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. If the right drawer has an odd number of pennies, operation r is disallowed
1. Understanding the Problem:
- There are two drawers, the left one has 64 pennies and the right has 0.
- what I need to do is let one of the drawers has 48 pennies by using L and R operations
- The question is possible to satisfy the condition
2. Devising a Plan:
- I have seen it when I was studying math in primary school
- It likes a tree diagram problem, so I can draw it on the paper to solve the problem
- Or I can use 64 pennies and do the operations
3. Carrying out a plan:
- First, because the left drawers has 64 pennies and it is an even number, so I will start the left operation by transferring half of them to the right drawer. As a result, right drawer and left drawer both have 32 pennies now.
- Then, 32 is still an even number soI will do the operation again so that the left drawer will have 16 pennies and the right drawer has 48 pennies. Problem solved.
- 64 0
- 32 32
- 16 48
4. Looking back:
- If the operation was continued, it would be a very long process
- To draw a tree diagram or do it are very helpful for this problem
- If the number is not 48 or it was a hard number like 48.35829820483... it may be difficult to get the correct number of pennies and solve the problem. But the solutions are the same