Fruit Bag Mix-Up Minimal Sampling

This brain teaser presents three mislabeled bags of fruit and asks for the minimal information needed to fix all the labels. The puzzle is about exploiting the fact that every label is known to be wrong, and that the contents must come from a small, fixed set of possibilities. The candidate has to reason about how one carefully chosen observation can unlock the entire configuration, rather than trying to brute-force check each bag. It is a typical logic and lateral-thinking question often seen in casual interviews, puzzle contests, and warm-up rounds for more technical assessments.

Solving it leans heavily on combinatorial reasoning, the pigeonhole principle, and the logic of mutual exclusivity. The efficient approach requires viewing each label as negative information and using that to constrain the possibilities before drawing anything. Interviewers look for clarity of thought, the ability to minimize redundant checks, and comfort with reasoning under constraints. They pay attention to whether the candidate can articulate why a single targeted sample is enough and how that observation forces all remaining labels to fall into place.

What it tests

This problem class is governed by the logic of forced elimination under constraint: when each item is uniquely mislabelled, every label provides negative information about its true contents. The key is that the system is overdetermined: knowing that all labels are wrong, and that there are only three possible arrangements, any single positive identification (like drawing a fruit) triggers a cascade of deductions. The principle holds because the constraints are mutually exclusive and collectively exhaustive: once one identity is fixed, the others must fall into place by process of elimination. This is a classic example of using contradiction and the pigeonhole principle in tandem: by ruling out the impossible, the possible must be true, even if it is not directly observed.