Optiver–styleQuant ResearcherQuantitative ResearcherQuestion #108
What is the expected number of moves required to exit the center of a 10x10 grid, assuming you can move one step in a random direction (up, down, left, right) at each move?
Build Your Approach
State the assumptions, try a simple case, then work toward a general solution. Check the result and explain how it changes if an assumption changes.
Try the free diagnostic with worked solutions →Get Free Interview Prep Resources
More Optiver–Style Quant Researcher Questions
You throw a standard die repeatedly, keeping a running total of the sums. What is the probability that when the running total exceeds 100 for the first time, the last die throw is a 2?Six dice are rolled simultaneously. What is the probability that the sum of the numbers shown is an even number?Provide a formal proof for the following: You have two groups of marbles—one group with 1 marble and the other with 2^n marbles. At each step, you can double the size of one group by taking marbles from the other group. Is it possible to reach a state where one group has 0 marbles and the other has 2^n + 1 marbles?What is the expected number of card draws before encountering an Ace in a standard 52-card deck, assuming cards are drawn one at a time without replacement?What is the probability that, given a random number from 1 through 1,000,000, the digit 7 appears at least once in the selected number?
Practice the Reasoning Behind the Answer
Bring your target roles and interview timeline to a free quant consult. Discuss your preparation priorities and how Quant Blueprint’s lessons, practice and mock interviews can help.
Book a Free Quant ConsultYour goals · your preparation · your next steps