MATCH WITS WITH MCKINSEY

E very spring, over 1,200 students put on their dark suits, tuck their portfolios under their arms and head for OCS, the Faculty Club or a local hotel. Before they can win lucrative and rewarding jobs in the consulting industry, they must survive the interview.

This isn't as easy as it sounds. Even getting an interview at many of these companies can be difficult. Each student receives 1,000 `points.' A student (call her `Sally') can spend 20 points to submit a resume and cover letter to certain exclusive companies, or to bid against her peers for limited interview slots. J. Christopher Paul `98 says, "Companies are looking to see how many points you are willing to spend on them. All you need to do to score an interview is spend the highest number of points."

Once Sally secures an interview, she must stand out from the mass of other candidates in order to win a job offer. But interviews can be tedious, nerve-wracking and just plain weird. Check out actual interview questions used by companies including Microsoft, Mercer, and Lehman Brothers. As for Sally, she must either think fast or start thinking about that job opening at McDonald's.

But it's not all bad news. For one thing, there are no points taken off for wrong answers. The interviewer is more interested in hearing a creative yet logical thought process. Paul explains that, based on what he has heard from people in the consulting business, "They're looking to see if you have a very deliberate and careful thought process. Even if in answering a question, you make a mistake, they want to see you catch your own mistake. It's not timed, it's not like the SATs." Of course, right answers never hurt anyone.

Questions:

1. There are two islands. Each island has one person living on it. Each person has a box, a key and a lock. Each key will only unlock its own lock. One of the people also has a pot of gold. A boatman paddles back and forth between the two islands. He will steal anything given to him unless it is in a locked box. How could the person with the gold send it to the other person without leaving his island?

2. A fairy arranges 100 gems in a line. First, she touches each gem. Then she touches every other gem, starting with the second one. Then she touches every third one, starting on the third gem. This pattern continues until she touches every 99th one (which is just the 99th one) and then every 100th one (which is just the 100th one). She tells you that the gems that she has touched an odd number of times will kill you and the ones that she has touched an even number of times will give you eternal life. Which gems kill you?

3. Why are manhole covers round?

4. What is the angle between the hands of a clock at 3:15?

5. You have three boxes. One has blue balls, another has red balls and the third has both blue balls and red balls. They are all labeled incorrectly with the labels "blue," "red" and "mixed." You have one opportunity to pick a ball from any box, and then you have to relabel the boxes correctly. Which box do you pick from and why?

6. You have a 10 by 10 by 10 cube made up of 1,000 smaller cubes. You submerge the large cube in a tank full of water. How many of the smaller cubes are wet on at least one face?

7. You are walking along a road and encounter two people. One person is a liar and the other always tells the truth. There's a fork in the road. One road will lead you to Harvard and the other leads to Yale. Both of the people know which road is which, but you do not. You can ask one of the people one question of your choice, and of course you'd rather go to Harvard. So what would you ask?

8. You have two bottles. One holds exactly seven cups of water and the other holds exactly three. How can you measure out exactly five cups of water?

9. Four men want to cross a narrow bridge at night, but they only have one flashlight. Only two people can cross at once, and since it is dark, one of them must have the light. When people walk together they must walk at the pace of the slower person. Each man walks at the following pace:

Man 1: one minute to cross

Man 2: two minutes to cross

Man 3: five minutes to cross

Man 4: 10 minutes to cross

The bridge will be blown up in 17 minutes. How can they all cross in time?

(Note: The bridge is too long for the flashlight to be thrown across it. The flashlight cannot shine a long distance. No one can be carried. There are no tricks.)

THE ANSWERS

1. The person with the gold puts the pot into his box. He locks it, but keeps his key. He sends it over with the boatman. The other one then puts his lock on the box and keeps his key. Then he sends it back to the first person. Then the first person removes his lock and sends it back to his friend. The second person unlocks the box, opens it and revels in his newfound wealth.

2. Do this one by factors. The first gem has only been touched once, because one only has itself as a factor. The second one has been touched twice, because two has two factors. In fact, all of the numbers have an even number of factors, except for the perfect squares. So only the gems in the positions of perfect squares will kill you.

3. The circle is the only shape that can't be tilted or rotated to fit into itself. Since we don't want our manholes to accidentally fall through the holes made for them, the round shape works best.

4. 7.5 degrees. When the minute hand reaches 3:00, the hour hand has already moved on toward 4:00. Since 15 minutes is a quarter of an hour, it has moved a quarter of the way from 3:00 to 4:00, which is a twelfth of 360 degrees.

5. Pick from the box labeled "mixed." The label is wrong, so the color of the ball is the color of all the balls in the box. The box with the label of the other color ("red" or "blue") must contain the mixed balls, since otherwise its label would be correct, and the remaining box must contain the balls of the other color.

6. There are 1,000 small cubes in the larger one. The part of the cube that touches no surface is 8 by 8 by 8, so it contains 512 unit cubes. Therefore 1000 - 512 = 488 unit cubes touch at least one surface.

7. Ask either of the two which road the other person would tell you to take to get to Harvard, and then take the opposite road. The liar will always point to the road to Yale, either because he is a liar or because he would lie about what the truth-teller would say. Since no matter who you ask, the liar has a part in the answer, you will always be told the road to Yale.

8. Fill the three-cup flask with water. Dump it into the seven-cup flask. Then refill the three-cup flask and dump it into the seven-cup flask. There now is one cup of water in the three-cup flask. Next, dump the water out of the seven-cup flask and fill it with water. Pour it into the three-cup flask up to the rim. There now is five cups of water left in the seven-cup flask.

9. First, the first man and the second man walk across, using up two minutes. Then the second man walks back with the flashlight, using up another two minutes. Then the third man and the fourth man walk across, using ten minutes. The first man walks back using one minute. The first man and the second man walk across using up two minutes. 2 + 2 + 10 + 1 + 2 = 17 minutes.