Eldragonfly, if you look at my follow up, I posted my exact method. Take 10 minutes and you'll be able to do exactly the same thing yourself. Why on earth would I want to lie about something that can be done, and indeed post how it can be done? If you want, post any two squares of opposite colours and I will give the solution (you can check back my method post as well, the solution will follow that method). I am fairly sure there is not a computer program that does this, so I think this is fair, but until I do this for anyone other than schoolfriends, you'll have to trust.
Originally posted by eldragonfly that is a knights tour starting on d4 perhaps.
You can start on any square and reach it again after 64 moves if you follow the numbers (either follow the numbers ascending or descending). Not sure what's going on in the rest of the replies after my last comment?
Originally posted by heinzkat You can start on any square and reach it again after 64 moves if you follow the numbers (either follow the numbers ascending or descending). Not sure what's going on in the rest of the replies after my last comment?
i believe there are different "flavors" of knight tours, if i am not mistaken.
Just taking a look at something here real quick, but I do believe a Knight's Tour of any flavor is impossible on a 4x4 board, making a 5x5 the most probable minimum size to make a Knight's Tour possible on any square board.
The issue with the 4x4 board is this.
1) Opposite corners have the same two jump off points, and must be taken together.
2) Due to this, you will start in a corner, then hop into the opposite corner and back out.
3) You don't want to enter the other set of 4 with the other 2 corners until all other squares have been visited. The reason is that you'll enter a jump in spot, into one corner, into the other jump in spot, and then wind up painted into the last corner.
4) Unfortunately, between the first 4 squares, and the last 4 squares is a fork in the road. You can travel along one set of 4 and be forced into the final 4 squares, or else you'll visit the other. You can take one way, but not both, unless you forego visiting one of the two remaining corners.
I did find a 5x5 solution. As with any odd x odd board, you'll end up on the same color square as you started and hence won't be able to connect start directly yo end as with the 8x8 board.
With the 5x5, all 4 corners are connected (but not split up) and must be taken at one time (as there are only 4 jump-in spots total). You'll therefore have to start or end in a corner. The remaining places to visit can easily be danced around in spirograph fashion.
Originally posted by greenpawn34 This just popped into my head whilst playing over a game
30 minutes ago.
White Knights on a1 and h8
Black Knights on h1 and a8
The a1 Knight Knight moves first, then a8, h8 and h1.
Same rules as standard a Knight's tour
No Knight can land on a square that has already been visited by a Knight.
All squares must be covered and the Knights mu ays take a
square furthest from the centre and you will eventually work your
way inwards.
a four knight tour where you start off the knights in there normal position then in 12 moves flip black and whites positions..without ever attacking another kinght . i played with that for awhile, it can be done.
02 Jul '08 21:41
Four Knight Tours
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