How To Ace The Brainteaser Part 2
STRATEGIES FOR SOLUTIONS
Employers who ask puzzles in interviews are often looking for people who are good at divergent reasoning. Divergent reasoning, as opposed to convergent reasoning, is the process of finding previously undiscovered solutions to problems.
The tools you need to solve problems with divergent thinking are origi- nality, adaptability, fluency, and inventiveness. Divergent thinkers examine all assumptions, stated and especially unstated. The typical divergent thinker will usually explore many possible solutions before finding the optimum one.
Convergent reasoning is likely to pick the first reasonable solution that presents itself. It is often based on an unaware acceptance of unstated assumptions. And once having articulated a solution, convergent thinkers tend to stick with that one alternative, defending it like a dog with a chew bone. The minds of convergent thinkers are trapped on one-way streets. Henry Ford’s famous slogan about model T Fords—“You can have any color you desire so long as it’s black”—is a classic example of conver- gent thinking. And while there are occasions where convergent thinking is desirable, the job interview is assuredly not one of them.
LET THE FORCE BE WITH YOU
By “the Force,” I mean the conventions of puzzles and brainteasers. Puzzle solvers have evolved a set of agreements about how puzzles behave. It’s a
world inhabited by characters that look like people but often act in ways that would in the real world appear totally goofy.
For example, there are a group of games called balance puzzles. In these puzzles, the challenge is to find among a group the one thing that weighs more or less than the others using the smallest number of weigh- ings. Fair enough. Let’s say it’s a coin. In the real world, you might do all kinds of things with the coin. You might saw it in half, melt it down, grind it into powder, chew on it, heft it in your hands, do a chemical analysis, look on the Internet, bribe a jeweler, etc. Some of these strategies may be inspired; others may be stupid; none of them have a place in a balance puzzle. Puzzle conventions won’t tolerate such distractions. So get into the spirit of this world. Embrace the constraints as offered and attend to the abstracted geometry of the challenge.
When puzzles are animated by humanlike creatures, it’s important to forget practically everything you know about complex, ambivalent human behavior. Puzzle creatures are simple, one-dimensional characters who exist only to serve the puzzle. They usually have but one motivation. Depending on the puzzle, these characters are concerned only with maximizing money, escaping the fire, moving items across a bridge, or behaving in predictable ways. Puzzle creatures understand probability, and when they are expected to act logically, they never fail. These creatures act instantaneously and are thor- oughly aware of the logical consequences of their actions. Puzzle creatures never make mistakes, nor are they ever uncertain. Puzzle creatures don’t have an altruistic bone in their bodies; they never do anything because they are nice or it’s the fair thing to do. When they act, it’s for their self-interest alone.
Even brilliant people can crumple under the pressure of a job inter- view. But don’t despair. Here are a few practical tips to make the task easier. Heed what dozens of interviewers, recruiters, and job coaches have to say about confronting puzzles and brainteasers.
• The obvious answer is always wrong. Depend on it—your first thought is undependable. The more obvious the answer seems, the more incorrect it is likely to be. Almost all puzzles are deeper than they appear to be—that’s what makes them puzzles. By all means, note the obvious answer. Even share it with the interviewer, but always with a measure of suspicion. Now take the obvious answer and con- sider why it’s wrong.
• Work the answer, not the question. All the information you need is al- ready there. Nothing is missing.
• Think first, and then speak. Don’t be afraid of silence. Take a minute or even two to think about the problem. “We want you to think, so think,” a Microsoft interviewer observes. Look like you think about every answer. Paradoxically, most interviewers reward deliberation more than speed, so even if you think you know the answer before the interviewer is finished with the puzzle, appear to think about it. Your first thought may be wrong. And never interrupt the interviewer.
• Break it down. Smaller is more manageable. If the puzzle involves five marbles, see what would happen with two marbles.
• Back-translate. Repeat what you have just heard. State the goal of the problem. You do this for several reasons: First, you get to hear the case all over again. Second, you show the interviewer that you were listening. And third, you do not end up answering the wrong question, which happens more often than you would think.
• A dialogue is better than a monologue. Be transparent. Think out loud. Let the interviewer see you struggle with the problem. Show the logic path your mind is taking. An interview is often structured like an exam, but a lot of answers can be worth partial credit. If you’re talking out loud, an interviewer knows where you are and can give you hints.
• Honor Occam’s razor. Favor the economical solution. Occam’s razor is the proposition that when two explanations account for a situation, the simpler explanation is better. In the case of job interview puzzles, you can be pretty sure that the puzzles are less complicated than the solutions you are considering. Keep it simple.
• We’re having fun, aren’t we? Use inclusive language—we and our—as you solve the problem. Inclusive language indicates your preference for teamwork and collaboration. If you do it right, it gives the impression that you are already part of the team.
• Ask questions; don’t just give answers. Sometimes this means chal- lenging the puzzle, but mostly it means asking clarifying questions. Make sure you are answering the problem being asked. Use questions to establish the scope of the problem before digging deep in one area.
• Calculus is never required. If you find yourself working a calculus problem, stop immediately. These puzzles never require more than simple arithmetic. In general, the more complicated the question, the simpler the answer.
• Work backward. Often the solution is easier when you start from the end of the puzzle and work backward.
• All things being equal, give the interviewer a unique answer. A good way to stand out is to give the interviewer a solution he or she has never heard before.
• Go for closure. Often you will drift back and forth between two or more equally attractive solutions. You must pick and commit yourself. You don’t have to have a good reason, except for the need to move on. That’s just good business, and interviewers will respect you for it.
• Ask for the answer. If you don’t get the answer or the interviewer indicates he or she has another answer in mind, ask for it. Never fail to turn the conversation into a learning opportunity.
HELP! I’M TOTALLY STUMPED
The human brain is a marvelous organ. It starts working the minute you are born and doesn’t stop until you are hit with one of these logic puzzles. When that happens, don’t worry. The way you handle a puzzle you can’t solve is almost as important as the way you handle a puzzle you can.
The biggest mistake is to get all flummoxed and react like a deer in headlights—too stunned to respond or survive. Worse is to act like a drown- ing swimmer, lash out at the interviewer, and take him or her down with you. A good response does not always mean coming up with the right answer, but it does mean showing good approaches to an unfamiliar problem.
The best thing is to keep your sense of humor. One very people-smart candidate responded to a very difficult puzzle this way: “Hmmm . . . one of us doesn’t know the answer.” Another, referring to the popular TV quiz show Who Wants to Be a Millionaire? in which contestants get to make one phone call for help, asked: “How many lifelines do I have?”
When you feel stuck, the first thing to do is to take a deep breath and ask for the puzzle to be repeated. Now listen. Sometimes the interviewer will sense something and provide a missing emphasis or detail. Then repeat the puzzle to the interviewer. “Let me see if I have this right . . .” Then repeat it again. Sometimes saying a puzzle aloud to yourself once or twice reveals some opportunity for taking it to the next level. Some candidates take time to write the problem down. Don’t let yourself be rushed.
Then ask questions. If there’s a detail you don’t understand, let the interviewer know. Own the difficulty. “I’m having trouble with this prob- lem. Can you help me understand . . .?” If none of this helps, ask for a hint. “I’m sorry. I seem to be stuck. Can you give me a hint?”
Don’t let interviewers see you panic, but let them see you think out loud. “You have to show them that your mind is cycling,” says former Microsoft developer Adam Barr. “Have your internal dialogue out loud. Show them that you’re curious. Let them see the answers you explore and the dead ends you’re considering; invite them to go with you down the blind alleys. Even if you never get right to the answer, they might be impressed by your strategy.”
Finally, if you really are at a dead end and have nowhere to go, just admit that you’ll need more time than you feel comfortable taking in a job interview. Don’t admit you can’t do the problem; just suggest you can’t do it in the time frame of the interview. Barr suggests wording like, “I’m sorry. I can’t work out the problem right here, but given time I’m sure I can do it. May I get back to you?” Even if you don’t get it, make sure the interviewer sees your curiosity and unflagging spirit. “I know I didn’t get it, but I’m really curious. Can you tell me what the solution is?” This kind of closure replaces the sting of failure with a sense of optimism about the next puzzle.
Some candidates feel insulted by puzzles and brainteasers and treat them like “illegal” questions. Some simply say, “My policy is not to respond to questions like that.” Others respond with a challenge of their own. “What does that puzzle have to do with my ability to perform on this job?” Most interviewers will respect your position. They won’t hire you, but they will respect your position. If it’s respect you want, then by all means pursue this course. If it’s a job offer you want, then accept that for a candidate to engage in conflict on a job interview is counter- productive. You may not like puzzles—you may find them insulting— but if you want to be considered for the job, there’s no alternative but to take your best shot.
The tools you need to solve problems with divergent thinking are origi- nality, adaptability, fluency, and inventiveness. Divergent thinkers examine all assumptions, stated and especially unstated. The typical divergent thinker will usually explore many possible solutions before finding the optimum one.
Convergent reasoning is likely to pick the first reasonable solution that presents itself. It is often based on an unaware acceptance of unstated assumptions. And once having articulated a solution, convergent thinkers tend to stick with that one alternative, defending it like a dog with a chew bone. The minds of convergent thinkers are trapped on one-way streets. Henry Ford’s famous slogan about model T Fords—“You can have any color you desire so long as it’s black”—is a classic example of conver- gent thinking. And while there are occasions where convergent thinking is desirable, the job interview is assuredly not one of them.
LET THE FORCE BE WITH YOU
By “the Force,” I mean the conventions of puzzles and brainteasers. Puzzle solvers have evolved a set of agreements about how puzzles behave. It’s a
world inhabited by characters that look like people but often act in ways that would in the real world appear totally goofy.
For example, there are a group of games called balance puzzles. In these puzzles, the challenge is to find among a group the one thing that weighs more or less than the others using the smallest number of weigh- ings. Fair enough. Let’s say it’s a coin. In the real world, you might do all kinds of things with the coin. You might saw it in half, melt it down, grind it into powder, chew on it, heft it in your hands, do a chemical analysis, look on the Internet, bribe a jeweler, etc. Some of these strategies may be inspired; others may be stupid; none of them have a place in a balance puzzle. Puzzle conventions won’t tolerate such distractions. So get into the spirit of this world. Embrace the constraints as offered and attend to the abstracted geometry of the challenge.
When puzzles are animated by humanlike creatures, it’s important to forget practically everything you know about complex, ambivalent human behavior. Puzzle creatures are simple, one-dimensional characters who exist only to serve the puzzle. They usually have but one motivation. Depending on the puzzle, these characters are concerned only with maximizing money, escaping the fire, moving items across a bridge, or behaving in predictable ways. Puzzle creatures understand probability, and when they are expected to act logically, they never fail. These creatures act instantaneously and are thor- oughly aware of the logical consequences of their actions. Puzzle creatures never make mistakes, nor are they ever uncertain. Puzzle creatures don’t have an altruistic bone in their bodies; they never do anything because they are nice or it’s the fair thing to do. When they act, it’s for their self-interest alone.
Even brilliant people can crumple under the pressure of a job inter- view. But don’t despair. Here are a few practical tips to make the task easier. Heed what dozens of interviewers, recruiters, and job coaches have to say about confronting puzzles and brainteasers.
• The obvious answer is always wrong. Depend on it—your first thought is undependable. The more obvious the answer seems, the more incorrect it is likely to be. Almost all puzzles are deeper than they appear to be—that’s what makes them puzzles. By all means, note the obvious answer. Even share it with the interviewer, but always with a measure of suspicion. Now take the obvious answer and con- sider why it’s wrong.
• Work the answer, not the question. All the information you need is al- ready there. Nothing is missing.
• Think first, and then speak. Don’t be afraid of silence. Take a minute or even two to think about the problem. “We want you to think, so think,” a Microsoft interviewer observes. Look like you think about every answer. Paradoxically, most interviewers reward deliberation more than speed, so even if you think you know the answer before the interviewer is finished with the puzzle, appear to think about it. Your first thought may be wrong. And never interrupt the interviewer.
• Break it down. Smaller is more manageable. If the puzzle involves five marbles, see what would happen with two marbles.
• Back-translate. Repeat what you have just heard. State the goal of the problem. You do this for several reasons: First, you get to hear the case all over again. Second, you show the interviewer that you were listening. And third, you do not end up answering the wrong question, which happens more often than you would think.
• A dialogue is better than a monologue. Be transparent. Think out loud. Let the interviewer see you struggle with the problem. Show the logic path your mind is taking. An interview is often structured like an exam, but a lot of answers can be worth partial credit. If you’re talking out loud, an interviewer knows where you are and can give you hints.
• Honor Occam’s razor. Favor the economical solution. Occam’s razor is the proposition that when two explanations account for a situation, the simpler explanation is better. In the case of job interview puzzles, you can be pretty sure that the puzzles are less complicated than the solutions you are considering. Keep it simple.
• We’re having fun, aren’t we? Use inclusive language—we and our—as you solve the problem. Inclusive language indicates your preference for teamwork and collaboration. If you do it right, it gives the impression that you are already part of the team.
• Ask questions; don’t just give answers. Sometimes this means chal- lenging the puzzle, but mostly it means asking clarifying questions. Make sure you are answering the problem being asked. Use questions to establish the scope of the problem before digging deep in one area.
• Calculus is never required. If you find yourself working a calculus problem, stop immediately. These puzzles never require more than simple arithmetic. In general, the more complicated the question, the simpler the answer.
• Work backward. Often the solution is easier when you start from the end of the puzzle and work backward.
• All things being equal, give the interviewer a unique answer. A good way to stand out is to give the interviewer a solution he or she has never heard before.
• Go for closure. Often you will drift back and forth between two or more equally attractive solutions. You must pick and commit yourself. You don’t have to have a good reason, except for the need to move on. That’s just good business, and interviewers will respect you for it.
• Ask for the answer. If you don’t get the answer or the interviewer indicates he or she has another answer in mind, ask for it. Never fail to turn the conversation into a learning opportunity.
HELP! I’M TOTALLY STUMPED
The human brain is a marvelous organ. It starts working the minute you are born and doesn’t stop until you are hit with one of these logic puzzles. When that happens, don’t worry. The way you handle a puzzle you can’t solve is almost as important as the way you handle a puzzle you can.
The biggest mistake is to get all flummoxed and react like a deer in headlights—too stunned to respond or survive. Worse is to act like a drown- ing swimmer, lash out at the interviewer, and take him or her down with you. A good response does not always mean coming up with the right answer, but it does mean showing good approaches to an unfamiliar problem.
The best thing is to keep your sense of humor. One very people-smart candidate responded to a very difficult puzzle this way: “Hmmm . . . one of us doesn’t know the answer.” Another, referring to the popular TV quiz show Who Wants to Be a Millionaire? in which contestants get to make one phone call for help, asked: “How many lifelines do I have?”
When you feel stuck, the first thing to do is to take a deep breath and ask for the puzzle to be repeated. Now listen. Sometimes the interviewer will sense something and provide a missing emphasis or detail. Then repeat the puzzle to the interviewer. “Let me see if I have this right . . .” Then repeat it again. Sometimes saying a puzzle aloud to yourself once or twice reveals some opportunity for taking it to the next level. Some candidates take time to write the problem down. Don’t let yourself be rushed.
Then ask questions. If there’s a detail you don’t understand, let the interviewer know. Own the difficulty. “I’m having trouble with this prob- lem. Can you help me understand . . .?” If none of this helps, ask for a hint. “I’m sorry. I seem to be stuck. Can you give me a hint?”
Don’t let interviewers see you panic, but let them see you think out loud. “You have to show them that your mind is cycling,” says former Microsoft developer Adam Barr. “Have your internal dialogue out loud. Show them that you’re curious. Let them see the answers you explore and the dead ends you’re considering; invite them to go with you down the blind alleys. Even if you never get right to the answer, they might be impressed by your strategy.”
Finally, if you really are at a dead end and have nowhere to go, just admit that you’ll need more time than you feel comfortable taking in a job interview. Don’t admit you can’t do the problem; just suggest you can’t do it in the time frame of the interview. Barr suggests wording like, “I’m sorry. I can’t work out the problem right here, but given time I’m sure I can do it. May I get back to you?” Even if you don’t get it, make sure the interviewer sees your curiosity and unflagging spirit. “I know I didn’t get it, but I’m really curious. Can you tell me what the solution is?” This kind of closure replaces the sting of failure with a sense of optimism about the next puzzle.
Some candidates feel insulted by puzzles and brainteasers and treat them like “illegal” questions. Some simply say, “My policy is not to respond to questions like that.” Others respond with a challenge of their own. “What does that puzzle have to do with my ability to perform on this job?” Most interviewers will respect your position. They won’t hire you, but they will respect your position. If it’s respect you want, then by all means pursue this course. If it’s a job offer you want, then accept that for a candidate to engage in conflict on a job interview is counter- productive. You may not like puzzles—you may find them insulting— but if you want to be considered for the job, there’s no alternative but to take your best shot.
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