So mining bitcoin is baced on the SHA-256 algortiem

 is it posible to Guess a random number and do the SHA-256 and then enter the result on the bitcoin website ( witch I do'nt know the url or any thing about it but there probebley is somthing like it ) and then if the number is corect the reward will be given.

 or maybe is there a way to just solve math problems on a paper to mine bitcoin?