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University of South Carolina High School Math Contest/1993 Exam/Problem 21

Revision as of 10:51, 23 July 2006 by Joml88 (talk | contribs)

Problem

Suppose that each pair of eight tennis players either played exactly one game last week or did not play at all. Each player participated in all but 12 games. How many games were played among the eight players?

$\mathrm{(A) \ }10 \qquad \mathrm{(B) \ }12 \qquad \mathrm{(C) \ }14 \qquad \mathrm{(D) \ }16 \qquad \mathrm{(E) \ }18$

Solution

There are ${8\choose 2}-12=16$ games.

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