You are on a grid, that looks like this:
01-02-03-04 | | | | 05-06-07-08 | | | | 09-10-11-12 | | | | 13-14-15-16
You start on 01, and you must end up on 16. You may go in any of the 4 directions (up, down, left, right). Easy, right? WRONG. Here's the catch:
If you go up, add where you end up. If you go down, subtract where you end up. If you go left, add 2. If you go right, subtract 2. You may start with any number, but you must end up with EXACTLY 0. Is it possible if you start with a running total of 0? If yes, how? If no, why? And which numbers can make it to 16 with 0? You may not use loops, because it's ridiculously easy to get to 0...(Example: if you want to get to 16 from 12, you must have 16, if you get there from 15, have 2)
Note: This is called Square of Numbers simply because there will be larger and larger squares each time we go up.