And Now For Something Totally Different

The 361,112 solutions for a 4x4 board includes all solutions, i.e. symmetry is ignored. However, the kings start in opposing squares. I do think however that the starting position of the king makes a big difference. I'm running an optimised version of the program now to find more than two solutions for an 8x8 board. I'm convinced there are thousands, if not millions.

Remember one King must follow the left path and the other King must
follow the right path at the same time.

They cannot meet as in normal chess.

Here are the paths.

http://img35.imageshack.us/img35/9650/kingstour.gif

I have seen those, thanks greenpawn34.

I have written the program to search for all combinations, regardless of the left/right directions, but as you pointed out: kings cannot "touch".

Oddly, I haven't find a solution yet... but it is churning 🙂 I find it difficult to believe that your board configuration only has 2 solutions. There must be more. I will keep the forum posted...

damn it! fundamental research in chess... who would have believed that!

Originally posted by Wumpus
I find it difficult to believe that your board configuration only has 2 solutions.

Am I reading it wrong?! From GP's initial post, for a *single* king there are two distinct tours with maximal distance and arriving back to form a cycle. Yes? No?

Then as a separate problem we try to follow such maximal paths simultaneously with both kings, albeit they can be on different paths. The number of solutions has not yet been mentioned for this variation of the puzzle.

That's it - both Kings have to follow the path laid down in:

http://img35.imageshack.us/img35/9650/kingstour.gif

At the same time.

I have one with the White King starting on f2 and the Black King on b5.

At the moment mine is only the solution - nobody knows how many
solutions there are.

I was asked in the Problemist club how I did it. I replied.

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I used Porters method of analytical progress for solving
chess problems of this nature. Most revolve around the number 7.

Counting from f8-f1 the square f2 is the 7th.
Counting from h5-a5 the square b5 is the 7th.

The Milan Formula also gave me a clue.

F is the 7th letter of the alphabet.
the second letter is 'B' so that gave me F2

'B' (2nd letter) + 5 (B5)=7

Therefore f2 and b5 had to be the start squares.

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Originally posted by greenpawn34
F is the 7th letter of the alphabet.

Cool, Scotland has a spare letter that the rest of us have to do without. Maybe it has the sound of someone clearing their throat. 😉

Originally posted by Schumi
Cool, Scotland has a spare letter that the rest of us have to do without. Maybe it has the sound of someone clearing their throat. 😉

Have I got to explain everything - are there no chess players on this site.

The Milan Formula.

A, B, C, D, E, G, F, H where f is the 7th letter was discovered written on
a piece of paper in Alekhine's coat pocket.

Nobody knew what it meant till Thelma Scroggins (1924-68) from
Preston one day declared it was the Milan formula and demonstrated
how every chess problem could be solved by making the g-file the f-file.

The exact method has been lost but if you move all the pieces from the f-file
to the g-file and visa versa then it usually works.



This is not checkmate - however if you move the King from g6 to f6 and
move the Queen from f7 to g7 (swapping the f & g files as per
the Milan formula) it is Mate.

You're a seriously funny serious man... you confuse me.