This challenge is much simpler once you realize that you are working within an 8x8 grid and that the arrow reference direction changes based upon your immediately previous move.  I have tried to think of way to put this into words and nothing I think of seems to be adequate.  Open up a spreadsheet and create an 8x8 grid.  Your starting point on this is the upper right hand corner of the grid and your two opening moves are down or down-left.  Assume you go down on the first move the arrows change in a way that it appears that your current location has no relation to your original location and this is where you are wrong.  The arrows have reoriented themselves so that if you select the up arrow you will continue to move down the grid.  Essentially the entire grid just swung around 180 degrees.  Now if you continue to click the up arrow you will continue to go down on the grid.  The grid only reorients itself when you change directions.  It is a little tricky when you choose a diagonal direction because it reorients itself so that clicking the up arrow (assuming there is one available) would make you move diagonally.  If you keep moving around and mapping the available moves, you will eventually come up with all of the available moves.  During this process you will eventualy find the square that is the ending point because instead of saying out of time, the message will be "too many moves".  You then need to figure out how you can get from the starting spot to the finish spot in 10 moves.