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?

  • SilverLous [comrade/them]@hexbear.netB
    1·
    7 days ago

    doesn’t visit usually mean “ends movement in that square”? 'Cause that means skipping squares is allowed. So just fill out the board until the last row and skip ahead of the end tile while doing so. Do the last row in an order that the last col is the same col as the end square, move to end square.