user12048: For example, a knight can go from b1 to d5 in 2 moves and in many other routes by an even number of moves. However, can it go to d5 in an odd number of moves?
I was wondering this because it would give me a little bit of insight into some theory.
Any help would be appreciated. Thank you.

user3270: No. There's a fairly simple proof by looking at the square colors: they alternate each move. That means the parity of the move count to travel between two squares is fixed.

12048: <p>For example, a knight can go from b1 to d5 in 2 moves and in many other routes by an even number of moves. However, can it go to d5 in an odd number of moves?</p>

<p>I was wondering this because it would give me a little bit of insight into some theory.</p>

<p>Any help would be appreciated. Thank you.</p>
 3270: <p>No. There's a fairly simple proof by looking at the square colors: they alternate each move. That means the parity of the move count to travel between two squares is fixed.</p>
