Three boxes, three labels, and they're all wrong. With a single gesture—removing a single fruit from a single box—it is possible to know the contents of all three. The question is: from what box?
The three mislabeled boxes
Riddle statement
You have three closed boxes with these labels: “Apples”, “Oranges” and “Mixed”.
You know that all three labels are wrong.
You can take a single fruit out of a single box, without looking inside. How do you find out the correct contents of the three boxes?
Show solution
Solution
Answer: Take a fruit from the box labeled «Mixed».
Explanation:
As all the labels are false, that box cannot be mixed: it has to contain only one type of fruit.
If an apple comes out, that box is really the one with apples.
If an orange comes out, that box is really the of oranges.
From there, the other two are determined by discarding, remembering that their labels are also false. A single extraction is enough.