Mock AIME 1 2005-2006/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.
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 = = , so + = . We can choose , , , , so points. But we need to multiply by to count the number of points on the other side of , so the answer is .