Difference between revisions of "2014 AIME I Problems/Problem 5"
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== Problem 5 == | == Problem 5 == | ||
| + | Let the set <math>S = \{P_1, P_2, \dots, P_{12}\}</math> consist of the twelve vertices of a regular <math>12</math>-gon. A subset <math>Q</math> of <math>S</math> is called "communal" if there is a circle such that all points of <math>Q</math> are inside the circle, and all points of <math>S</math> not in <math>Q</math> are outside of the circle. How many communal subsets are there? (Note that the empty set is a communal subset.) | ||
== Solution == | == Solution == | ||
Revision as of 19:49, 14 March 2014
Problem 5
Let the set 
consist of the twelve vertices of a regular 
-gon. A subset 
of 
is called "communal" if there is a circle such that all points of are inside the circle, and all points of not in are outside of the circle. How many communal subsets are there? (Note that the empty set is a communal subset.)
Solution
See also
| 2014 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
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