This question was posed to me, and I was surprised that I could not find a solution (as I thought that all rook tours [open or closed] were possible). Starting from a8, could a rook visit every square on the board once, ending on f3?
I tried a few times, with a few different strategies, but I always ended up missing one square.
It’s really easy to burn pairs of rows or columns, so the problem space could be reduced…
…but at some point (4x4), I was able to convince myself that it is impossible (at least at this size and state):
…but it might be possible that shaving off column or row pairs is also discarding a solution?
Did you start from the square labeled “end”?
Don’t think of it as the number being the order of the steps, think of it as being how many are left lol