I believe the answer is '0' , start by using a gris 2 x 2, you cannot possibly get to the opposite corner by using all nodes. the same is true for a 4 x 4 grid and also a 6 x 6. This can be proven by coloring points alternatively black and white. On an even sided grid, any trip should start at one color and end at the other -- but since opposite corners have the same color, this isn't possible. |