Three jars, all labeled wrong, and one peek inside fixes every label
Three jars sit on a shelf, one holding only apples, one holding only oranges, and one holding a mix of both. Every single label is wrong; none of the three jars holds what its label claims. You may pull out and look at exactly one piece of fruit from exactly one jar of your choosing, without looking inside the jar itself. Which jar do you pick, and how do you correctly relabel all three?
Reveal the answer
Pick a piece of fruit from the jar labeled 'Mixed'. Since every label is wrong, that jar cannot actually be mixed, so it must hold only whichever fruit you just drew, apples or oranges; relabel it accordingly. The jar labeled with the fruit you didn't draw cannot actually hold only that fruit either, since its label is also wrong, so it must be the mixed jar. The remaining jar gets the last label by elimination. One fact, that all labels are false, turns a single observation into complete information about all three containers.