Week 7 Worksheet - penny piles

We did a worksheet called "penny piles."

Here was the condition: You are sitting in front of two drawers. The left drawer contains 64 pennies, the right drawer contains nothing. Can you arrange things so that one of the drawers has 48 pennies, using combinations of the following two operations, l and r? 

l : If the left drawer has an even number of pennies, you may transfer half of them to the right drawer. If the left drawer has an odd number of pennies, operation l is disallowed. 

r: If the right drawer has an even number of pennies, you may transfer half of them to the left drawer the right drawer has an odd number of pennies, operation r is disallowed.

Choose another number in the range [0, 64]. 

Starting from the same initial position, can you arrange things so that one of the drawers has that number of pennies?

I started with [0,64] then I divided 64 by 2 then we had 32 and 32, so 64 became 32 and we added 32 to 0. As the result, we had [32,32]. We repeated the process again and again until we had number 1 (i.e: 1, 63)

Are there any numbers in that range that are impossible to achieve?

We could have any number from 0 to 64 because we were given the range [0,64]. From my solution, as it was shown below,  all the numbers from 0 to 64 were covered and achieved.

What about starting with a different number of pennies in the left drawer?

By starting with a different number of pennies in the left drawer, we would receive the same result.

My solution to this worksheet: