Can a knight jump into a square in both an odd and even number of moves?

Question

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.

Answer 1

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.