Exploring a Hexagon

What this random walk on a hexagon interview question tests

This is a medium-difficulty probability question commonly used by quantitative trading and financial engineering firms to assess whether you can set up and solve an expected return time problem on a finite, symmetric graph. It rewards both careful problem formulation and correct application of probability theory.

To solve problems like this, candidates typically model the particle's state space, exploit symmetry to reduce the number of unknowns, and set up a system of linear equations relating expected hitting times. The key insight is recognizing which states are equivalent under the problem's symmetry, then solving for the expected return time to the origin. Interviewers value clear state definitions and logical equation setup as much as the final numerical answer.

• Markov chains and state transitions
• Expected value and first-passage time
• Symmetry and state reduction
• Systems of linear equations