osmarks/documentation
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

Edit ‘quant_interview_questions’

Browse Source
This commit is contained in:
osmarks
2026-02-21 22:04:39 +00:00
committed by wikimind
parent 4bb1dd03e9
commit a5d082900e
1 changed files with 4 additions and 3 deletions
Download Patch File Download Diff File Expand all files Collapse all files

7
quant_interview_questions.myco
View File

@@ -94,7 +94,7 @@
* A group has 70 members. For any two members X and Y there is a language that X speaks but Y does not, and there is a language that Y speaks but X does not. At least how many different languages are spoken by the members of this group?
* An 8x8 chessboard can be entirely covered by 32 dominoes of size 2x1. Suppose we cut off two opposite corners of chess (i.e. two white blocks or two black blocks). Prove that now it is impossible to cover the remaining chessboard with 31 dominoes.
* There are 51 ants sitting on top of a square table with side length of 1. If you have a square card with side 1/5, can you put your card at a position on the table to guarantee that the card encompasses at least 3 ants?
* What is the minimum number of colors needed to paint the plane so no two points 1 unit apart share a color?
* What is the minimum number of colors needed to paint the plane so that no two points 1 unit apart share a color?
* A bond prospectus states: “This bond will default if and only if its default cannot be proven in ZFC set theory.” What is the bond’s credit rating?
* Assume 100 zombies are walking on a straight line, all moving with the same speed. Some are moving towards left, and some towards right. If a collision occurs between two zombies, they both reverse their direction. Initially all zombies are standing at 1 unit intervals. For every zombie, you can see whether it moves left or right. Can you predict the number of collisions?
* Two bullets are put into a gun's round barrel consecutively, which has capacity of 6. The gun is shot once, but no bullet is fired. Does rolling the barrel (shuffling) before next shot increase the probability of firing a bullet?
@@ -103,10 +103,11 @@
* We have a weighted coin which shows a head with probability p, (0.5<p<1). How do we get a fair toss from this? That is, how do we toss this coin in such a way that we can have probability of winning = losing = 50%?
* Calculate the VaR of a portfolio whose returns follow a nowhere-differentiable function (e.g., Weierstrass curve) with Hausdorff dimension 1.5.
* You’re on a game show with countably infinite doors. Behind one is a car; the rest have goats. After you pick a door, the host (who knows what’s behind all doors) opens all but one other door, revealing goats. Should you switch?
* There is a regular die and a special invisible die. You know that regular die has integers 1 to 6, but don't know what's on the invisible dice. After tossing, I speak the sum of outcome of both die. It so happens that the outcome is an integer between 1 to 12, with equal probability (1/12 each). Can you guess what are the numbers printed on special invisible dice?
* I have a regular die and a special invisible die. You know that regular die has integers 1 to 6, but don't know what's on the invisible dice. After tossing, I speak the sum of outcome of both die. It so happens that the outcome is an integer between 1 to 12, with equal probability (1/12 each). Can you guess what are the numbers printed on the special invisible die?
* Two witches make a nightly visit to an all-night coffee shop. Each arrives at a random time between 0:00 and 1:00. Each one of them stays for exactly 30 minutes. On any one given night, what is the probability that the witches will meet at the coffee shop?
* In a repeated Prisoner’s Dilemma, what is the Nash equilibrium?
* A stick is broken into 3 parts, by choosing 2 points randomly along its length. With what probability can it form a triangle?
* p and q are two points chosen at random between 0 & 1. What is the probability that the ratio p/q lies between 1 & 2?
* A very innocent monkey throws a fair die. The monkey will eat as many bananas as are shown on the die, from 1 to 5. But if the die shows '6', the monkey will eat 5 bananas and throw the die again. This may continue indefinitely. What is the expected number of bananas the monkey will eat?
* What is the expected number of coin tosses required to get n consecutive heads?
* What is the expected number of coin tosses required to get n consecutive heads?
* On Monday, a fair coin is flipped. If it lands as heads, you are awoken on Tuesday and Wednesday. If it lands as tails, you are awoken on Thursday. Whenever you are awoken, you are given the opportunity to buy a call option expiring Friday for a particular security. You have access to relevant data up to Monday, but are not told what day it is when awoken, and after each awakening your memory of that awakening is erased. How should you determine whether to buy the option?