2006 SMT/General Problems/Problem 16
Problem
Points are placed on a circle with center such that and for all positive integers . What is the smallest for which ?
Solution
The condition we are looking for is , because if any other , than must be a multiple of 360. This is because the central angle formed between two consecutive points is 110 degrees, and because we have rotated times by the time we place .
We want the first that satisfies the conditions from the problem, therefore, our answer is or