Fast powers test

What is the fastest way to test if an int is a power of two?

Lots of 0's

How many zeros are on the end of n! ? Assume n is big. So n! is REALLY big.

What's wrong with...

...this code?

How many combinations?

A TripAdvisor Rubick's Cube has owl heads on it, which can be misoriented. How many (times) MORE combinations are there of this cube vs. one that has blank stickers?