How do you escape the circle?
Company: Morgan Stanley
Role: Data Scientist
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Technical Screen
A dog runs continuously along the boundary of a circle of radius 1 at speed 4. You start at an arbitrary point strictly inside the circle and can run at speed 1 anywhere inside the disk.
If the dog is at the same boundary point at the instant you reach the boundary, you are caught. Otherwise, if you reach an unoccupied boundary point, you immediately escape.
Can you guarantee escape? If yes, describe a strategy and justify why it works.
Quick Answer: This question evaluates spatial reasoning, continuous pursuit-evasion strategy and mathematical proof skills, requiring geometric insight and analysis of relative motion in a continuous setting.