Problem:
In the pattern below, the cat moves clockwise through the four squares and the mouse moves counterclockwise through the eight exterior segments of the four squares.
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If the pattern is continued, where would the cat and mouse be after the th move?
Answer Choices:
A.
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Solution:
There are four different positions for the cat in the array, so after every fourth move, the cat will be in the same location. Because , the cat will be in the rd position clockwise from the first, or the lower right quadrant. There are eight possible positions for the mouse. Because , the mouse will be in the th position counterclockwise from the first, or the left-hand side of the lower left quadrant.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions