Optimal Egg Drop Strategy for 100 Floors

This classic quant interview question is about designing an optimal testing strategy under uncertainty with limited resources. You must balance exploration and conservatism while planning for the worst case, not the average. It sits at the intersection of discrete optimization, combinatorics, and game-theoretic reasoning, making it a staple in quant prep and a favorite in the industry.

It trains your ability to formalize a vague puzzle into a rigorous optimization problem, reason about worst-case outcomes, and work backwards from a performance target. You practice turning intuition about "risking a failure" into a structured search policy and recognizing patterns that emerge from careful counting and bounding arguments.

This matters in quant interviews because real trading, risk management, and model calibration involve sequential decisions with finite budget: time, capital, and data. Interviewers use it to see whether you can design efficient adaptive experiments, justify tradeoffs, and articulate a clear, logically consistent strategy under constraints.

What it tests

This class of problems is governed by the principle of minimizing the worst-case number of trials in a sequential search with limited resources, using adaptive step sizes. The key insight is that when you have a limited number of 'failures' (like eggs that can break), you want each test to maximize information gained while preserving enough resources for subsequent finer searches. The optimal approach is to use the first resource (egg) to partition the search space into intervals that shrink as you proceed, so that no matter when the first failure occurs, the remaining search with the second resource never exceeds the total drop budget. This leads to a triangular number structure: the sum of the decreasing intervals must cover the entire search space, ensuring that the worst-case scenario is as favorable as possible. The pattern holds because each additional drop allows you to check one more floor than before, balancing the risk of early failure against the need to cover all possibilities.