Jan 03, 2010

Just wanted to hear from different monkeys on examples of brain teasers you faced on interviews...

1111 x 1111

"What we can, we must; and because we can, we must"

1111 x 1111 = 1111000 + 111100 + 11110 + 1111 = 1234321

Notice the pattern: 11 x 11 = 121 111 x 111 = 12321 1111 x 1111 = 1234321 11111 x 11111 = 123454321 ...

rominet:
1111 x 1111 = 1111000 + 111100 + 11110 + 1111 = 1234321

Notice the pattern: 11 x 11 = 121 111 x 111 = 12321 1111 x 1111 = 1234321 11111 x 11111 = 123454321 ...

Nice try, but there is no way you would be able to come up with a patern like that in your head while stressed out interviewing, plus adding up 1111000 + 111100 + 11110 + 1111 in your head is pretty challenging.

The way I did it in my head was like I would do it on a piece of paper and it took me about 5 seconds.

``````            1111
``````

# x 1111

``````  -----          1111
---      1111
-   1111
1111
``````

and just add the numbers up vertically to get 1234321

Walk into an interview and the first thing that happens is that one of the partners throws me a quarter. He says "if you stack quarters one on top of another, how many will you need to reach the top of the Sears (Willis now) Tower?" Follow up to that, "if you take all those quarters to cover the area of this paper, can you reach the floor of this room to the ceiling?" Followed by how many fish are in the world?

^ what he said.

You have 50 white balls, 50 black balls, and two buckets. How should you allocate the balls (you have to use them all) so that you have the best probability of pulling a white ball out of a random bucket?

pantherdb26:
You have 50 white balls, 50 black balls, and two buckets. How should you allocate the balls (you have to use them all) so that you have the best probability of pulling a white ball out of a random bucket?

I'd put 25 black balls in the bottom of each barrel and 25 white balls on top of the black ones. Maybe not what you were looking for, but it would guarantee you a 100% chance of grabbing a white ball, no matter the barrel you picked from (assuming that you didn't dig into the bottom and that the circumference of the barrel isn't too large).

pantherdb26:
You have 50 white balls, 50 black balls, and two buckets. How should you allocate the balls (you have to use them all) so that you have the best probability of pulling a white ball out of a random bucket?

Put 1 ball in the first bucket, then the rest of the balls in another. Your probability for picking a white ball will in this way be maximized :)

This last one is a trick question isn't it? if you are picking out of a "random bucket" then you might as well be picking from a huge bucket with all the balls in it. no matter what you do your chances will be 50/50

right?

wrong. you're assuming that you have to split up all the balls uniformly.

----------------- Will throw some poo for silver. Just send me a PM.

1. Do this by induction. Suppose the chessboard is 1x1. Then there is clearly 1 square in total. Now, 2x2. here you have 1 square that has dimension 2x2, and 4 squares that have dimension 1x1. Making 1+4 = 5 in total. Now 3x3. you have 1square that is 3x3, 4 that are 2x2 and 9 that are 1x1. Making 1+4+9 = 14.

Noticing a pattern?

If you have a nxn chessboard. You will have 1 nxn square, 4 (n-1)x(n-1), 9 (n-2)x(n-2) .....

Or more concisely, for i = 1 to n, you have i^2 squares of size (n+1-i).

So to find the total number of squares in an nxn chessboard, just add the first n squares.

In this case, it's 1^2 + 2^2 ........+ 8^2.

-MBP

1. The question is too vague. What operations are you allowed?
-MBP

2) 1.3^2-.01

Let n be a fixed positive integer greater than 1...

1. Ask if you can draw it on a piece of paper with 8 square by 8 squares since it makes it a lot easier to visualize.

start with the smallest square combo so you instantly have 64. I started with 8 after, but you can easily do it with 1,2 and the pattern should be just as easy to recognize. 8 block squares = 1 (the entire board), 7 block squares = 4, 6 block squares = 9...at this point you need to tell the interview that using the pattern you would assume that 5 block squares = 16, 4= 25, 3=36, 2=49, 1 =64 (which I already did). Add them up and you get 204 squares.

1. I am not really sure of all the rules but would 1 +2/3 +.02 be a possibility---using all digits and uses 2 twice.
"Greed, in all of its forms; greed for life, for money, for love, for knowledge has marked the upward surge of mankind. And greed, you mark my words, will not only save Teldar Paper, but that other malfunctioning corporation called the USA."

^That's what I was thinking too, but technically it's 1.3^2 - 0.01, which doesn't satisfy the condition.

-MBP

Sorry, I was referring to the post by streetlegend.

gekko, I also thought that yours might work, but it's not an exact answer, if we are told that we can round to the nearest hundredth, then it would be 1 +2/3 +0.01, which has the same problem I outlined earlier.

-MBP

everythingsucks:
Sorry, I was referring to the post by streetlegend.

gekko, I also thought that yours might work, but it's not an exact answer, if we are told that we can round to the nearest hundredth, then it would be 1 +2/3 +0.01, which has the same problem I outlined earlier.

let me help you out right there, they really don't give a fuck what the answer is. The purpose of the question(s) is to see how your mind works...in that problem's case, do you have simple problem solving skills and can you make numbers work work to your advantage. As you can see there are multiple ways to get the same answer, which makes this probably the best brainteaser related to IBD I have ever seen,,,I mean that is what a banker does, takes numbers that normally equal 6 and makes them look like 7.65. Don't get hung up on the technicals of rounding too much. I am sure that those two above answers would have been acceptable to the interviewer, but you can ask him about rounding.

"Greed, in all of its forms; greed for life, for money, for love, for knowledge has marked the upward surge of mankind. And greed, you mark my words, will not only save Teldar Paper, but that other malfunctioning corporation called the USA."

for questions two, all operation are allowed but not sure 0.02 (.02) count as one 0 or two 0s....

Anyone with a better answer for question 2?

lol, thanks gekko. Coming from a pure math background, I need a reality check every once in a while.

-MBP

wkc207 as gekko pointed out, both answers are fine. Just state your assumptions first (rounding to nearest hundredth or by .02 you mean 0.02 etc.)

-MBP

1 + 1 - .32 = 1.68

progolfer...forgot to add the zero..i'll take credit for the whole thing

cclow:
progolfer...forgot to add the zero..i'll take credit for the whole thing

You're supposed to subtract it.

# 1)

For a NxN Chessboard: 1. You get NxN 1-squres. 2. You get (N-1)x(N-1) 2-squres--going left to right you get (N-1) 2-squares, and likewise going down. 3. You get (N-2)x(N-2) 3-qaures--same logic; just draw a picture and check. ... N. You get 1 N-square.

So it's simply 1+2^2+...+7^2+8^2. There's a formula for the sum of squares but I'm sure the interviewer will be satisfied enough with that expression.

1) I would say 8*8=64, if you don't remember a chess board is 8 by 8 you can count the number of different chess pieces when you set it up

2) I did 2-(1/3)+.02 or 2-(1/3)+.01 if they get mad about the rounding

put 1 white ball in one bucket and the rest in the other bucket.

----------------- Will throw some poo for silver. Just send me a PM.

PooSlinger:
put 1 white ball in one bucket and the rest in the other bucket.

Pretty sure that no matter how you divide them, you will get the same 50/50 split.

(1/50).5 + (49/50).5 = .5 (20/50).5 + (30/50).5= .5

That's why I just said put the 25 black balls on the bottom, then put the 25 white balls on top of the black ones. I could be wrong on this one, but it makes sense to me.

AverageGuy:
PooSlinger:
put 1 white ball in one bucket and the rest in the other bucket.

Pretty sure that no matter how you divide them, you will get the same 50/50 split.

(1/50).5 + (49/50).5 = .5 (20/50).5 + (30/50).5= .5

That's why I just said put the 25 black balls on the bottom, then put the 25 white balls on top of the black ones. I could be wrong on this one, but it makes sense to me.

Who said you have to put 50 balls in each bucket? I agree with 1 white in one bucket and the 99 others in the other.

PooSlinger:
put 1 white ball in one bucket and the rest in the other bucket.
I'm pretty sure this answer is correct, assuming the odds of picking any given bucket is 50% and not dependant on the number of balls in the bucket.

You have eight weights and a balance (scale that determines which side weighs more). Exactly one weight is heavier than the others. What is the minimum number of times you need to use the balance to determine which weight is heaviest?

IlliniProgrammer:
You have eight weights and a balance (scale that determines which side weighs more). Exactly one weight is heavier than the others. What is the minimum number of times you need to use the balance to determine which weight is heaviest?

I was asked a variation of this brain teaser by an MD during a FT interview. He asked how one could find the heaviest weight using the scale only twice. Hadn't heard it before, but I worked through it and got the right answer. I ended up getting an offer, and I'm pretty sure that correctly answering this brain teaser made the difference.

For Illini Programmer's brainteaser:

1) 4 on each side, heavier side has heavier weight, choose those 4 weights 2) 2 on each side, heavier side has heavier weight, choose those 2 3) 1 on each side, heavier side is heavier weight

IlliniProgrammer:
PooSlinger:
put 1 white ball in one bucket and the rest in the other bucket.
I'm pretty sure this answer is correct, assuming the odds of picking any given bucket is 50% and not dependant on the number of balls in the bucket.

You have eight weights and a balance (scale that determines which side weighs more). Exactly one weight is heavier than the others. What is the minimum number of times you need to use the balance to determine which weight is heaviest?

easy, its 2 times.

divide into 3 groups. weigh two groups, and you'll find out which group the heavy weight is in. eliminate all other groups. weigh 2 of the weights in the heavy group and voila.

damn i wish i got some some these questions...they sound pretty easy to me

search you lazy b*******

Array

.

wso sells one

For the question about the buckets and balls I'd put 49 white balls and 50 black balls in one bucket and one white ball in the other bucket. I could be wrong about that. I never got any probability questions in my interviews but got a few things like "how much does a 747 weigh? How many people voted in X City last year? How many boxing gloves were sold in X state last year?"

I don't really see it as sad. Working in IBD doesn't necessarily require the amount of intellect as someone working in software development at Google does.

2-4 are extremely doable. 1 and 5 are retarded.

I like 2-4. Lol if you can get #1 and wtf at #5

2 is high school science 3 is in every puzzle book and 4 is middle/high school math - anyone who cannot immediately get them should be dinged 1 is retarded 5 involves "lateral thinking" which most companies explicitly choose not to test because it is stupid to test for.

For the mental arithmetic ones you guys should look at vedic mathematics. My grandfather taught it to me growing up and it means I can pretty much do any simple mathematical problem in a few seconds. Just an example:

45^2 always ends in 25 and starts with 4 times one more than 4 so 4 x 5 = 20. Put them together and you get 2025

35^2 = 1225 (3x4)

65^2 = 4225

etc

I got one during interview (successfull) in one of the Big4 firms. The clock shows 3-15 time. What is the angle (exactly, without rounding, of course) between hour and minute hands.

Not a tough one but I liked it a lot (coincidence?).

Clock @ 3:15 2 glasses with orange & water mixed together 9 coins, find the odd one out with a set of scales

1.5 chickens, 1.5 eggs, 1.5 days. how many eggs does one chicken lay in one day. 3:15 degree one

I had 4 for my technical interview.

Try reading "Heard on the Street"

Had on average 5/superday for BB S&T SA.

S&T, hedge funds, and AM I have received brainteasers. Either Superdays or 1st rounds. They just want to see how you think and communicate your thought process.

Is it better to be up front and say you don't know if a brainteaser really baffles you, or better to try even if you get it totally wrong?

"Do whatever it takes to keep the legend of Wall Street as it was truly intended live on. When you think back on investment banking of the early 21st century, remember the heat—remember the passion. But mostly, remember the titans. " - LSO

Soul_Reaper:
Is it better to be up front and say you don't know if a brainteaser really baffles you, or better to try even if you get it totally wrong?
If you don't know, but have any semi-intelligent thoughts, just tell your interviewer(s) that you aren't quite sure but this is how you're thinking about it...... They might give you a hint that will help you solve it.