Difference between revisions of "University of South Carolina High School Math Contest/1993 Exam/Problem 21"
| Line 1: | Line 1: | ||
== Problem == | == 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? | ||
| − | <center><math> \mathrm{(A) \ } \qquad \mathrm{(B) \ } \qquad \mathrm{(C) \ } \qquad \mathrm{(D) \ } \qquad \mathrm{(E) \ } </math></center> | + | <center><math> \mathrm{(A) \ }10 \qquad \mathrm{(B) \ }12 \qquad \mathrm{(C) \ }14 \qquad \mathrm{(D) \ }16 \qquad \mathrm{(E) \ }18 </math></center> |
== Solution == | == Solution == | ||
| + | There are <math>{8\choose 2}-12=16</math> games. | ||
== See also == | == See also == | ||
* [[University of South Carolina High School Math Contest/1993 Exam]] | * [[University of South Carolina High School Math Contest/1993 Exam]] | ||
Revision as of 20:07, 22 July 2006
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?
Solution
There are 
games.
