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The Medal Count
In a 4 person race, medals are awarded to the fastest 3 runners. The
first-place runner receives a gold medal, the second-place runner receives a
silver medal, and the third-place runner receives a bronze medal. In the event
of a tie, the tied runners receive the same color medal. (For example, if there
is a two-way tie for first-place, the top two runners receive gold medals, the
next-fastest runner receives a silver medal, and no bronze medal is awarded).
Assuming that exactly three medals are awarded, and that the three medal
winners stand together with their medals to form a victory circle, how many
different victory circles are possible?
(A) 24
(B) 52
(C) 96
(D) 144
(E) 648
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