Quick Java solution to:

http://beust.com/weblog/2011/10/30/a-new-coding-challenge

@Test
    public void doIt() {
        final int n = 40;
        int[] max = new int[5];
        for (int i = 1; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                for (int k = j + 1; k < n; k++) {
                    for (int l = k + 1; l < n; l++) {
                        final int v = cnt(new int[]{i, j, k, l});
                        if ( v > max[0] ) {
                            max = new int[] {v,i,j,k,l};
                        }
                    }
                }
            }
        }
        System.out.println( " max: " + max[0] + " (" + max[1] + ", " + max[2] + ", " + max[3] + ", "
 + max[4] + ")" );
    }

    public int cnt( final int[] a ) {
        int cnt = 0;
        for (int p = 1; p <= 40; p++) {
            boolean b = false;
            for (int i = 0; i < 4; i++) {
                b = b || p == a[i];
            }
            for (int i = 0; i < 4; i++) {
                for (int j = i + 1; j < 4; j++) {
                    b = b || p == a[i] + a[j];
                    b = b || p == a[i] - a[j];
                    b = b || p == a[j] - a[i];
                }
            }
            for ( int i = 0; i < 4; i++ ) {
                for ( int j = i + 1; j < 4; j++ ) {
                    for ( int k = j + 1; k < 4; k++ ) {
                        b = b || p == +a[i]+a[j]+a[k];
                        b = b || p == +a[i]+a[j]-a[k];
                        b = b || p == +a[i]-a[j]+a[k];
                        b = b || p == -a[i]+a[j]+a[k];
                        b = b || p == -a[i]-a[j]+a[k];
                        b = b || p == -a[i]+a[j]-a[k];
                        b = b || p == +a[i]-a[j]-a[k];
                    }
                }
            }
            b = b || p == +a[0]+a[1]+a[2]+a[3];
            b = b || p == -a[0]+a[1]+a[2]+a[3];
            b = b || p == +a[0]-a[1]+a[2]+a[3];
            b = b || p == +a[0]+a[1]-a[2]+a[3];
            b = b || p == +a[0]+a[1]-a[2]-a[3];
            b = b || p == -a[0]-a[1]+a[2]+a[3];
            b = b || p == -a[0]+a[1]-a[2]+a[3];
            b = b || p == -a[0]+a[1]+a[2]-a[3];
            b = b || p == +a[0]-a[1]-a[2]+a[3];
            b = b || p == +a[0]-a[1]+a[2]-a[3];
            b = b || p == +a[0]+a[1]-a[2]-a[3];
            b = b || p == +a[0]-a[1]-a[2]-a[3];
            b = b || p == -a[0]+a[1]-a[2]-a[3];
            b = b || p == -a[0]-a[1]+a[2]-a[3];
            b = b || p == -a[0]-a[1]-a[2]+a[3];
            cnt += b ? 1 : 0;
        }
        return cnt;
    }