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A,B and C choose a integer between 1 and 100 in turn to minimize the difference between the integer they choose and an unknown uniformly distributed random integer. B knows what A chooses and C knows what A,B choose. What is A's optimal strategy?
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Quantitative Researcher

Interviewed at WorldQuant

4.1★
Dec 14, 2016

A,B and C choose a integer between 1 and 100 in turn to minimize the difference between the integer they choose and an unknown uniformly distributed random integer. B knows what A chooses and C knows what A,B choose. What is A's optimal strategy?

First round: basic probability, combinatorics. A bear wants to catch 3 fish from a river. when he has caught 3 fish, he'll leave. when a fish comes, there is a 1/2 chance he'll catch it. what's the probability that the 5th fish will not be caught?
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Quantitative Researcher Intern

Interviewed at Jane Street

4.4★
Oct 6, 2017

First round: basic probability, combinatorics. A bear wants to catch 3 fish from a river. when he has caught 3 fish, he'll leave. when a fish comes, there is a 1/2 chance he'll catch it. what's the probability that the 5th fish will not be caught?

1. code the n term of Fibonacci, using iteration, then use recursion only, then use recursion and memorization. What is the time complexity and space complexity for all three cases. 2. Linear regression of X and y, X is n-dimensional and y is 1-dimensional, how would beta, standard error of beta, r2, and t-stat of beta change if you duplicate the data. Can you explain the results intuitively? 3 London has p probability of rain. You have 3 friends, they have 2/3 probability of telling truth, and 1/3 probability lying. Suppose all friends tell you rain, what is the probability it rains? 4. Leetcode
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Quantitative Researcher

Interviewed at Two Sigma

3.9★
Feb 20, 2018

1. code the n term of Fibonacci, using iteration, then use recursion only, then use recursion and memorization. What is the time complexity and space complexity for all three cases. 2. Linear regression of X and y, X is n-dimensional and y is 1-dimensional, how would beta, standard error of beta, r2, and t-stat of beta change if you duplicate the data. Can you explain the results intuitively? 3 London has p probability of rain. You have 3 friends, they have 2/3 probability of telling truth, and 1/3 probability lying. Suppose all friends tell you rain, what is the probability it rains? 4. Leetcode

You are given two eggs, and access to a 100-storey building. Both eggs are identical. The aim is to find out the highest floor from which an egg will not break when dropped out of a window from that floor. If an egg is dropped and does not break, it is undamaged and can be dropped again. However, once an egg is broken, that’s it for that egg. If an egg breaks when dropped from floor n, then it would also have broken from any floor above that. If an egg survives a fall, then it will survive any fall shorter than that. The question is: What strategy should you adopt to minimize the number egg drops it takes to find the solution?. (And what is the worst case for the number of drops it will take?)
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Quantitative Analyst

Interviewed at Tower Research Capital

4.1★
Nov 22, 2013

You are given two eggs, and access to a 100-storey building. Both eggs are identical. The aim is to find out the highest floor from which an egg will not break when dropped out of a window from that floor. If an egg is dropped and does not break, it is undamaged and can be dropped again. However, once an egg is broken, that’s it for that egg. If an egg breaks when dropped from floor n, then it would also have broken from any floor above that. If an egg survives a fall, then it will survive any fall shorter than that. The question is: What strategy should you adopt to minimize the number egg drops it takes to find the solution?. (And what is the worst case for the number of drops it will take?)

There is a unit cube with internal mirror faces. A ray is emitted into the cube from one vertex, reflects off four faces (without touching vertices or edges), and stops at the opposite vertex from which it started. What is the minimum possible distance the ray travels? The answer should be decimal format approximated to 4 digits of precision, i.e. format a.bcd as in 1.234.
avatar

Quantitative Researcher

Interviewed at WorldQuant

4.1★
Dec 21, 2015

There is a unit cube with internal mirror faces. A ray is emitted into the cube from one vertex, reflects off four faces (without touching vertices or edges), and stops at the opposite vertex from which it started. What is the minimum possible distance the ray travels? The answer should be decimal format approximated to 4 digits of precision, i.e. format a.bcd as in 1.234.

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