Find the maximum size of an intersecting antichain on a set of n elements; see http://math.stackexchange.com/questions/1825450.

Question1825450.java

import java.util.ArrayList;
import java.util.List;

public class Question1825450 {
	public static void main (String [] args) {
		for (int n = 1;;n++) {
			int nsubsets = 1 << n;
			int max = 0;
			outer:
			for (long bits = 0;bits < 1L << nsubsets;bits++) {
				int bitCount = 0;
				for (int j = 0;j < nsubsets;j++)
					if (((bits >> j) & 1) == 1)
						bitCount++;
				if (bitCount > max) {
					List<Integer> subsets = new ArrayList<Integer> ();
					for (int j = 0;j < nsubsets;j++)
						if (((bits >> j) & 1) == 1)
							subsets.add (j);
					for (int i = 1;i < subsets.size ();i++) {
						int ai = subsets.get (i);
						for (int j = 0;j < i;j++) {
							int aj = subsets.get (j);
							if ((ai & aj) == 0 || (ai | aj) == ai || (ai | aj) == aj)
								continue outer;
						}
					}
					max = bitCount;
				}
			}
			
			System.out.println (n + " : " + max);
		}
	}
}