Problem:
A number of linked rings, each thick, are hanging on a peg. The top ring has an outside diameter of . The outside diameter of each of the other rings is less than that of the ring above it. The bottom ring has an outside diameter of . What is the distance, in , from the top of the top ring to the bottom of the bottom ring?
Answer Choices:
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B.
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E.
Solution:
The top of the largest ring is above its bottom. That point is below the top of the next ring, so it is above the bottom of the next ring. The additional distances to the bottoms of the remaining rings are . Thus the total distance is
The required distance is the sum of the outside diameters of the rings minus a overlap for each of the pairs of consecutive rings. This equals
The problems on this page are the property of the MAA's American Mathematics Competitions