The following is an example of looking at something in a totally new way and using a totally different logic set to come up with an answer to an otherwise very difficult problem. I am going to give you a series of numbers. There are two questions. 1) What is the next number in this sequence 2) What is the function that produces these numbers 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, ? This problem is rated "genius" level for ingenuity. Good luck.
I solved it in my head using matricies, therefore it would be difficult (and time consuming) to stipulate a formula. My number came out to be: 111113113221 am i correct? if not, i will do it again on paper (i'm afraid i mixed up a number in my head somewhere)