"Intellectuals solve problems, geniuses prevent them." ------ Albert Einstein

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How would you design Bill Gates's bathroom? ( taken from the book How Would You Move Mount Fuji? by William Poundstone. This article has been contributed by ReadnSurf Editorial Team. ) In August 1957, William Shockley was recruiting staff for his Palo Alto, California, start-up, Shockley Semiconductor Laboratory. He felt like he was on the cusp of history, in the right place at the right time. All that he needed was the right people. Shockley was leaving nothing to chance. Today's interview was Jim Gibbons. He was a young guy, early twenties. He already had a Stanford Ph.D. He had studied at Cambridge too — on a Fulbright scholarship he'd won. Gibbons was sitting in front of him right now, in Shockley's Quonset hut office. Shockley picked up his ....continued below.....

There's a tennis tournament with one hundred twenty-seven players, Shockley began, in measured tones. You've got one hundred twenty-six people paired off in sixty-three matches, plus one unpaired player as a bye. In the next round, there are sixty-four players and thirty-two matches. How many matches, total, does it take to determine a winner?

Shockley started the stopwatch. The hand had not gone far when Gibbons replied; One hundred twenty-six. How did you do that? Shockley wanted to know. Have you heard this before?

Gibbons explained simply that it takes one match to eliminate one player. One hundred twenty-six players have to be eliminated to leave one winner. Therefore, there have to be 126 matches.

Logic puzzles, riddles, hypothetical questions, and trick questions have a long tradition in computer-industry interviews. This is an expression of the start-up mentality in which every employee is expected to be a highly logical and motivated innovator, working seventy-hour weeks if need be to ship a product. It reflects the belief that the high-technology industries are different from the old economy: less stable, less certain, faster changing. The high-technology employee must be able to question assumptions and see things from novel perspectives. Puzzles and riddles (so the argument goes) test that ability.

Like it or not, puzzles and riddles are a hot new trend in hiring. Fast-forward to the present — anywhere, almost any line of business. It's your next job interview. Be prepared to answer questions like these:

How many piano tuners are there in the world? If you could remove any of the fifty U.S. states, which would it be? How long would it take to move Mount Fuji?

In the human resources trade, some of these riddles are privately known as impossible questions. Interviewers ask these questions in the earnest belief that they help gauge the intelligence, resourcefulness, or "outside-the-box thinking" needed to survive in today's hypercompetitive business world. The strangest thing about these impossible questions would probably be this: No one knows the answer. I have spoken with interviewers who use these questions, and they have enthusiastically assured me not only that they don't know the "correct answer" but that it makes no difference that they don't know the answer.

The popularity of today's stress- and puzzle-intensive interviews is generally attributed to one of America's most successful and ambivalently regarded corporations, Microsoft. The software giant receives about twelve thousand resumes each month. That is amazing when you consider that the company has about fifty thousand employees, and Microsoft's turnover rate has been pegged at about a third of the industry average. Microsoft has more cause to be selective than most companies. This is reflected in its interview procedure. Microsoft's hiring focuses on the future tense. More than most big companies, Microsoft accepts rather than resists the "job candidate as blank slate." Its stated goal is to hire for what people can do rather than what they've done.

Below are several of the most difficult interview puzzles. It is easy enough to verify the right answer to a logic or math puzzle. It is trickier to divine the intended or optimal responses to questions that have "no right answer." For these I have made use of reports from both interviewers and interviewees.

"Let's play a game of Russian roulette," begins one interview stunt that is going the rounds at Wall Street investment banks. "You are tied to your chair and can't get up. Here's a gun. Here's the barrel of the gun, six chambers, all empty. Now watch me as I put two bullets in the gun. See how I put them in two adjacent chambers? I close the barrel and spin it. I put the gun to your head and pull the trigger. Click. You're still alive. Lucky you! Now, before we discuss your resume", I'm going to pull the trigger one more time. Which would you prefer, that I spin the barrel first, or that I just pull the trigger?"

The spin-the-barrel option is the simpler of the two to analyze. There are two bullets in six chambers, or, to put it more optimistically, four empty chambers out of six. Spin the barrel, and you've got a four-in-six, or two-in-three, chance of survival.

For the other option, look at it this way. The four empty chambers are all contiguous. One of them just spared your life. For three of these four empty chambers, the "next" chamber in succession will also be empty. The remaining empty chamber is right before one of the two bullets. That means you have a three-in-four chance of survival when you don't spin.
Three-fourths is better than two-thirds, so you definitely don't want the barrel spun again.

Why are manhole covers round rather than square?

The answer interviewers consider the best is that a square cover could fall into its hole, injuring someone or getting lost underwater. This is because the diagonal of a square is √2 (1.414 . ..) times its side. Should you hold a square manhole cover near-vertically and turn it a little, it falls easily into its hole. In contrast, a circle has the same diameter in all directions. The slight recess in the lower part of the cover prevents it from ever falling in, no matter how it's held.

A more flippant answer (not that this question merits any other kind) is "because the holes are round." Maybe that's not so flippant: Holes are round, you might claim, because it's easier to dig a round hole than a square one.

Another answer is that a person can roll a circular cover when it needs to be transported a short distance. A square cover would require a dolly or two persons. Perhaps a lesser reason is that a round cover need not be rotated to fit the hole.

How many points are there on the globe where, by walking one mile south, one mile east, and one mile north, you reach the place where you started?

Microsoft's grading system for each answer is roughly as follows:
0 points: No hire, 1 point: No hire, ° + 1 points: Fair, ° * ° + 1 points: The "right" answer.

Start by drawing a mental map: One mile south, one mile east, and one mile north covers three sides of a square. You ought to end up a mile east of where you started. The situation seems impossible, and you might think the answer is zero points.

Try again. The only way to make sense of the situation is to remember that the compass directions are relative ones applied to the surface of a sphere. At the North Pole, every horizontal direction is south. As long as you start precisely at the North Pole, you can walk a mile in any direction and that will count as walking south. Not only that, but a subsequent one-mile-east leg will curve in a circle centered on the North Pole. At any rate, it will if you interpret the puzzle to mean that you not only point yourself due east but constantly adjust your direction so that your bearing remains due east throughout the second mile. That then allows a final, straight, one-mile-north leg returning to the pole. The journey looks like a wedge of pie rather than an open square.

So the North Pole is one point where this could happen. Notice that it couldn't happen at the South Pole. At the South Pole, every direction is north. You can't go a mile south from the South Pole.

You might therefore think the answer is one point, and again you're wrong. You're wrong because you can manage such a journey near the South Pole. Imagine starting out from a point a little more than a mile from the South Pole. You travel a mile due south, make a 90-degree turn east, and execute a complete circle about the South Pole of one mile circumference — at every point traveling due east, of course — and then backtrack north a mile to the starting point.

There is not just one point from which you can do this but an infinity of them. You can start from any point that is the correct distance from the South Pole. There is a complete circle, centered on the South Pole, of possible starting points.

What is the "correct distance"? The one-mile circumference circle must have a radius of l/2π miles. The starting point of the journey must be a mile farther from the pole than that, or 1+ l/2π miles, which comes to about 1.159 miles.

We're still not done. Suppose you started a little closer to the pole. You go a mile south, then travel continuously due east in a smaller circle, centered on the pole, of 1/2 mile circumference. You will go full circle twice. Then backtrack a mile north. This scheme nets another infinity of possible starting points, each 1 + 1/4 π miles from the pole.

You can also manage a route in which you circle the pole three times, four times, or any whole number n of times. Each yields a new circle of starting points 1 + 1/2nπ miles from the pole. There is an infinite ensemble of ever-closer circles, each with an infinity of starting points.

How many times a day do a clock's hands overlap?

Most people quickly realize that the answer has to be twenty-four, give or take. The issue is nailing down that "give or take" part.

Recognize, first of all, that there is nothing capricious about the overlaps. Both hands move at fixed speeds. Therefore, the time interval between overlaps is a constant. This constant interval is a little more than an hour. At midnight, the hour and minute hands are exactly superimposed. It takes an hour for the minute hand to make a complete circuit. In that same time, the hour hand has moved 1/12 of a circuit to the numeral 1. It then takes another five minutes for the minute hand to catch up to where the hour hand was, in which time the hour hand has crept a bit farther....

Before getting sucked into a Zeno's Paradox, let's settle for the moment by saying that the interval is a little more than sixty-five minutes. We also know that the exact interval has to divide evenly into twenty-four hours, since the day ends as it started, with both hands up and overlapping. In fact, it has to divide evenly into twelve hours. The way the hands move in the P.M. is an exact replay of the way they move in the A.M.

Focus on the twelve-hour period from midnight to noon. The hands cannot overlap twelve times in that period, for if they did, it would mean that the interval between overlaps was 12/12, or exactly one hour — and we know it's a bit more than sixty-five minutes. No, there must be eleven overlaps in a twelve-hour period. That means the interval between overlaps is 12/11 hour, which comes to 65.45 minutes. This must be the precise interval that we balked at calculating a moment ago.

Doubling eleven gives twenty-two overlaps in a twenty-four-hour period. Twenty-two is the answer—unless you want to split hairs. Should you count the overlap at the midnight that begins the day, and also at the midnight that ends the day, the answer is twenty-three.

How would you design Bill Gates's bathroom?

There are two key points in answering this question. One is that Bill Gates gets what Bill Gates wants. The other is that you're supposed to come up with at least some ideas that Gates wants but wouldn't have thought of on his own (otherwise, what's the point of hiring you to design his bathroom?).

You're supposed to start off saying that you'd sit down with Gates and listen to what he wants his bathroom to be like. You'd get the budget and deadlines up front. You'd suggest a lot of ideas and see which ones he likes. Then you'd make a plan and show it to Gates for feedback. The plan would go through many cycles of revision. Meanwhile, you'd make sure the project came in on time and within budget. This much applies to any design question.

As to the ideas you come up with, be warned that it's tough to top the reality. Gates's bathtub has a feature that lets him fill it to desired temperature from his car. For real.

Putting computer technology throughout the home, bathroom included, is something that Microsoft people take seriously. Microsoft's research divisions are pursuing things such as "smart" medicine cabinets and cupboards that tell you when your prescription needs refilling or you're out of toilet paper. So if you want to impress Microsoft's interviewers, you're not going to get much mileage out of talk of electrically warmed toilets. Here are a few ideas of the slant they're looking for ("futuristic" but possible for today's money's-no-object consumer):

1. A feature that automatically locks medicine cabinets or cupboards containing household chemicals when an unaccompanied child enters the bathroom. Gates's house already has rudimentary ways of "knowing" when someone is in a room, and who that someone is.

2. A hands-free notepad. Everyone gets great ideas in the bathroom. You don't want to use a PDA when your hands are wet, and if there's one room in the house that isn't going to have a PC in it, it's the bathroom. All you need is a voice-recognition device that can record a spoken message after you say a code phrase such as "Memo for Bill." The device automatically e-mails the message to your mailbox so it's ready for you at work.

3. A mirror that doesn’t reverse left and right. It's a video screen with a hidden camera, showing your own image the way other people see you. It makes it much easier to use scissors to trim a stray hair.

In front of you are two doors. One leads to your interview, the other to an exit. Next to the door is a consultant. He may be from our firm or from a rival. The consultants from our company always tell the truth. The consultants from the other company always lie. You are allowed to ask the consultant one question to find out which is the door to your interview. What would you ask?

Since you have no way of knowing whether the consultant will tell you the truth, it is pointless to ask something such as "Is this the right door?" or "Do you work here?" You will get an answer that may or may not be correct. Having used up your one and only question, you cannot determine which. Instead, you have to invent a question where it doesn't matter whether the person tells the truth or lies.

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