Rook's Tour

Fremen

Right, I'm stuck on a problem which I won't get a solution to for a week. The damn thing's going to be stuck in my head until I get a solution, and I have better things to do this week.

Here's where YOU come in. Let's see if you can't help me with my sums, Hrrgh?

Consider an 8x8 chessboard and a piece, R, that starts at the lowest left square and takes a tour of the board, visiting each square, never visiting a square twice, and ending up at the starting square. Each move goes from a square to an adjacent square in either the horizontal or vertical direction. Thus the tour requires 64 moves. Is it possible that in such a tour R takes the same number of horizontal moves as vertical ones?

I've managed to find a path such that the horizontal and vertical moves differ by two, but I'm stuck now. I'm starting to think it's not possible.

This is Stan Wagon's current 'problem of the week'. Archives here:

http://mathforum.org/wagon/

ZorbaTehZ

Is it not 65 moves since it returns to the original square?

EDIT: It is 64, nevermind me.

Fremen

Right, I'm stuck on a problem which I won't get a solution to for a week.

I got the solution, it's "No", it's not possible. The irritating part is that there was no proof provided.

Grr :mad:

ZorbaTehZ

I can't find the problem on that page, could you link it? Or are you just using the mailing lists?

Fremen

Yeah, mailing lists. It'll be on there in a week or so