Number of possible cycles in collatz conjecture I had been following all the blogs, but I would like to understand, whether an attempt has been made to understand how many cycles are possible apart from the 1-4-2-1 cycle in collatz problem

A cycle other than the $1-4-2-1$ cycle has not been found. If such a cycle was found, then the conjecture would be disproved. 
If it was proven that no such cycles exist, then the conjecture would still not be solved, since there could be initial values of $n$ for which the recursion diverges.

This is an open problem. Some results regarding cycles of specific types have been proven. 
