Bite-sized brain teaser to solve in a minute or less.
The Mislabeled Jars
Category: Logic, Deduction
Three jars are labeled “Apples,” “Oranges,” and “Apples & Oranges,” but all labels are incorrectly placed. You may draw just one fruit from one jar (without looking) to fix all labels. Which jar do you pick from, and how do you relabel all jars correctly?
Solution
Since all labels are incorrectly placed:
The jar labeled "Apples & Oranges" contains either apples or oranges.
The jar labeled "Apples" contains either oranges or both types of fruit.
The jar labeled "Oranges" contains either apples or both types of fruit.
How to determine the correct jars:
Pick from the “Apples & Oranges" jar.
Since the label is incorrect, it contains only one fruit type.
If you draw an apple, this jar is the “Apples” jar.
If you draw an orange, this jar is the “Oranges” jar.
Second jar:
If the “Apples & Oranges" jar contains apples then the oranges have to be in the jar labeled "Apples" since they cannot be in the jar labeled "Oranges." In that case, the "Apples" jar must be labeled "Oranges."
If the “Apples & Oranges" jar contains oranges then the apples have to be in the jar labeled "Oranges" since they cannot be in the jar labeled "Apples." In that case, the "Oranges" jar must be labeled "Apples."
Third jar:
The remaining jar will contain both types of fruit and must be labeled "Apples & Oranges."
