Problem:
A particle moves through the first quadrant as follows. During the first minute it moves from the origin to . Thereafter, it continues to follow the directions indicated in the figure, going back and forth between the positive and axes, moving one unit of distance parallel to an axis in each minute. At which point will the particle be after exactly minutes?
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Answer Choices:
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Solution:
If is even, after minutes all the lattice points of the square have been visited, and the particle is at . Now, , and . After 1936 minutes the particle is at minutes later its location is , and 9 minutes after that it is at .