Find heavy bean in 18 with least weighs

This classic brainteaser is about using a balance scale in the most informative way to isolate a single heavy bean among many identical ones. It sits at the intersection of discrete math, information theory, and puzzle-style quant prep, making it a favorite in high-pressure quant interviews and assessment centers.

Working through this trains your sense of information efficiency: how to structure experiments so that each observation rules out as many possibilities as possible. It sharpens your ability to think in terms of logarithmic growth, base changes, and systematic elimination under strict resource limits, all central themes in advanced quant prep.

For quant interviews, this matters because it mirrors how quants design trading experiments, A/B tests, and diagnostic checks under data or time constraints. Interviewers use it to probe structured thinking, rigor, and comfort with abstract optimization.

What it tests

When a problem involves identifying a unique item with a distinguishing property (like being heavier) among otherwise identical items, and you have a tool (like a balance scale) that gives three possible outcomes per use, the optimal strategy is to maximize the information gained from each use by splitting the candidates into three nearly equal groups. Each weighing eliminates two-thirds of the possibilities, so the number of weighings required grows logarithmically with the number of items, specifically as $\lceil\log_{3}(n)\rceil$. This is because each weighing partitions the search space into three, and the process continues recursively until only one candidate remains. The reason this works is that the balance scale's trinary outcome matches the logic of base-3 search, allowing you to systematically and efficiently narrow down the possibilities.