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This is a simple problem suitable for a candidate who has displayed aptitude for algebra
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A marching band is parading down Main Street at a constant speed The bass drum player has a dog that runs to the front row and then back to its owner, going back and forth, also at a constant speed The distance between the back row and front row of the marching band is 50 feet In the time the dog went back and forth, the bass drum player marched 50 feet Find the length of the dog s path
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While this can be done with a little hit or miss arithmetic, algebra makes it easier: While the band went x feet ahead, the dog ran 50 While the band went 50 So x/(50 x x x x 2x x x 35 (50 2,500 2,500 x) (50 x) (50 x x x) x dog ran x x)/x x
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Solution: 35 feet
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92 FOUR PEOPLE ON A BRIDGE
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Candidates report that this problem shows up at many Microsoft job interviews Its solution requires an elegance of thought, the formation of an algorithm, and a demonstrated ability to juggle three or four things
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at once Almost everyone will need a paper or pen to solve this Some interviewers draw out the puzzle on a whiteboard and invite the candidate to stand up and solve it
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Four programmers must cross a rickety bridge at night The bridge can only hold two of them at a time, and they have one flashlight between them The four programmers cross at different speeds: Alex requires one minute, Sam requires two, Pat requires four, and Francis requires eight What is the shortest time in which they can all cross
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Hint: Get the two slowest people across first First, assume that it s, in fact, possible I ve never known an interviewer to present a problem like this and watch the candidate grapple with it, only to say, Actually, it s not possible Now the solution to this problem is counterintuitive For some reason, most people want to get the fastest people across first The most obvious solution that occurs to most people after working on this problem for a bit is as follows: Alex Alex Alex Sam far side (2 minutes) 3 minutes) 7 minutes) 16 minutes) 8 minutes) Pat far side (4 minutes, total
Alex near side (1 minute, total Alex near side (1 minute, total
Francis far side (8 minutes, total
This is a good solution because it uses Alex to ferry the flashlight back after each trip Alex is the fastest, so this seems to make sense Sam, Pat, and Francis each need to cross the bridge, so that s 2 + 4 + 8 = 14 minutes, and Alex has to come back twice, so that s 2 more minutes for a total of 16 How could that not be optimal Ole Eichorn, who has administered this puzzle to dozens of job candidates, analyzes the solution set at length on his blog The Critical Connection (http://w-uhcom/):
After giving a suboptimal answer to this problem, many people refuse to believe it is wrong I love this problem for exactly this reason If candidates work it out by themselves, terrific, they get full credit, but if they get the good-but-wrong answer and accept that it is wrong, and continue digging, I give them full credit for that, too (There is a bit of an aha! involved) Sometimes people don t believe there s a better answer, and start to argue with you; that s a bad sign; it is good to have confidence, but not good to be closed to new ideas So, how could this be done any better Let s come back to Eichorn: The optimal answer to this question is actually 15 (Yep, it is, I ll tell you how in a moment) Now if you were to ask: How can the four programmers cross in 15 minutes, you may very well stump candidates This isn t what you want Ideally you want candidates to chew on the problem, work out a solution, and then defend it This gives you a lot more insight into how candidates think, and they have a sense of accomplishment Otherwise if they fail to get 15, they ll feel bad, and you ll feel like you tricked them The key insight the thing which is a bit of an aha! is to have Francis and Pat cross at the same time They re the two slowest, so essentially this gives you the second-slowest crossing for free It isn t obvious how to make this happen, though; here s the most likely first attempt: Francis Pat far side (8 minutes) 12 minutes, already some16 minutes, you
Pat near side (4 minutes, total thing seems wrong)
Pat Alex far side (4 minutes, total know this won t work )
Pat had to come back with the flashlight This made his 4 minutes far from free, because not only does he have to come back, he has to cross again Not good So what if Pat didn t have to come
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