wu :: forums - Print Page


    
      
        wu :: forums
        (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi)
      

        riddles >> easy >> Chess knight moves
        
(Message started by: BNC on Jan 29^th, 2003, 10:48am)

Title: Chess knight moves
Post by BNC on Jan 29^th, 2003, 10:48am

A knight is placed on a chessboard, on the top left square. Can the knight, following legal knight chess moves, get to the bottom right square, after being at every square precisely once?

Title: Re: Chess knight moves
Post by towr on Jan 29^th, 2003, 12:55pm

...
[hide]In every jump the knight goes from one color to the other. Top left and bottom right are the same color. Since he's allready on one square, the knight needs to jump 63 times to have been on all squares. This means he will be on a different color than the one on which he started (top left). And thus a different color than bottom right (which, still, is the same color as top left)[/hide]
...

Title: Re: Chess knight moves
Post by Garzahd on Jan 29^th, 2003, 2:39pm

...
[hide]Barring the case mentioned in towr's answer, a chess knight CAN hit all 64 squares exactly once. He can *even* do so such that numbering the squares in the order the knight touches them makes an 8x8 magic square. [/hide]
...

Title: Re: Chess knight moves
Post by mistysakura on Jan 30^th, 2003, 2:28am

But it has to be the top-left to bottom-right, [hide]making the squares the same color.[/hide] Therefore, it is impossible.

Title: Re: Chess knight moves
Post by towr on Jan 30^th, 2003, 6:02am

how about we change "after being at every square precisely once?" to "after having jumped to every square precisely once?" (meaning it has to, at some point also jump to the corner it started on)

Title: Re: Chess knight moves
Post by Chronos on Feb 3^rd, 2003, 4:43pm

Quote:

(meaning it has to, at some point also jump to the corner it started on)

That "some point" isn't very mysterious, though. If your variant is solveable, then the "jump to the original square" must be on the second move. There are only two squares which "connect" to a corner square, and you use one up on the first move, and also use one up moving back onto the square, leaving you without any place to go when you leave the corner the second time... Unless "just left the first time" and "about to return to the corner" are at the same point.