Flag:b64_bz_unwrap

Challenge 1:
Let f(n) be the number of 1s in the binary representation of n^13 + 12 where ^ denote exponent

Let g(n,1) = f(n),
    g(n,2) = f(f(n)),
    g(n,3) = f(f(f(n))), etc.

Find g(3,2^48).

Provide the solution and your code used to find it.


Challenge 2:
There is a long line of bowls with a machine next to each. When bowl[i] has more than 14 M&Ms, the machines take 3 seconds to divide them as follows:
1. N = bowl[i]
2. Simultaneously
   A. bowl[i-1] += N/2 (round down)
   B. bowl[i+1] += N/2 (round down)
   C. bowl[i]    = N mod 2
3. Rest

All bowls start empty. One bowl labeled "B", gets a new M&M every hour. A bowl may receive M&Ms from up to three machines at a time.

How many days will pass before the machines take a full hour to settle from the chain reaction caused by adding an M&M to B?

Provide the solution and your code used to find it.