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Quantitative trader Interview Questions

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N points lie on a circle. You draw lines connecting all the points to each other. These lines divide up the circle into a number of regions. How many regions is this? Assume that the points are scattered in such a way as to give the maximum number of regions for that N.

14 Answers

n choose 4 + n choose 2 + 1

I don't think the above answer is right.What happens if N is less than 4? Even if N is at least four, it still doesn't work For example, take the case when 4 lines are drawn, you can make 11 regions, but Dimitar's formula gives 4c4+4c2+1=8 The way you do it, is you start out with 1 region with 0 lines. Then you draw 1 line to get 2 regions. When the maximum number of regions is created, each new line will cross every previous line and will create a new region each time it crosses line. It also creates a new region just by being created. So the 2nd line makes 2 new regions, the third line makes 3 new regions, the fourth line makes 4 new regions etc. So the answer is the sum of the first N natural numbers +1. In general this is the formula N(N+1)/2+1

Hi, I also get Dimtar's formula, you may use the recursion method to do it, which takes some time. Is there any easy way to get this one? Btw, when there are 4 dots on a circle, I think it shoud still give 8 regions. I think 11 is the answer to another problem. If you make n cuts on a circle, the max shares you can create.

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If we flip a coin 100 times, what is the probability of getting even number of heads?

13 Answers

Imagine I flip 100 coins in a sequence, and you need to guess the sequence. You are allowed to ask one yes/no question. What do you ask to maximize the probability of guessing the sequence?

9 Answers

You flip four coins. At least two are tails. What is the probability that exactly three are tails? Do this in your head, you are not allowed to write anything down for this question.

8 Answers

How many digits in (100)^10 Strategy for winning one dollar for every heads in 100 throws of coin toss. What question would you ask if you could ask one question to the person who knows the entire seq of the 100 coin tosses

7 Answers

Find the smallest positive integer, x, such that the product of all the digits of x is 10,000

7 Answers

Tell us about a time when you get angry

6 Answers

How many 0s in 100! ?

5 Answers

In a best of 7, first to 4 competition (I think the nba finals was used in his phrasing), what are the odds that a game 7 is played?

6 Answers

Approximate the number of book titles ever published

3 Answers
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