Find the maximal size of a subset of Z_3^3 without a line; see http://math.stackexchange.com/questions/201994/center-of-mass-of-triangle

Question201994.java

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

public class Question201994 {
    public static void main (String [] args) {
        List<Integer> masks = new ArrayList<Integer> ();
        for (int bits = 0;bits < 1 << 27;bits++) {
            int count = 0;
            int r1 = 0;
            int r2 = 0;
            int r3 = 0;
            for (int bit = 0;bit < 27;bit++)
                if ((bits & (1 << bit)) != 0) {
                    count++;
                    r1 += bit;
                    r2 += bit / 3;
                    r3 += bit / 9;
                }
            if (count == 3 && r1 % 3 == 0 && r2 % 3 == 0 && r3 % 3 == 0)
                masks.add (bits);
        }

        int max = 0;
        outer:
        for (int bits = 0;bits < 1 << 27;bits++) {
            for (int mask : masks)
                if ((bits & mask) == mask)
                    continue outer;
            int count = 0;
            for (int bit = 0;bit < 27;bit++)
                if ((bits & (1 << bit)) != 0)
                    count++;
            max = Math.max (max,count);
        }

        System.out.println ("maximal number of points without line: " + max);
    }
}