when they freeze. For all these reasons, giving the majority of consumers every advantage to unlock their auto- mobiles inclines designers to open car doors by turning to the right.

17 REFRIGERATOR IN A ROOM

A nice thought experiment that allows candidates to repurpose a com- mon consumer item.

You are locked into an empty room with only a working refrigerator plugged into a standard electric outlet. The room is uncomfortably warm, and your goal is to cool the room to the maximum extent possible. What can you do?

Most candidates immediately think about opening the refrigerator to cool the room down. You can admit to that thought, but be wary. First of all, first impressions are never correct. Second, think deeper. What does a re- frigerator really do? It’s really a heat pump. It takes heat away from the contents of the refrigerator and empties the heat into the room. Opening the door of an operating refrigerator would be the worst move. Here’s one candidate’s response:

Pull the plug on the refrigerator, and then open it. This will even out the lower temperature in the refrigerator with the higher tem- perature of the room, which will drop a little. The stupidest thing to do is to open the refrigerator without pulling its plug. It will then suck the heat of the room into its cooling compartment and get rid of it again through the cooling ribs on its backside, adding even more heat in the process. Being open, the cooling compartment will never be cold enough to trip the thermostat, and the fridge will be running constantly, in effect acting as an oven.

Solution: Unplug the refrigerator and open the door, allowing the cooler air in the refrigerator compartment to cool the room air a little bit. That’s the best you can do.

18 WEIGHT ON MOON AND EARTH

Why should such a simple question create such complexities? Experi- ence shows that if a candidate doesn’t immediately get the solution to this puzzle, it is very unlikey he or she will ever get it without a hint. The trap here is that the mind immediately goes to the main difference between the earth and the moon—the difference in gravitational pull— and then stops there.

What weighs more on the moon than on the earth?

Let’s consider two excellent responses, one literal, one figurative.

First the literal. It takes a special mentality to move from one critical dif- ference to consider what other differences may apply. In this case, the salient difference is that the moon has less gravity than the earth. True enough. But don’t stop there. What other differences exist? Earth has an atmosphere and the moon does not. And what is one property of an atmosphere? It provides buoyancy. Things with definite mass definitely float on the earth and therefore have no weight. So, on the moon, any balloon filled with a lighter-than-air gas, such as helium or hydrogen, would work for an answer.
Some people may object that the balloon would nevertheless weigh as much on the moon as on earth. Granted the mass of the balloon remains unchanged, but weight is something else. On earth, helium balloons don’t weigh anything because the atmosphere supports them. If you tried to put a helium-filled balloon on a scale, no weight would register because the buoyancy of the balloon is greater than the pull of gravity on the balloon. But on the moon, the moon’s gravity would definitely pull it against a scale. Therefore, on the moon the balloon will actually register some weight, even with the moon’s gravity one-sixth that of earth.

Extra credit: Note that it would be impossible to conduct this experi- ment. No inflatable balloon can exist on the moon or in a vacuum, as it will immediately explode.
Now a stunning metaphorical response voiced by my friend David Jones of Evanston, Illinois, proving that with the right attitude, every “technical” puzzle permits a satisfying nontechnical response:

What weighs more on the moon than on the earth? The conscience of an astronaut, if the astronaut left for the moon on the morning of his wife’s birthday and he forgot to acknowledge it.
Solution: Any lighter-than-air balloon or the conscience of an astro- naut.

19 THE CORK AND BOTTLE

Some interviewers actually have a coin, bottle, and cork available as props as they pose this puzzle. If so, they act out the terms of the puzzle as they state it. But I recommend that puzzles stay in the abstract realm.

I’m going to put this coin in this bottle and then stop the
opening of the bottle with this cork. Can you remove the coin
without taking out the cork or breaking the bottle?

Hint 1: Waiters at restaurants solve this puzzle every day.

Hint 2: Let’s say you’re opening a wine bottle, and in the process you break the cork.
The out-of-the-box insight interviewers look for here is that the cork may be pushed into the bottle. Candidates who understand this are pre- sumed to be able to address business problems in a jujitsu-like fashion, in which they use the strength of the problem against itself. Unfortu- nately, most candidates can’t get past the bottleneck assumption that the cork must be extracted from the bottle.
Solution: Push the cork into the bottle and extract the coin. 

20 GREAT PYRAMIDS OF EGYPT

This puzzle was used on the radio show Car Talk. On one level, it is a trick question. But on another, it gives candidates who are not locked into assumptions a chance to shine. The puzzle can be quite perplexing to candidates who are locked into a particular mind-set.
A young man took a trip to visit the Great Pyramids of Egypt in 1995. He was deeply moved by the trip and vowed that one day he would return with his children so that they could also see the wonders of the Great Pyramids. The man fulfilled his vow, and in 1969, he and his son visited the Great Pyramids. How is this possible?

Hint: How old are the Great Pyramids?

If you, as a candidate, find yourself speculating about time travel and being one’s own grandfather, I have one word of advice: don’t go there. These interview questions are never about fantasy. There is a solution here; you just have to get past the assumption, the mental blinders that are trapping you. The assumption is that the puzzle starts in AD 1995. Wrong. The puzzle actually is framed before the Common Era, when the pyramids would still have been considered ancient.

Solution: The young man first visited the Great Pyramids in 1995 BC. In 1969 BC, 26 years later, he fulfilled his vow to his son.

21 HOW COLD IS IT?

This deceptively simple problem is so confusing in its statement that many candidates freeze up as they consider it. Its solution requires a bit of mental recalibration, a skill that is of inestimable value in business, where scaling problems often pop up.

What is the temperature when it’s twice as cold as zero degrees?
Hint: Don’t be confused by the word zero; just reframe the puzzle by remembering that heat can be thought of as a liquid, that cold is a measure of the absence of heat, or that cold represents the slowing down of molecular motion.

In order for this puzzle to make sense, the candidate must recalibrate the question. It’s good to have some knowledge of the common temper- ature scales and how to convert among them. Often a conversation be- tween the candidate and the interviewer is required. One candidate offered this exchange:

CANDIDATE: Before I answer that question, I need to understand the scale. Zero degrees in what scale?

The interviewer may specify a scale or say, “We’re not sure.”

CANDIDATE: Since “cold” is really just absence of heat, let’s cal- culate how much heat we have to start with and then calculate half of that. We can calculate this problem in the familiar temper- ature scales of Fahrenheit and Celsius. The problem wouldn’t make sense in the Kelvin scale, where 0 degrees Kelvin is also known as absolute zero at which point all heat is gone. So I’m assuming we are talking about a starting temperature above absolute zero. Nevertheless, it’s convenient to work in the Kelvin scale. Absolute zero is about  273 degrees Celsius, or about  460 degrees Fahrenheit. So, starting in the Celsius scale, 0 degrees Celsius is 273 Kelvin. Half of that is 136.5 de- grees Kelvin, or  136.5 degrees Celsius. In Fahrenheit, 0 de- grees F is equivalent to 255.4 K. Twice as cold as 255.4 K is 127.7 K, or  230 degrees F.

Solution: 136.5 degrees K;  136.5 degrees C;  230 degrees F.

Extra credit: Mention that the absolute zero version of the Fahrenheit scale is the Rankine scale. Add 460 degrees to Fahrenheit temperatures to obtain the Rankine temperature. So 0 degrees Fahrenheit is 460 degrees Rankine, twice as cold of which becomes 230 degrees Rankine.

22 HOURGLASS WEIGHING

At first blush, this is reminiscent of the trick puzzle that goes, “What weighs more, a ton of bricks or a ton of feathers?” Of course, a ton is a ton. But is it? This pearl of a thought puzzle touches on some important elements of physics and logic.

An hourglass timer is being weighed on a sensitive scale, first when all the sand is in the lower chamber and then after the timer is turned over and the sand is falling. Will the scale show the same weight in both cases?

There are actually two plausible responses. One response is that falling grains are essentially weightless and exert no force on the scale as long as they are falling. Hence, the hourglass will weigh less after it is turned over. The other response is that from the instant that the first grain of falling sand strikes the bottom of the hourglass to the instant the last grain falls, the force resulting from the impact of the sand on the bottom of the glass remains constant and helps make the total weight equal to the weight of the hourglass before being inverted. When the stream begins to fall, the freely falling sand does not contribute to the weight, and so there is slightly less weight registered for the first few hundredths of a second. As the last grains of falling sand strike, there is a short time interval when the weight exceeds the initial weight. For each grain of sand now striking the bottom, no longer is there a grain of sand leaving the upper chamber, and so the hourglass weighs more.
Solution: In reality, the inverted hourglass weighs more.

23 TWO SURGICAL GLOVES, THREE PATIENTS

A perplexing problem framed in the antiseptic world of surgery. There is nothing theoretical about this solution. It can be implemented in the real world.

A one-armed surgeon needs to operate on three patients, one after another. But the surgeon has only two individual surgical gloves. How can the surgeon operate on the three patients in turn without risking infection for the patients or for himself? Hint: Gloves are reversible.

Safety in this case necessitates that every operation requires a surgical glove whose surface has not been contaminated. This is for the protection of the patients as well as the surgeon. The interviewer is looking for you to find the “aha!” factor that will allow an elegant solution to this puzzle. Please don’t even bother to think about creative ways to reuse surgical gloves.

To start, it’s always good for the candidate to repeat the puzzle:

Let me see if I have this. The situation is that the one-armed surgeon needs three clean gloves for three patients but has only two gloves. In other words, how can the surgeon operate safely with three patients using just two gloves? The gloves not only protect the patients from the surgeon, but ensure that no diseases are passed from one patient to the other.

I’m aware of only one satisfactory answer:

The solution starts with the surgeon putting on two gloves, one over the other. She then operates on patient number 1. Then the surgeon removes the outermost glove, leaving the other one on. She now operates on patient number 2. Finally the surgeon takes the glove discarded from the surgery with patient number 1, reverses it, and puts it on over the remaining glove. She can then operate on patient number 3.

The puzzle is actually more compelling in its original wording, involv- ing a man with two condoms and three partners. It has been reworded here to work, more or less, in the present context. Don’t even ask how a one-armed surgeon changes gloves.

Solution: Put on two gloves, one over the other, and then reverse the first glove.

24 THREE HIKERS

This is a puzzle that tests the use of resources. Most business problems involve similar estimations about priorities and resources.

Three friends are hiking to a remote destination in a wilderness area. The hike takes six days. Each person can carry only enough food and water for four days. Without sacrificing anyone or endangering anyone’s life, the goal is to get as many people as possible safely to the destination. How many people can safely get to their destination?

The “aha!” factor is to understand that two of the hikers basically serve as food bearers to extend the range of the third hiker.

Call the hikers Tom, Dick, and Harry. Each hiker starts out with a four-day supply of food and water. After the first day, Tom gives a one-day supply to both Dick and Harry. This leaves Tom with a one-day supply to return to the starting point. Now Dick and Harry each have a four-day supply again. After the second day, Dick gives Harry a one-day supply and keeps a two-day supply for himself so that he can get safely back to the starting point. This gives Harry a four-day supply of food and water, sufficient for the four days remaining on his journey.

Solution: One hiker can make it. 

25 GLASS HALF FULL

Ideally, the interviewer will use a water glass as a prop as this puzzle is presented. Sometimes a drawing of a water glass is offered.

Here’s a glass of water. The water is in a transparent glass that is a perfect right cylinder. It appears that the glass is half full, but how can you really be sure? How can you accurately determine whether the glass is half full, more than half full, or less than half full? You have no rulers, writing utensils, or other tools.

Hint: Use the geometry of the cup.

Let’s start off with a solution that most candidates think of first and examine why it’s not good enough. Holding the glass upright, the candidate uses the palm of her left hand to cover the glass. Now she makes a pinching gesture with the index finger and thumb of her right hand. She puts her thumb at the base of the glass and her index finger adjacent to the water level, thereby gauging the height of the water surface from the base of the glass. Now she freezes the distance between her two fingers. She then flips the glass upside down with her left hand; no water falls out since she’s sealed the opening with her left palm. Next she puts her frozen right hand, acting as a gauge, against the glass and checks to see if the inverted water level aligns with her index finger. If so, the glass is exactly half full. This may seem like a good solution, but it’s actually inaccurate, because the palm of the hand is not a per- fectly flat surface. Also, the technique will most likely lose some water in the inversion.

The most elegant solution requires the insight that the geometry of the glass offers an absolutely precise solution. The solution is eas- ier to demonstrate than to describe. Carefully tilt the glass toward you so that the water almost spills out, but doesn’t. The geometry of the glass (remember, it’s a perfect right cylinder) is such that if the glass is exactly half full, the water level in the inside of the glass will be touching the upper inside rim of the bottom. If any of the inside bot- tom surface of the glass is exposed, the glass is less than half full. If the level is above the inside bottom ring of the glass, it is more than half full.

Solution: Exploit the inherent geometry of the glass by noting that a perfect right cylinder is half full at the point when the liquid level simul- taneously touches the outside rim and inside rim of the glass.

26 HELP DESK! COW WON’T GIVE MILK

Koen van Tolhuyzen, a Web developer in Belgium, was confronted by this puzzle in a job interview in July 1999. “The interview started as a standard job interview,” van Tolhuyzen recalls. “I had to give a small description of myself, my goals, my expectations. Then the interviewer said the following: ‘I’m going to ask you a question that might sound very weird. I’ll give you a few moments to think about it.’At first it looked kind of stupid. But afterwards I found it a very good question. You don’t always have to ask technical questions to IT people to see if they are good candidates.”
You’re working in a help desk environment for farmers. At a certain moment, you get a phone call from a farmer who says, “My cow, who always stands in the middle of the grass, doesn’t give any milk anymore.” How will you try to detect and resolve the farmer’s problem?

The goal of this interview question is to see if the candidate’s problem- solving skills include the intuitive, creative, logical, analytical attributes that a good help desk technician requires. What happened is a role-playing scenario. The interviewer played the farmer, and the candidate got to ask questions. Van Tolhuyzen re-creates the exchange:

At first I started asking questions about the cow, its age, color, etc. The interviewer always answered with “Let’s say the cow is five years old, white, but that’s totally irrelevant.” Then I started asking questions about the current situation: “Have you had this problem before?” “Is the cow always in the middle of the grass?” “Where was she standing the last time when she did give milk?” When I estab- lished that the cow did give milk before, I looked for the changes in behavior or environment. That proved to be the key. The help desk is all about detecting changes in states.

In fact, there are no answers to this puzzle; there are only questions. But Leilani Allen of Mundelein, Illinois, a former chief information officer, rightly notes that the interviewer rigged the puzzle by declaring certain facts irrelevant. “Real help desk callers don’t do that,” she says. “The trick at help desks is to triage the questions to quickly identify what part of the system appears to be malfunctioning (e.g., hardware, software, user) and then ask the ‘what changed’ questions.”

27 WHAT’S THE TEMPERATURE OUTSIDE?

This is an example of a projective puzzle. The clues are so scant that candidates basically have a blank canvas from which to work.
You are stuck inside an office building, and you want to know what the temperature is outside. How do you find out?

Hint: How far out is outside?

The way this puzzle is stated, with no specified constraints, tells the candidate that the interviewer is looking for as many potential solutions as possible. While the constraints are unstated, most candidates under- stand that it’s not in their interests to have as their only response, “Break a window and put your hand (or a thermometer) outside,” or “Watch the weather report on TV.” In any case, the interviewer will shoot down the offered solutions. Nevertheless, start simple to test the unstated con- straints of the problem. Whatever the candidate says, he or she should be prepared for an objection. Here’s a typical scenario:

CANDIDATE: Well you could use X to find the temperature. INTERVIEWER: OK, let’s say there are no Xs lying around. CANDIDATE: OK, perhaps you could try Y.
INTERVIEWER: Y is broken. What else?

Eventually, the candidate has to consider what “outside” means in this puzzle.
CANDIDATE: I’m going to define “outside” as outside the atmos- phere of the earth, in deep space, where the temperature is absolute zero.

Let’s see the interviewer argue with that kind of vision! If the candidate is sufficiently outside the box, the solution becomes clear.

28 ROPE-CLIMBINGMONKEY

Sometimes the interviewer will have a simple diagram of this puzzle.
A rope passes through a pulley. On one end of the rope is an iron weight. At the other end of the rope hangs a monkey of equal weight. What happens if the monkey starts to climb up the rope? (See Figure 3.3.)

Hint: Assume that this is a perfect machine—the pulley is frictionless, and the mass of the rope and pulley is negligible.

Start by considering the initial equilibrium situation, before the monkey starts to try to climb. The monkey’s weight acts downward, pulling the rope with a force w, and the rope transfers this force directly to the weight on the other end of the rope, pulling the weight upward with a force w. However, the weight also pulls downward with an equal force w, which pulls the rope

with a force w, which acts on the monkey. Therefore both the weight and the monkey are pulled downward by their own weights and pulled upward by the rope with equal forces. This is why the situation is in equilibrium, and is why neither the monkey nor the weight move. Another way of saying all this is to say that the monkey balances the weight, so they don’t move. Let a candidate who paid attention in physics class explain the rest:

Now, what happens when the monkey tries to climb the rope? The monkey exerts an additional force on the rope, so it pulls the rope down with a force that is now greater than w. How is this possible? In exactly the same way as any person would climb any rope—when the person hangs from a rope, the rope is pulled by the person’s weight, but when the person climbs it, he or she pulls the rope with a larger force. Hopefully, whatever is supporting the rope is strong enough not to break under this extra force and the person can climb the rope. This exertion of a greater force than one’s weight happens every time someone does a chin-up, or in fact just stands up from the sofa.

The monkey pulls the rope. On the other end of the rope, the weight is now pulled upward not just by the monkey’s weight w, but by its climbing force too. It is only pulled downward by its own weight, w, though, so the net force is upward. Therefore the weight will accelerate upward.

Solution: The monkey is pulling down on the rope hard enough to pull itself up. This pulling action increases the effective weight of the monkey. The tension in the rope increases just enough to cause the weight to rise at the same rate as the monkey.

29 RECLAIMING ROPES

Sometimes the interviewer will have a simple diagram of this puzzle.

Two 50-foot ropes are suspended from a 40-foot ceiling, from hooks about 20 feet apart. If you are armed with only a knife, how much of the rope can you salvage?

Some candidates can solve this in their heads; others do well to draw it out first before answering. In fact, almost all the rope can be salvaged. Here’s one response:

The answer is almost all of it. Here’s how. Let’s tie the ropes together. Now I climb up one of the ropes. As close as possible to the ceiling, I tie a loop in the rope. Now I cut the rope just below the loop. Now I run the rope through the loop and tie both ends to my waist. I can now swing to the other rope and climb that one. I now pull the rope going through the loop tight and cut the other rope as close as possible to the ceiling. I can now swing down on the rope through the loop. I lower myself to the ground by letting out rope. I retrieve the rope by untying it at my waist and pulling the rope through the loop. I now have all the rope except for the piece required for the loop.
Solution: Almost all of it.

30 WHICH IS THE MAGNET?

This is a puzzle that requires some knowledge of physics and magnetism.

You have two cylindrical rods of iron, identical in size and shape. One is a permanent magnet. The other is just nonmagnetized iron—attractable by magnets, but not a permanent magnet itself. Without any instruments, how can you determine which is which?

Take the two bars, and put them together like a T, so that one bisects the other (see Figure 3.4). If they stick together, then bar B is the magnet.

If they don’t, bar A is the magnet. That’s because bar magnets display no magnetic force at their centers since the two poles cancel out. So if bar A is the magnet, then bar B wouldn’t be attracted to its center. How- ever, bar magnets are quite alive at their edges (i.e., the magnetic force is concentrated). So if bar B is the magnet, then it will attract the iron of bar A at any point.
Solution: Configure the two magnets like a T. 

31 CHAINWITH 21 LINKS

This is a classic puzzle that appears in many puzzle books. But even can- didates who’ve heard it before need to figure it out all over again each time they do it.
What is the least number of links you must cut in a chain of 21 links to be able to give someone all possible number of links up to 21?

Hint: Think factors.

Break down the problem, because the statement of the problem has two challenges: to calculate the least number of cuts and to calculate where those cuts are to be made. The key to the solution is to find the fewest numbers that can be combined to make 21. The answer is to cut links 4 and 10. What you end up with are three sections of 3, 5, and 11 links each, plus the 2 cut links that can serve as single-link units. To give all possible number of links up to 21:

1: 1
2: 1+1
3: 3
4: 3+1
5: 5 or 3+1+1 6: 5+1
7: 5+1+1
8: 5+3
9: 5+3+1
10: 5+3+1+1
11: 11
12: 11+1
13: 11+1+1
14: 11+3
15: 11+3+1
16: 11+5
17: 11+5+1
18: 11+5+1+1 19: 11+5+3
20: 11+5+3+1 21: 11+5+3+1+1

Solution: Two cuts at links 4 and 10. 

32 GOLD CHAIN

Here’s another chain puzzle requiring a slightly different mental leap.
You have a gold chain with seven links. You need to hire an assistant at a fee of one gold link per day for seven days. Each day, the assistant needs to be paid for his or her services without overpayment or underpayment. What is the fewest number of cuts to the chain to facilitate this arrangement?
Hint: Making change.

The major insight required for this puzzle is that the assistant is pre- pared to give change. It is not the case that you need to pay the assis- tant with one link at a time. The solution is to cut the third link. That cut will separate the chain to create three chains of four links, two links, plus the single cut link itself.

Day 1: Give the assistant the cut link.
Day 2: Take back the cut link; give the assistant the two-link chain.
Day 3: Give the assistant the cut link.
Day 4: Take back both the cut link and the two-link chain; give the assistant the four-link chain.
Day 5: Give the assistant the cut link.
Day 6: Take back the cut link, give the assistant the two-link chain. Day 7: Give the assistant the cut link.
Solution: One cut, at the third link.

33 FREEZING SEVEN ICE CUBE TRAYS

Given the prevalence of icemakers in modern freezers, this puzzle sounds positively old-fashioned. Many young candidates have never seen an ice cube tray. But familiar or not, the puzzle calls for the abil- ity to find an out-of-the-icebox solution.

You have an old-fashioned refrigerator with a small freezer compartment that could hold seven ice cube trays stacked vertically, but there are no shelves to separate the trays. You have an unlimited supply of trays, each of which can make a dozen cubes, but if you stand one tray on top of another before it’s frozen, it will nest part way into the one below and you won’t get full cubes from the bottom tray. Given these constraints, what is the fastest way to make ice cubes?
Hint: Building blocks.

Many situations require using the outcome of the process under consideration as a catalyst to solve the problem. The solution to this puzzle uses one of the outcomes. By using frozen cubes as spacers to hold the trays apart, you can make 84 cubes in the time it takes to freeze two trays. Here’s how: Fill one tray, freeze it, and remove the cubes. Place two cubes in the opposite corners of six trays, and fill the rest with water. Freeze all six, plus a seventh you put on top, at the same time.
Solution: Use 12 frozen ice cubes as spacers to hold the trays apart.

34 ICE AND WATER

One interviewer likes to ask this question when the candidate is served a glass of water with ice in it.
Consider a glass of water with an ice cube in it and with the water level at the very brim of the glass. What happens to the water level as the ice melts? Will the water level go up and overflow the glass, go down, or remain unchanged. Why? Ignore evaporation and the effects of surface tension.
Most of us have encountered this situation before. As ice melts in a full glass, do we find that we need a napkin to mop up the overflow? The answer is no. But the important part of this puzzle is not the answer, but the explanation of why. Here’s one candidate’s response:

Let me think out loud a minute. Ice is less dense than water. That’s why it floats. We also know that ice occupies more volume than water. We know this because a full bottle of water will shatter as it freezes and the ice expands. So the first thought is that the water level will drop. But I know from experience that a glass full of ice doesn’t overflow when the ice melts. Why is that? I think that’s because the ice is floating with a section of the ice sticking up above the water level. Thus, when the ice melts, it shrinks, but this is counterbalanced by the volume of ice that is sticking up out of the water. Thus, there will be no change in the level of the water from the melting ice.

Solution: The water level is unchanged.

Extra credit: Note that if the ice were completely submerged, the water
level would fall as the ice melted.

35 POLAR ICE CAPS MELTING

Here’s another version of the Ice and Water puzzle, although with a strangely opposite answer. Again, the explanation is of more interest than the answer itself.

What will happen to the level of the oceans if the polar ice caps
melt? Will the level of the oceans rise, fall, or remain the same?

The first thought is that if the polar ice caps melt, all the additional water will cause the oceans to rise. In this case, the first thought, so often a false start, is actually correct. If the world’s ice melted, the water would flow into the ocean and raise the level significantly. In New York City, this would mean that the Atlantic Ocean would rise to the level of the sixteenth story of the Empire State Building.
So what’s the difference between the polar ice caps melting and ice melting in a glass? In the latter case, the ice is floating. In the former, much of the polar ice caps, especially in Antarctica, is actually on land and thus not displacing ocean water.

Solution: The oceans would rise. SCENARIOS

These puzzlelike scenarios were developed by Peter Herzog, managing director of the Institute for Security and Open Methodologies, to screen and train applicants for positions in network security. People responsible for security need to be able to think outside the box because the threats they are hired to thwart always come from people who operate outside the box. These scenarios have proved very effective in identifying applicants who have the creativity, analytical expertise, and observation skills that make for excellent security administrators, according to Herzog. The four steps in each scenario are carefully constructed to force candidates to think creatively. These are Herzog’s general instructions:

In these scenarios, you are asked to assume different professions from electrician to postal worker to doctor and then answer the questions accordingly. Within each of these professions, I will ask you to describe methods for performing a task. Each scenario has four questions. Your answers should be brief and to the point.

After each set of answers, Herzog and the candidate talk about the answers. That’s the whole point: the conversation that these scenarios prompt. The scenarios emphasize speed. Herzog gives candidates about a minute for each step. Contact information for Herzog and the Institute for Security and Open Methodologies can be found in Appendix E, “Additional Sources and Links.”

36 SCENARIO 1 — ELECTRICIAN

You are an electrician. In front of you is a light hanging from the ceil- ing, and behind you is a light switch on the wall. The light is currently on.
1. List 10 ways to turn off the light.
2. List 10 components of a functioning light.
3. List 10 ways to tell if the light is off.
4. List10way stop revent someone from being abletoturn off the light.

Herzog looks for candidates who have the fluidity of mind and con- fidence under stress to quickly rattle off plausible answers. Answers are rarely right or wrong, although some answers are clearly better than others. Herzog expects obvious answers as well as more creative ones. What he looks for most is a display that the candidate has a deep understand- ing of the processes involved. “They need to show me that they know there’s a big picture behind a lightbulb,” he says. For example, here are the five most common responses to the first question (10 ways to turn off the light):

1. Turn switch off.
2. Break bulb.
3. Rip out wiring.
4. Overload electricity.
5. Cut electricity to room.

The opportunities for conversation are rich. Some candidates come up with answers that are profound. For example, here’s a response from a candidate with an understanding of social engineering:
Pay someone to turn off the light.
Is this candidate being cute or actually revealing an epistemological paradox about light:
Close your eyes.
Other responses reveal the special expertise of candidates. One with a background in quantum physics offered:
Devise an instrument to cancel the light by emitting light of the exact wavelength but opposite phase of the light from the lightbulb.

37 SCENARIO 2 — POSTALCARRIER

You are a postal carrier for an independent express postal service. You have a book-sized package to deliver.
1. List 10 ways to identify the receiver of the package.
2. List 10 things that would stop you from delivering the package. 3. List 10 reasons for delivering the package at all.
4. List 10 ways to identify the sender of the package.

38 SCENARIO 3 — RECORD STORE OWNER

You own an independent record store, which grew out of your intense fas- cination with music. The success of your store depends on your customers, who are also music enthusiasts.
1. List 10 ways to categorize the records in the store.
2. List 10 ways to identify the musical tastes of a customer.
3. List 10 ways to protect your inventory from theft.
4. List 10 things that would influence a customer not to buy from you.

39 SCENARIO 4 — SOLDIER

You are a solider in full field gear during wartime. You are stationed at the only bridge that crosses over a gorge.
1. List 10 ways to prepare for the coming enemy.
2. List 10 ways to prevent the enemy from crossing the bridge.
3. List 10 ways to discern friendly bridge users from the enemy.
4. List 10 problems the enemy could cause if they crossed the bridge.
Herzog recalls one pertinent response to question 1: Build a million bridges over the gorge and line all but one of the bridges with explosive mines. Only the allies know which bridge is safe to cross. This answer corresponds to an actual network security strategy for wireless net- works, which protects one true node by constructing millions of virtual nodes that lead to nothing.

40 SCENARIO 5 — SAFETY INSPECTOR

You are a licensed safety inspector for an independent occupational safety consortium. You have been brought to a large factory to review the safety of the machine tools due to a high number of accidents.
1. List 10 questions you would ask the foreman of this factory.
2. List10concernstheemployeesmayhavewiththecurrentriseinac- cidents.
3. List 10 changes that would make the factory a safer place to work.
4. List 10 concerns the employees may have with the implemented changes.

41 SCENARIO 6 — COMPUTER HELP DESK

SUPPORT PERSON

You work telephone help desk support for a large corporation dedicated to assisting its employees with support questions worldwide. You are the front line of defense, which means you receive all support matters.

1. List 10 questions you may ask to diagnose the problem.
2. List 10 resources you could use to solve the problem.
3. List 10 concerns the caller may have with following your advice. 4. List 10 ways you can assure 

better service.

42 TAPERED COKE CANS

This Microsoft favorite has shown up on countless job interviews and has become totally overused. Yet like bell bottoms from the 1960s, these puzzles once thought hopelessly out of fashion will make a comeback. Gerry Bollman, director of university recruiting, Booz-Allen & Hamilton, Cleveland, agrees that the Coke can question makes sense for a manu- facturing or operational process position. For technical positions, the puzzle is designed for the candidate to display some creativity and engi- neering savvy in a new knowledge domain. Even though I am not satisfied that this puzzle is useful for jobs other than perhaps beverage container manufacturing, it is included here because it was at one time so popular and can reappear.

Why are Coke and beer cans tapered at the top and bottom?

Hint: What issue are process-oriented operations most concerned with?

To this question, the inevitable responses of almost all candidates go to increasing the strength of cans, especially to resist internal pressure of the carbonated contents. This response is not inaccurate, but like all obvious answers, it is not the complete picture. The first generations of Coke and beer cans were not originally tapered; nor were the tapers added to make the cans stronger. The bottoms and tops of cans are now tapered less for engineering reasons than for business reasons. The tapers allow the cans to be made with just a little less material and so save costs. Across billions of cans, these micro savings add up to big bucks.

Now that the cans used the thinnest possible amount of aluminum, engineers had a problem with the top. Architecturally, the strongest part of the can needs to be the top to withstand the strong stresses of the con- sumer forcing open the flip top. For this reason, manufacturers found it necessary to minimize the top’s diameter. This step required adding a bevel to connect the top of the can to the slightly larger diameter of the can itself. This bevel represents the taper at the top. As for the bottom, cans need to be symmetrical so they can stack easily.

The Microsoft blogs are full of anecdotes about the Coke (sometimes Pepsi) can questions. First, the response of a software engineer who got the job:

I’m pretty sure the reason is strength. The difference between pop and vegetables (which are canned in straight-sided cans) is the pressure inside. Hopefully it won’t be too great at the moment you pop the top, but shake the cans up inside a hot semitrailer truck for a few hours and the pressure gets pretty high. That’s also why they have concave bottoms, and how it happens that you sometimes get a can with the bottom bulging out; think of the pressure it takes to do that.
Now here’s a college junior who applied for an internship at Microsoft. He didn’t get it. Can you guess why?

I assume sharp, square corners could not handle the pressure as well. The rounder a body, the better it withstands inside (or out- side) pressure. A sphere, however, isn’t practical. To stack the cans, and place them on a table without having them role off, they need to be relatively flat at top and bottom. So tapering the ends of the cylinderlike can gives the best overall result.