slog 8

Today I worked on solving the problems that Professor Heap posted. One of the problem solving questions was: "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?"
The steps to correctly and accurately solving a problem are: understanding the problem, devising a plan, carrying out the plan, looking back and figuring out when and how you're stuck.
To understand the problem and devise my plan, I had to read and understand the two operations L and R. These two operations state:
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. If the right drawer has an odd number of pennies, operation R is disallowed.
In order to figure out this problem I got a piece of paper and wrote down L and R on a piece of paper. I put 64 on the left side, and 0 on the right. Since the left side had an even number of pennies, I transferred half of the pennies to the right side, using operation L. Now, each drawer would contain 32 pennies. Then I performed operation R and transferred half of the 32 pennies from the right drawer into the left drawer. This left 16 pennies in the right drawer and 48 pennies in the left drawer.
I played around with this pattern using different numbers, and found that it did not work for many of them. For example, if you have 28 pennies in the left and 0 in the right, splitting up the pennies eventually leads to there being odd numbers of pennies in each drawer, therefore you can no longer carry out either of the operations.