How many steps does a knight need to reach the bottom right square from the opposite top left square on a 101x101 board?
I am sure that he needs 67 steps or more because the sum of the coordinates of the starting square is 1+1=2 and the sum of the coordinates of the target square is 101+101=202. (So the difference is 200.) In each step the sum of the coordinates increases by (maximum) 3. So he needs at least 67 steps. I think 67 steps is not enough, but I can't prove how many he n.eeds
Any help would be appreciated!