Brainteasers from Interviews - Part 2

150 Most Frequently Asked Questions on Quant Interviews

by Dan Stefanica, Rados Radoicic, and Tai-Ho Wang, second edition, FE Press 2019, 281 pages

Probability and Stochastic Calculus Quant Interview Questions

by Ivan Matic, Rados Radoicic, and Dan Stefanica, FE Press 2021, 334 pages

Challenging Brainteasers for Interviews

by Rados Radoicic, Ivan Matic, and Dan Stefanica, FE Press 2023, 345 pages

Problem 1. A room has \(n\) computers, less than half of which are damaged. It is possible to query a computer about the status of any computer. A damaged computer could give wrong answers. How can you discover an undamaged computer?

Problem 2. You are given three piles with \(5\), \(49\), and \(51\) pebbles respectively. Two operations are allowed:
  • (i) merge two piles together, or
  • (ii) divide a pile with an even number of pebbles into two equal piles.
Is there a sequence of operations that would result in \(105\) piles with one pebble each?

Problem 3. The new campus of University College is a perfect disk of radius \(1\)km. The Coffee Company plans to open \(7\) coffee shops on campus. Where do they have to be placed in order to minimize the maximum (straight-line) distance that a person anywhere on the campus has to walk to find a coffee shop?

Problem 4. Compute the integral \[ \int_{0}^{\frac{\pi}{2}} \ln{(\sin{x})} \,dx. \]

Problem 5. A bug starts at the vertex \(A\) of a triangle \(ABC\). It then moves to one of its two adjacent vertices. How many paths of length \(8\) end back at vertex \(A\)? For example, one such path is \(ABCABCABA\).