The principle is simple - when a knight moves once, it lands on a square of a different colour; if it moves again, it is always on a square the same colour as the original one. Therefore all squares of a different colour to the original one will always require an odd number of moves to reach; all of the same colour an even number of moves (which means that all squares on the diagonals to the knight require an even number of moves; 1 square diagonally is not the only exception to your rule)!
Knight movements
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Some people might find this post to be rubbish, but I just could not hold it in either.
I have been studying the movements of the knight on the chess board for four solid months now, and have come to the conclusion that there is a certain pattern in which the knight can reach a certain square.
If we count the displacement of the distance of the squares from the knight, we will see that to reach a square even no. of blocks away, it takes an even no. of moves, and to reach a square odd no. of blocks away, it takes an odd no. of moves. I will elaborate the concept with the help of the following diagrams.
The knight is able to reach the one square distance on the diagonal in two steps.
I thank you for your patience in reading this, and would like you to single out any more exceptions in the knight movements.