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:
A.
B.
C.
D.
E.
Solution:
The top of the largest ring is above its bottom. That point is 2 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
OR
The required distance is the sum of the outside diameters of the 18 rings minus a 2-cm overlap for each of the 17 pairs of consecutive rings. This equals
The problems on this page are the property of the MAA's American Mathematics Competitions