Problem:
The square in the first diagram "rolls" clockwise around the fixed regular hexagon until it reaches the bottom. In which position will the solid triangle be in diagram
Answer Choices:
A.
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B.
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C.
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D.
E.
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Solution:
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Keep track of the "bottom" side of the square in the first figure. In the fourth figure, it will appear on the left, so the solid triangle will be in the position shown in .
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Each time the square "rolls" to the next edge of the hexagon, it turns through an angle of . In going from the top to the bottom of the hexagon, the square makes three such turns for a total of . This represents one complete revolution and of a second revolution.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions