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?