Problem:
A frog located at , with both and integers, makes successive jumps of length 5 and always lands on points with integer coordinates. Suppose that the frog starts at and ends at . What is the smallest possible number of jumps the frog makes?
Answer Choices:
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B.
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E.
Solution:
Because , the smallest number of jumps is at least 2 . The perpendicular bisector of is the line with equation , which has no points with integer coordinates, so 2 jumps are not possible. A sequence of jumps is possible; one such sequence is to to to .
The problems on this page are the property of the MAA's American Mathematics Competitions