Three Fruit basket puzzle (Baskets of apples, oranges & mixed fruits)

Three Fruit basket puzzle:

There are 3 baskets or boxes containing apples, oranges and mixed fruits (apples and oranges).

• Apple baskets containing apples.
• Orange baskets containing oranges.
• Mixed baskets containing both apples and oranges.

All baskets are labelled wrongly i.e. basket containing apples may be labelled either as orange or mixed and similarly basket containing mixed may be labelled either oranges or apples etc.

Constraint:

• You are allowed to pick only one fruit from any basket

You need to put the correct labels, on all baskets or boxes. How can you achieve it?

Solution to three fruit basket puzzle:

1. As all the baskets are labelled incorrectly, The basket labelled as ‘mixed’ does not contains the mixed fruits.
   • Basket labelled (‘mixed’) will either contain oranges or apples.
   • Pick any fruit from basket (labelled as ‘mixed’).
   • Suppose the picked up fruit is orange, then it is a basket of oranges.
     • If picked up fruit is apple, then basket is containing apples.
   • We assumed that picked up fruit is orange, then ‘mixed’ labelled basket is actually containing oranges.
2. Now, let us move towards the basket, which is labelled as ‘apple’.
   • We have already identified the ‘oranges’ in step 1.
   • The basket labelled ‘apple‘, will not be contains apple fruits
     • As the labels are incorrect on all baskets.
     • ‘apple’ basket will contain either oranges or mixed fruits.
     • As we have already identified oranges earlier (Point no 1), so ‘apple’ basket will contain ‘mixed’ fruit.
   • Looking at above assertions, We are sure that ‘apple’ basket will  actually contains ‘mixed’ fruits.
   • So, we have identified the correct apple fruits.
3. Now, let us move towards the basket, which is labelled as ‘oranges’.
   • We have already identified
     • ‘mixed’ label basket is containing oranges (Point no 1)
     • ‘apples’ label basket is containing mixed fruit(Point no 2)
   • The basket labelled with ‘oranges’ will contains the apple fruits.

We have correctly identified all baskets, containing the actual fruits.