In the fruit question you missed a key part of the question. All buckets a mislabelled. The answer is to pick from the mixed bucket (it has to either be apple or orange because of the mislabelling), you now know whichever fruit you chose is in this bucket. We'll pick an orange for clarity. So at this point the bucket labelled "mixed" is known to actually be the bucket of oranges, and we have 2 more mislabelled buckets. Because we know they are all mislabelled, it would be safe to say the "apple" labelled bucket does not contain apples, plus we know it can't be the orange bucket either. This must be the mixed bucket, which leaves the basket labelled oranges to actually be mixed.