Top Companies Interview Problems/ Puzzles

[mpalanieppan]

I might be wrong here but i think if the pirates are ranked from 1 to 5 then #1 just have to give 1 coin to no #5 and 2 coins to #4 and take 97 coins for himself

[luke]

Originally Posted by mpalanieppan

I might be wrong here but i think if the pirates are ranked from 1 to 5 then #1 just have to give 1 coin to no #5 and 2 coins to #4 and take 97 coins for himself

what if the 4 other pirates don't agree with this plan? they'll kill you and take those 97 coins away ...

[mpalanieppan]

My bad, i should have explained why i chose the above answer. Sorry...

My reasoning is along the following line: (Assume pirates ranked 1-5 - descending seniority)

Consider only 3 pirates (i.e#1,2 dead somehow) :The best deal for the most senior, i.e, #3 is to give 1 coin to #5 and take 99 coins for himself. Certainly #4 will disagree since he is next in line (i.e he will have the chance to propose a division if #3 dies). But #5 will agree since if he disagrees to this deal, 2 out of three pirates against this proposal, and #3 will be killed. Next will be #4's turn and by then only 2 ppl left. #4's vote counts as half; #4 can choose to take all 100 coins for himself and #5 gets nothing.

Now consider 4 pirates(i.e just #1 dead): If the most senior now, #2, were to die, in the next level, that is when #3 is the most senior, #4 gets nothing, only #5 gets one coin and #3 takes 99 coins, as seen above. Now, there are 4 pirates, so for #2 to secure his proposal, he just have to get the vote of one more person. Hence, the best deal for him is to give 1 coin to #4 and takes 99 for himself; #4 certainly must agrees to this deal because if he disagrees, 3 out of 4 pirates against this proposal, #2 will be killed, it goes to the next step and #4 will then get nothing.

Now consider 5 pirates (as is our question): If #1 were to die, in the next step as described above, it turns out that #3 and #5 gets nothing - only #4 gets one coin and #2 gets 99 coins. So , if #1's proposal is not accepted by majority and he is killed, #3 and #5 gets nothing. So both of them will vote if they get at least something - so #1 just has to give #3 and #5 each one coin and take 98 coins for himself.

This solution is slightly different from the one i proposed above. In the above, I just added one more to the maximum #4 and #5 will get if #1 were to die. But i missed out this line of reasoning, which seem to give more for #1.

Of course, this is based on the fact that all of the pirates are both very greedy and very logical.

[littlebigone]

wah...good thinking pala...you've got me convinced

[huilinchin]

woa, mpalanieppan, I am curious to know how long you took to solve this question. Excellent and well done!!!!!!!!!!!!!!

Recursion is definitely the way to go for this question. This question illustrates how we can solve big problem by solving tiny parts of it.
Prof Rudich used to say that anyone can solve this types of problems as long as they have practice and it is not true that only intelligent people can do it.

So, I urge everyone who read this forum thread to try. For those who have been answering the questions, I hope you will continue trying the coming questions.

BIG BIG applause to mpalanieppan for correctly explaning and answering question 6.

Answer for question 6:
If the pirates are numbered from #1 to #5, and the senior pirate is pirate #1, the senior pirate will give no coin to #2, one coin to #3, no coin to #4 and one coin to #5. The senior pirate will get 98 coins for himself.

Explanation quoted from mpalanieppan:
Consider only 3 pirates (i.e#1,2 dead somehow) :The best deal for the most senior, i.e, #3 is to give 1 coin to #5 and take 99 coins for himself. Certainly #4 will disagree since he is next in line (i.e he will have the chance to propose a division if #3 dies). But #5 will agree since if he disagrees to this deal, 2 out of three pirates against this proposal, and #3 will be killed. Next will be #4's turn and by then only 2 ppl left. #4's vote counts as half; #4 can choose to take all 100 coins for himself and #5 gets nothing.

Now consider 4 pirates(i.e just #1 dead): If the most senior now, #2, were to die, in the next level, that is when #3 is the most senior, #4 gets nothing, only #5 gets one coin and #3 takes 99 coins, as seen above. Now, there are 4 pirates, so for #2 to secure his proposal, he just have to get the vote of one more person. Hence, the best deal for him is to give 1 coin to #4 and takes 99 for himself; #4 certainly must agrees to this deal because if he disagrees, 3 out of 4 pirates against this proposal, #2 will be killed, it goes to the next step and #4 will then get nothing.

Now consider 5 pirates (as is our question): If #1 were to die, in the next step as described above, it turns out that #3 and #5 gets nothing - only #4 gets one coin and #2 gets 99 coins. So , if #1's proposal is not accepted by majority and he is killed, #3 and #5 gets nothing. So both of them will vote if they get at least something - so #1 just has to give #3 and #5 each one coin and take 98 coins for himself.

Thanks for trying!

-Hui Lin ^_^

[huilinchin]

We have been trying questions from the computer-related companies only. It's now a good time to explore the interview process of the finance and banking industry.

Big thanks to Chen Chow for sharing the interview process of CAPITAL ONE.

Sample question of Case Interview from Capital One:

You have just been appointed the manager of the Cross Sells team at Capital One, which evaluates opportunities to market non-credit card products to our credit card customers. These cross sells usually involve building relationships with outside vendors who sell us products that we, in turn, can sell to our customers at a premium.
One potential cross sell opportunity that is sitting on your desk right now is the Prepaid Phone Card -- a piece of plastic you can use to pay for long distance telephone calls. You use the card by calling in to a 1-800 number, entering the card's PIN number, and then entering the destination telephone number. The minutes left on the card are kept track of by the outside vendor -- your only responsibility is to market the product in a way that maximizes profit for Capital One.
Take a few moments to consider some of the most important factors that will influence your decision on whether to pursue the Phone Card cross sell.

Question:
Luckily, the vendor who wants to sell us the Phone Cards has already provided a lot of the information you need in an introductory e-mail. The e-mail has several key points:
The card may be sold at any price, and other companies have sold the cards for up to $0.75 per minute.
The card may be sold with any number of minutes on it.
Capital One must pay $0.20 per minute sold.
Capital One must pay $2.00 per card sold for account set-up, which includes card materials, the vendor's system programming, and postage.
The vendor notes that the Phone Card could be a good addition to Capital One's cross sell program, which ordinarily offers products in the $5 to $30 price range.
Let's assume that Capital One has decided to sell 60-minute Phone Cards at a price of $30 each. How much profit do we make on each card sold?

Source: Capital One
Answers are provided in the sub-links of the url below. Try to attempt the question before looking at the answer.
http://www.capitalone.com/careers/interviewtips.shtml

You will also get a lot of recruiting information besides the interview process.

Thanks to Chen Chow again for sharing the useful link!
Hope more members can send me a private message in ReCom if you have new questions to share. It can be anything related to the work-industry.

-Hui Lin ^_^

[mpalanieppan]

I spent about one hour plus for this question, but actually it came in stages. The original answer i gave first was slightly diff (97). But i asked the same question to my friend here and when we were discussing whether we can improve, we realized that the same process applied earlier can be done again at the final stage and get a better answer......

And, thank you hui lin for collecting and posting these questions for everybody's benefit....

[luke]

I don't know if I understood it wrongly or what .. but Question 7 is too straight that I wonder if there's any trick in it ... the answer I got is $16 per card sold ...

we get $30 for a card ... then we have to substract $2 for the price of the card ... and then substract (60 minutes x $0.20 =) $12 more .. so in the end we have to pay the vendor $14 per card .. that leaves us with $16 ...

mm is there any trick in it?

[huilinchin]

luke, according to the website, that is the first answer. I am glad you did not take a peep at the answer.

Step 4 (of 6) - First Answer
Capital One's profit per card is $16. For your reference, the equation is shown below.
X = Profit per card sold
X = (Revenue per card) - (Expense per card)
X = $30 - (($0.20*60) + $2.00)
X = $16

But does anything big seem missing from this equation? Click here when you think you know what we've left out.

Source: http://www.capitalone.com/careers/firstanswer.shtml
(Don't click the next page of the above link if you want to try what is missing).

Now, read the following and then try again.

Step 5 (of 6) - Other Factors
The thing that we haven't considered yet is marketing costs. (In reality, we haven't considered several things, but the lack of marketing expense has the biggest impact by far.) Basically, it will cost Capital One some money to tell our customers about the Phone Card offer, but we didn't include any of that expense in the equation on the previous page.
But how should we market this product? There are several different distribution channels we could use.

Statement Inserts - Little slips of paper we put inside customers' monthly statements, which they return to us when they mail us their payments.

Bangtails - Slips of paper that are attached to the backs of the envelopes that customers use to mail in their payments. If they are interested in buying the product, they can rip off the stubs and put them inside the envelopes.

Statement Messages - A line or two of text typed on the remittance stub of each statement (the part a customer rips off and mails back with the check). It might say something like, "Check this box if you would like to purchase a Capital One Phone Card, good for 60 minutes of long distance calling, for only $30!"

Direct Mail - We could send our customers a letter?separate from their monthly statement?describing the Phone Cards in detail.

Outbound Telemarketing - We could place telephone calls to our customers describing the cards and asking them if they would like to purchase one.

Please take a few moments to think about the distribution channels above. How are they similar? How are they different?

What factors would be most important in determining which distribution channel you should use? In other words, what additional information would you need to know about each channel to decide which is best? For the purposes of this case, you do not need to think about all the variables for every distribution channel?just try to think of the two main variables that apply to all of them.

Answer: http://www.capitalone.com/careers/factorsexp.shtml

Final Answer for the question:
http://www.capitalone.com/careers/finalanswer.shtml

There are other sub-links on the website that is worth looking at.

-Hui Lin ^_^

[huilinchin]

I am publishing this question a bit later to give time to everyone to try the banking and finance question. I learn new financial terms myself by only reading the case interview. Try to go through the banking and finance question first before trying this question.

You are most welcome, pala. Thanks for trying the questions.
Glad that more members are contributing their questions and hope that more can participate. If you have one, do share. It can be anything related to the work-industry.

Question 8:
Source: From the book, "How to move Mount Fuji?"

There are three switches in a hallway. One switch controls a light fixture in a room at the far end of the hall. The door to the room is closed, and you can't see whether the light is on or off. You need to find out which of the three switches controls the light. How can you be certain of finding that out, making just one trip to the room?

Happy trying.

-Hui Lin ^_^