Extracting rightmost N bits of an integer

Question

In the yester Code Jam Qualification round http://code.google.com/codejam/contest/dashboard?c=433101#s=a&a=0 , there was a problem called Snapper Chain. From the contest

Answer 1

I think we can recognize this kind of problem by calculating the answer by hand first, for some series of N (for example 1,2,3,..). After that, we will recognize the state change and then write a function to automate the process (first function). Run the program for some inputs, and notice the pattern.

When we get the pattern, write the function representing the pattern (second function), and compare the output of the first function and the second function.

For the Code Jam case, we can run both function against the small dataset, and verify the output. If it is identical, we have a high probability that the second function can solve the large dataset in time.