Let's say I have a collection of $2^n$ labeled objects, and I want to find one of them. If I can ask yes-no questions about it, binary partition would immediatly lead us to the desired object in $n$ steps. But what if noise is introduced in our search?
For example, what would be the lowest number of searches so that we can always resist at most a single error for a given $n$? Two? $m$ errors? And finally, is this linkeable with error correcting codes theory?
This is the problem of "Searching with Lies", first posed by Ulam. Near-optimal solutions exist using error-correcting codes, but the exact answer is known only for very small number of lies and is a combinatorial tour de force. More details in earlier answer here:
What is the least amount of questions to find out the number that a person is thinking between 1 to 1000 when they are allowed to lie at most once