Try to solve a game of consolidating numbers; see http://math.stackexchange.com/questions/1341929

Question1341929.java

import java.util.Arrays;

public class Question1341929 {
	public static void main (String [] args) {
		for (int n = 2;;n++) {
			int nslots = 2 * n - 1;
			int [] p = new int [nslots];
			int max = 0;
			int [] best = null;
			for (int bits = (1 << (nslots - 2));bits < 1 << (nslots - 1);bits += 2) {
				int hi = nslots - 1;
				int lo = 0;
				for (int i = nslots - 1;i >= 0;i--)
					p [i] = (bits & (1 << i)) != 0 ? hi-- : lo++;
				int value = value (p);
				if (value > max) {
					max = value;
					best = p.clone ();
				}
			}
			for (int i = 0;i < nslots;i++)
				best [i]++; // add 1 for humans
			System.out.println (n + " " + max + " " + Arrays.toString (best));
		}
	}
	
	
	static int max = 1000;
	static int [] v = new int [max];
	static int [] left = new int [max];
	static int [] right = new int [max];
	
	static int value (int [] p) {
		int n = (p.length + 1) >> 1;
		
		for (int i = 1;i <= n;i++)
			v [n + i - 2] = v [n - i] = i;
		
		for (int i = 1;i < p.length;i++) {
			left [i] = i - 1;
			right [i - 1] = i;
		}
		
		left [0] = right [p.length - 1] = -1;
		
		for (int i : p)
			play (i);
		
		return v [p [p.length - 1]];
	}
	
	static void play (int i) {
		play (i,left,right);
		play (i,right,left);
	}
	
	static void play (int i,int [] n1,int [] n2) {
		if (n1 [i] != -1) {
			v [n1 [i]] += v [i];
			n2 [n1 [i]] = n2 [i];
		}
	}
}