Pigeon Hole explanation I understand that the pigeonhole principle is supposedly a quite simple concept. However could you please explain to me the reasoning of how you reach this answer. Thank you.
Question: A basket cannot contain more than $24$ apples. What is the minimum amount of baskets you must have, to ensure you have at least $5$ baskets with the same number of apples in them (all baskets have at least $1$ apple contained within).
Answer of this question being $97$ baskets.

There are different versions of PigeonHole Principle, but they all basically amount to: 
if number of containers is exceeded by number of objects, then some container has something happen with certainty (or certain probability in a non-equiprobable case) 
The logic of this statement, can be done via repeated use of the pigeonhole principle with strict limits. If We have a container that can hold 24 baskets( last container can be partially filled), each one having a different number of objects, 1 through 24, it will take 5 of these large containers to have 5 baskets with the same amount at most. 4 large containers are not enough but 4 containers contain $4\cdot 24 =96$ baskets. only adding 1 more basket in a fifth container, forces a collection of 5. Because, each of the first 4 containers had a basket with each allowed amount in it. adding that basket gets us 97 baskets put into 5 containers. 
