Understand the problem
Left drawer has 64 pennies and the right one has none.
1. First Question
Can you arrange things so that one of the drawers has 48 pennies, using the following two operations:
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.
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.
2. Second Question
What about arranging things so that one of the piles has other numbers in the range [0,64]
3.Third Question
What about starting with a different number of pennies in the left drawer?
Devise a plan
Work Backwards
Carry out the plan
First Question
48 - 16
48 - 16
32 - 32
64 - 0
Second Question/Third Question: You can still be successful.
34 - 30
60 - 4
62 - 2
63 - 1
64 - 0
Look back
Pretty simple after using the hint of working backwords.
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