Writing
Quantitative
thinking
Finance, probability, data — written for people who like to work through the math.
- 01How Many Circles Will You Create in Your Bowl of Ramen? There are 100 noodles in your bowl of ramen. You select two of their ends randomly and connect them, then put the resulting -maybe deformed- noodle back…Quant Interview #Estimation#expectation
- 02Non-Markovian Paper Toss Challenge: 298 Wins What is the probability of hitting a bin exactly 298 times out of 300 throws, when your hit rate equals your cumulative win rate? A clean induction proof.Quant Interview #probability#induction
- 03Decoding Probabilities: The Minimum Value of P(X)=0 X is a random variable, taking positive integer values and having: E[X] = 1, E[X^2] = 2, and E[X^3] = 5. What is the smallest value that the probability…Quant Interview #moments#probabilities
- 04Detecting Unfair Coins: How Many Flips Needed? You receive a coin that is either fair (with a 50% probability of getting heads) or unfair (with a 42% probability). How can you detect the fair coin? And…Quant Interview #coins#confidence interval
- 05Fast Python Challenge: Estimating Pi to 15 Digits Write a code for estimating Pi up to 15 digits in under 1 second! Introduction Currently, the record for the best estimate of Pi approximates it with a…Quant Interview #Estimation#Pi
- 06Doubling Data in OLS Linear Regression: Effects Explored What happens if you duplicate the data used in OLS linear regression? You can encounter this problem in many forms; the one I first received was asking…Quant Interview #machine learning#Python
- 07Mastering the Number-Guessing Game: Strategies Beyond 50% Two numbers are randomly chosen from the closed interval [0,1]. Afterward, you see the first number. You now must guess if the unseen number is greater or…Quant Interview #expectation
- 08Expected Count in the 'Sum Over One' Game You play a game where you sum independent identically distributed uniform random variables over the interval [0,1]. The first time the sum exceeds one,…Quant Interview #expectation
- 09Discovering the Minimum Pairwise Correlation: X, Y, Z X, Y, and Z are three random variables with mutual pairwise correlation rho. What is the minimum possible value that rho can take? Definitions and…Quant Interview #induction
- 10Calculating Expected Distance to Center on a Disc The expectation of distances on a disc: On a unit disc, what is the expected distance from a uniformly random point to its center? At a glance and letting…Quant Interview #disc#expectation
- 11Probability Analysis: Comparing X to 4Y in Random Variables Solve the following random variable comparison: what is the probability that X > 4Y if : 1. X, Y independent, standard normally distributed? 2. X, Y…Quant Interview #probabilities
- 12Drawing Cards for an Ace: Calculating Expectations Drawing cards from a standard shuffled poker deck, how many cards do you expect to draw until you get an ace? Introduction: This question was asked by one…Quant Interview #expectation
- 13Solving a Logarithm Inequality: Log vs Fraction Solve the logarithm inequality: which is higher, log₂(3) + log₃(2) or 13/6? Two methods — bounding with powers of 2 and 3, and algebraic manipulation via a quadratic.Quant Interview #numerical
- 14Plane Boarding Puzzle: Will the Last Person Get Their Seat? There are 100 people in line to board a plane that seats all of them. The first person in line is drunk and decides to take a random seat. Every person…Quant Interview #induction#probabilities
- 15Coin Flip Game: Can You Win with Fewer Tosses? Rick and Morty play a game where they flip 20 and 21 coins, respectively. What is the probability that Rick gets more heads? Introduction: As with most…Quant Interview #induction#probabilities
- 16Optimal Strategy in a Number Guessing Game You play a number guessing game in which you must pick a real number x, between 0 and 924. At the same time, the number y is uniformly and randomly…Quant Interview #expectation#game theory
- 17Max Chunks from 5 Cuts in a Sphere: Solving the Puzzle By cutting a sphere with five planes, what is the maximum number of resulting chunks you can obtain? Introduction: Most of the time, with this type of…Quant Interview #recurssion
- 18Squid Game Bridge: Calculating Survival Odds Ahead of the players is the Squid Game Bridge with 18 steps, each made of a pair of glass tiles: one of them can hold the weight of a player, while the…Quant Interview #probabilities#squid game
- 19Find the Guaranteed Majority Element in a Vector In a vector of length 2n, an element appears at least n+1 times. Find the most frequent element of the vector. Introduction: One obvious algorithm scans…Quant Interview #algorithms
- 20Calculating Odds for Third Player's Tennis Win Three equally skilled tennis players play in a tournament. After each round, the winner plays against the third player. The first to reach two consecutive…Quant Interview #probabilities
- 21Logical Pirates' Treasure Split: Who Gets What? A crew consisting of 3 democratic pirates finds a bounty of 100 coins. The strongest pirate must propose a bounty split and all pirates vote. If the vote…Quant Interview #game theory#induction
- 22Decoding IMO 1985's Simplest Geometry Problem A circle has its center on the side AB of the cyclic quadrilateral ABCD. The other three sides are tangent to the circle. Prove that AD + BC = AB…Math Olympiad #geometry
- 23Expected Rolls to See Every Number on a Die A fair 6-sided die is rolled until you get every number on the die. The order in which the numbers appear does not matter. What is the expected number of…Quant Interview #expectation
- 24Solving IMO 1984's Easiest Math Problem Prove that 0 ≤ yz + zx + xy − 2xyz ≤ 7/27, where x, y, z are positive real numbers with x + y + z = 1. A classic IMO 1984 inequality solved with AM-GM and Lagrange multipliers.Math Olympiad #inequality
- 25Expected Tosses for Three Consecutive Heads A fair coin is tossed repeatedly until three consecutive tosses are heads. What is the expected number of coin tosses? Solution: Let x be the expected…Quant Interview #expectation
- 26Grid Path Probability: Through the Center to Cheese A mouse starts at the bottom left corner of a [math]8 \times 6[/math] grid. At each step, he can only move RIGHT or UP, moving on the grid lines. He wants…Quant Interview #combinatorics#probabilities
- 27Analyzing 'South Park' for Stock Market Strategies - The Portfolio Is a South Park Stock Market trading strategy viable? After the previous post, we gathered the data needed to construct our portfolio. First, we will have…Python
- 28Investment Strategy for a Highly Volatile Stock For a given stock, you are certain that for the next 100 days, it will move either 10% up or 10% down each day. You can invest now, but if you choose to…Quant Interview #expectation
- 29Expected Sum of Distances in a Triangle In a triangle with sides 45, 60, respectively 75, what is the expected sum of distances from a point to its sides? Solution: Before we can actually find…Quant Interview #expectation
- 30Renault - an affordable rEVolution Renault - Passion for Life 🟩 Company Outlook Headquartered near Paris, the Renault group is made up of the namesake Renault marque and subsidiaries:…Stock Research
- 31Analyzing 'South Park' for Stock Market Strategies - The Data Is a South Park Stock Market trading strategy viable? In the following, we will use Python to get a list of all the mentions of public companies mentioned…Python #Python
- 32Smart Leverage Use on eToro: Key Considerations Things you need to consider when using leverage on eToro : Fees (aka the cost of capital/interest rate) While leverage fees vary from one stock to…Trading
- 33My Top Investment Pick: The Case for Orange (ORA.PA) Why is ORA.PA (Orange) my largest holding? 🟩 𝐂𝐨𝐦𝐩𝐚𝐧𝐲 𝐨𝐮𝐭𝐥𝐨𝐨𝐤 Operates in 27 countries, primarily providing telecom services, but recently…Stock Research
- 34Exploring Stock Merger Arbitrage: APHA/TLRY Case What is Stock Merger Arbitrage? What is Arbitrage? In economics, a strategy that takes advantage of a price difference between two or more markets is…Trading