Why is it so difficult to find a nonce while validating a block in Bitcoin

Question

I know that a block is based on a random number called a nonce that is unknown to the miner. Then how is that number actually verified as the correct nonce and not some arbitrary number? And why is it so difficult to determine?

Answer 1

A nonce is just "some arbitrary number". In order to understand how it is found, you have to understand the hashing process by which blocks are produced. 

Cryptographic hashes are a mathematical way of turning any set of data into a random number, called a hash. This is a one way process, that is, it's easy to calculate the hash of some value but the vice versa - to find a value with a specific hash - is impossible to determine.

Having even a slightly different set of value will produce a totally different hash, and so that the only way to find a hash with a particular property is to calculate them again and again till the miner gets lucky!

So when a miner is checking billions of hashes per second, they are actually changing the nonce to something else, then checking the hash of the whole block; then changing the nonce to something else, then checking the hash of the (now slightly different) block; then changing the nonce again, and so on. You get the idea.