__Puzzle:__

This problem is also called Jelly Beans problem. This is the most commonly asked interview puzzle.

You have 3 jars that are all mislabeled. One jar contains Apple, another contains Oranges and the third jar contains a mixture of both Apple and Oranges.

You are allowed to pick as many fruits as you want from each jar to fix the labels on the jars. What is the minimum number of fruits that you have to pick and from which jars to correctly label them?

Labels on jars are as follows:

__Puzzle Solution:__

Let’s take a scenario. Suppose you pick from jar labelled as Apple and Oranges and you got Apple from it. That means that jar should be Apple as it is incorrectly labelled. So it has to be Apple jar.

Now the jar labelled Oranges has to be Mixed as it cannot be the Oranges jar as they are wrongly labelled and the jar labelled Apple has to be Oranges.

Similar scenario applies if it’s a Oranges taken out from the jar labelled as Apple and Oranges. So you need to pick just one fruit from the jar labelled as Apple and Oranges to correctly label the jars.

We know that every jar has wrong label on it, now we know that “apple and orange” label jar is either apple or orange, so we will pick one fruit let suppose this fruit is an apple so the label of this jar should be “apple”, so now “apple and orange” jar is now —–> “apple” jar

then jar which labeled orange is “apple and orange” because we know that this jar has wrong label and we have already find the “apple” jar. so now orange jar is “apple and orange” jar and obviously “apple” jar is “apple and orange” jar.

The key is in picking first from the jar that is labelled “Apple & Oranges”. If you pick first from any of the other 2 jars, it will lead to confusion.

Who is the mathematician who came up with the 3 mislabeled jar problem?

What if we don’t know how if jars are mislabeled or not? Then how many fruits will it take to label it correctly?