# Is it possible to settle k children on n seats carousel to be balanced?

I have a question. I have to find out if there is some way(if it's possible) to settle k children on the carousel with n seats to have a balanced carousel. Is there some formula? The only pattern I can see here is that when the number of seats is a prime number, there are just two ways for children when there are none or as many as the number of seats. I draw a table

``````n\k 0 1 2 3 4 5 6 7 8 9 10
2   o - o
3   o - - o
4   o - o - o
5   o - - - - o
6   o - o o o - o
7   o - - - - - - o
8   o - o - o - o - o
9   o - - o - - o - - o
10  o - o - o o o - o - o

``````

All I can now know is if the carousel is balanced. But I also don't think it's necessary.

``````    static final double eps = 0.0001;
public static boolean balanced(int[] carousel) {
double sumX = 0;
double sumY = 0;
for(int i = 0; i < carousel.length; i++) {
if (carousel[i]>0) {
double alpha = i*2* Math.PI/n;
sumX += Math.cos(alpha);
sumY += Math.sin(alpha);
}
}
return Math.abs(sumX) < eps && Math.abs(sumY) < eps;
}
``````