Define the function f(n):N→N as follows:
f(n)={n2+12n if n is odd , if n is even .
For how many integral n∈[1,100] does f(f(...f(n)))=1 for some number of applications of f?
This problem is taken from this year's MATHCOUNTS State Competition. I enjoyed solving it, so I'm sharing it with you! Enjoy solving it, and post a creative solution!