Problem:
Greta Grasshopper sits on a long line of lily pads in a pond. From any lily pad, Greta can jump pads to the right or pads to the left. What is the fewest number of jumps Greta must make to reach the lily pad located pads to the right of her starting position?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
An optimal strategy would be jumping as close as possible with the right jumps and then fine tuning with the left jumps. It will take at least jumps to get to . Clearly, we cannot get to in one more jump, so cannot be right. With jumps, the only way to move forward is with jumps right and the one jump left, but that puts us at . This shows that cannot happen. Using jumps, we can jump right twice and jump left thrice, but that puts us at . Jumping right thrice and left twice would put us at . This shows that cannot happen either. Finally, with jumps, we can jump right thrice and left four times, putting us at .
Thus, is the correct answer.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions