Mock AIME 1 2005-2006/Problem 1
Problem 1
points are evenly spaced on a circle. Given one point, find the maximum number of points that are less than one radius distance away from that point.
Solution
Number the points ,
,
,
. Assume the center is
and the given point is
. Then
=
, and we need to find the maximum
such that
degrees. This can be done in
divided by
\frac {1003}{3}
334.333\dots
n
1
335
p_2
p_3
p_335
334
2
p_1$, so the answer is \boxed{668}.