Funny Quant story for Quant Apply @ Morgan Stanley

[IlyaKEightSix]

cstassen, I believe the answer to your question is 99. I remember such a question posed by my math major friend in college, and I believe the person in the back of the line gives a certain signal if there are an odd amount of white hats, and the other signal if there are an even number of hats, and then the next person can just count and decide what color his hat is, and then it bubbles up until everyone but the last person knows what color their hat is.

 

[alain]

100 people with white and black hats are to be executed. They have to stand in a line, and the execution will start from the back. nobody knows what colour their hat is, all they know is what the hats IN FRONT of them are. The executioner asks the guy in the back what colour his hat is - if he says the right color, he will be spared, and the executioner moves on to the next person in the line. What is the maximum number of people the group can save with certainty, if everybody acts in their own interest but if the group can collaborate?

There is a lot of ambiguity in this problem. 100 people with black and white hats, do they know the total amount of black and white hats? What type of collaboration? If they are only allow to say WHITE or BLACK, there is no room for collaboration at all.

You need to give more details. In an interview, your ability to discover or ask about those details is also measured. That's part of your thinking process.

 

[John]

The way the problem is stated, it is totally irrelevant what color of hat the persons in front of his/her are wearing. Like Alain said, you don't know the total of either color of hat, so you cannot get any hint to what he/she him/herself is wearing.

 

[doug reich]

The way it's stated, it sounds like you could very easily save all the people: each person tells the person in front of them what color that person's hat is. The last two people switch, and the former "last" person is told what color his hat is. "Collaboration"!

 

[John]

or..... why not just switch hat with the person in front and then swith it back

 

[cstassen]

maybe i was unclear - you can hear what the person behind you says. sorry for leaving that out.

they are allowed to collaborate in the sense that before lining up, they can decide on a strategy for what each person should say. each person should only say "white" or "bklack" - they can't both say what their own hat is and also say something to the guy in front of you. if he says what is on top of his head, he won't get killed.

and that is all you need, no info about total number of white versus black is needed

 

[IlyaKEightSix]

John, with my solution, you don't need to. The strategy is this: the person in the back will say white if he sees an even number of white hats, or black if he sees an odd number of white hats. Say there were 50 white hats and 49 black hats in the line ahead of him.

The person in the back (let's call him person 1) will say white.

Then person 2 will count the white hats ahead of him, knowing that there are an even number of white hats. If he counts the 50 white hats, he has a black hat, and if he counts 49 white hats, it means he has a white hat.

Now this problem, of course, has some unrealistic human assumptions in that the people will be able to keep perfect memory of how many white and black hats there were called out already.

But given this assumption, this strategy is guaranteed to save all but one person, and then that last person still has a 50% chance of making it out alive.

 

[alain]

this strategy is guaranteed to save all but one person, and then that last person still has a 50% chance of making it out alive

When you say the last person, you are talking about the first one to call BLACK or WHITE, correct?

 

[IlyaKEightSix]

Yes I am. Once again, I've seen this problem before. Though I hope this forum shows enough of my aptitude so I can get into Goldman Sachs this recruiting season.

 

[alain]

dude, why do you have this love for Goldman? What about any other place?

 

[cstassen]

Ilya, your solution is right, but one actually doesn't have to remember everything that has been said priorly. Think it over again...

Alain: because we are the best of course!

 

[alain]

Alain: because we are the best of course!

You are already in. Poor Ilya is not in yet but he will stop short of nothing to join GS.

 

[cstassen]

If you want to swim with the big boys, don't jump into the small pool I agree, though!

You are already in. Poor Ilya is not in yet but he will stop short of nothing to join GS.

 

[AnideJ]

Second choice? JPMorgan Chase because they're the only other bank really remotely above this whole subprime mess, but they're glutted with Bears employees, so my chances seem slim there. But it's a far second choice.

Third choice? Lehman Brothers. Simply because a girl I knew from high school has interned there twice, and she knows what the heck she's doing and her advice to me has always been good (on an off-topic note, I miss her like hell...I swore I'd catch up in college and have fallen further behind it seems).

After that, I'm thinking Deutsche Bank or Group One. Deutsche seems another popular interning spot for friends of mine, so I'm guessing it's decent, and Group One has a lot of Lehigh alums.

Now, why Goldman?

Because Goldman Sachs cleans house. Their "where would I fit in best" job application was pure genius, and if there was one merit to this subprime/credit crisis, it's to show which firms are worth working for, and which are run by lemmings and imbeciles that probably wouldn't be able to make heads or tails of their own quantitative departments.

And because I know what I could do with the money and power earned by people at Goldman Sachs that prove themselves through hard work and dedication. Alternative energy. Zero emissions transportation. K-12 education in math, science, engineering, economics, and finance (keep that MfA going, Jim Simons!).

But first and foremost, I need to prove myself to myself, that I can leverage my education to make good of myself. And when I make something more of myself than I already am, I want to see to the fact that America makes use of its potential a lot more than it does.

Came into America at 4 years old, $15 and two suitcases between me, my mother (a piano teacher), and my dad (a real estate broker). I've come this far, as a result of my own merits. And I believe Goldman matches my philosophy of no shortcuts, merit, talent, dedication, motivation, and hard work.

And no, this isn't a sales pitch. It's just that I've never gotten anywhere with glib, and only recently read a book on how to do it slightly better (Dale Carnegie's book), so I've become so used to getting anywhere with my own merits that I don't want it any other way.

 

[IlyaKEightSix]

Ilya, your solution is right, but one actually doesn't have to remember everything that has been said priorly. Think it over again...

Alain: because we are the best of course!

I didn't remember everything. I just remembered the question and how much I was trying to bend my brain around it the first time.

I remember the times I did a really great job, but more than that, I remember the times when I blundered, and learn from them.

 

[alain]

<offtopic>
Ilya, It looks like you only know about big banks but there is a lot more out there. GS is not the only one that clean house. It happens it's the only one you hear about. You should try to research or find out more about other places.

At the same time, keep the rhetoric and the "fan boy speak" down. There are people that had it worse than you and don't advertise it.

 

[gstanczak]

Ilya, your solution is right, but one actually doesn't have to remember everything that has been said priorly. Think it over again...

You just need to remember whether there are odd or even number of blacks hats (hehe) and whether your position in line is odd or even.

 

[cstassen]

No you don't you have to hear what the guy behind you says, and be able to see in front of you. that's it!

You just need to remember whether there are odd or even number of blacks hats (hehe) and whether your position in line is odd or even.

 

[finmathguytr]

Ilya, your solution is right, but one actually doesn't have to remember everything that has been said priorly. Think it over again...

since all prisoners are allowed to talk to each other and to set a strategy, mine would be this: the first one to be executed is to say the color of hat in front of him, so that the second shall know what to say. if there is n person, we have 1/2 chance to save all prisoners and another 1/2 to save n-1.

 

[IlyaKEightSix]

The people are lined up in alternating colored hats.

Congratulations, everybody dies.