Penny Piles (Problem Solving)

Understand the problem: 

There are two drawers. The left drawer contains 64 pennies, and the right drawer is empty. With the following two operations:

L: if the left pile has an even number of pennies, transfer half of them to the right pile. If the left pile has an odd number of pennies, operation L is disallowed.

R: if the right pile has an even number of pennies, transfer half of them to the left pile. If the right pile has an odd number of pennies, operation R is disallowed.

Devise a plan:

To find out if it is possible to have 48 pennies in a drawer, we can carry out the two operations and see if we can make 48.

To try out if other numbers in the range of [0,64] are possible, we can draw a tree diagram to investigate all the different possibilities. Once an operation is carried out, it opens up two new possibilities. This kind of branching is perfect for a tree diagram. 

Carry out the plan: 
How to make 48:
Carry out L: 32  32
Carry out L again: 16  48 or Carry out R: 48  16

Other numbers in the range of [0,64]"

Note: I accidentally started the tree diagram off with no pennies in the left and 64 in the right instead of the other way around as presented in the problem. This does not affect the result because either way, the same numbers will be made. 

To check if all the numbers in the range of [0,64] are included, we only have to go through and check that the numbers in the range [0,32] are present in the tree diagram, as these numbers will pair up with a number in the range [32,64] because the total number of pennies in the drawer is always 64.

Conclusion:
It is possible to make 48, and all the other numbers in the range of [0,64].