Difference between revisions of "2003 AMC 12A Problems/Problem 9"
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<math> \mathrm{(A) \ } 1\qquad \mathrm{(B) \ } 2\qquad \mathrm{(C) \ } 4\qquad \mathrm{(D) \ } 8\qquad \mathrm{(E) \ } 16 </math> | <math> \mathrm{(A) \ } 1\qquad \mathrm{(B) \ } 2\qquad \mathrm{(C) \ } 4\qquad \mathrm{(D) \ } 8\qquad \mathrm{(E) \ } 16 </math> | ||
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| + | == Solution == | ||
| + | If <math>(2,3)</math> is in <math>S</math>, then <math>(3,2)</math> is also, and quickly we see that every point of the form <math>(\pm 2, \pm 3)</math> or <math>(\pm 3, \pm 2)</math> must be in <math>S</math>. Now note that these <math>8</math> points satisfy all of the symmetry conditions. Thus the answer is <math>D</math>. | ||
Revision as of 10:45, 16 November 2008
Problem
A set 
of points in the 
-plane is symmetric about the orgin, both coordinate axes, and the line 
. If 
is in , what is the smallest number of points in ?
Solution
If is in , then 
is also, and quickly we see that every point of the form 
or 
must be in . Now note that these 
points satisfy all of the symmetry conditions. Thus the answer is 
.
