Check out Janggi (Korean Chess), our featured variant for December, 2024.


[ Help | Earliest Comments | Latest Comments ]
[ List All Subjects of Discussion | Create New Subject of Discussion ]
[ List Earliest Comments Only For Pages | Games | Rated Pages | Rated Games | Subjects of Discussion ]

Single Comment

Chess Geometry[Subject Thread] [Add Response]
Ben Reiniger wrote on Sun, Nov 17, 2013 10:39 PM UTC:

I think the 4-coloring of the hex board can help to prove this. See
wikipedia's 4-coloring image

If a leap has odd SOLL, then in any right angle diagonal-orthogonal path--say m diagonal and n orthogonal as before--we must have that m and n have different parities (else 3m^2+n^2 is even). Then the starting and landing cells have different colors in the 4-coloring.

But each orthogonal-diagonal pair of directions at right angles involve exactly two colors, one of which is the starting cell's color. So traveling along distinct orthogonal-diagonal directions lands at distinct color cells.