A chess board riddle

[l)ragon]

Care to prove this?
Edit:

Do you realy think anyone would paste '33,439,123,484,294' diagrams to prove this lol ;p

[Yoni]

No. See guideline "C" in my blacked out hint.

[K]

This sounds like that proof Euler did on the bridges in that town.  Graph theory and what not.  We talked about it in my algorithms class.  T'was so long ago, so I don't remember much.

[Yoni]

Over 140 thread views and still no solution. Oh well. I will post the proof here for anyone who's still interested.

First, paint the squares in the chess board black and white.
Do it like a regular chess board.

Observe the following property:
1. The starting corner and the ending corner of the rook have the same color.
(If the rook started on a white corner, it must travel to the other white corner, and if it started on a black corner, it must travel to the other black corner.)

Also note:
2. The rook must make 63 steps in its journey.
(It has to go through every square once. It's already in the first, so it must make 63 moves.)

Now, let's look at the properties of a move:
3. When a rook makes 1 move, it always moves to a square of a different color than it is now.
Simply because any adjacent square to a white square is black, and vice versa.

Now, to further generalize property #3, observe the following sequence of moves:
Let's say the rook starts at a white square, and starts a journey.
Then it travels through squares of the colors: Black, White, Black, White, Black, etc...
It's no problem to see (and prove by induction, too) the following:
4. When a rook makes an odd number of moves, it always moves to a square of a different color than it is now.

Now, knowing the above properties, we can ask: Can the rook make its journey?
5. The rook cannot make its journey. If it were able to, it would make 63 steps (according to #2), therefore end up in a square of a different color than it started with (according to #4), which cannot possibly be the ending square (according to #1). Q.E.D.
Now that you know the solution, attempt my other riddle!
http://forum.valhallalegends.com/phpbbs/index.php?topic=8999.0