[ List Earliest Comments Only For Pages | Games | Rated Pages | Rated Games | Subjects of Discussion ]
Check out Janggi (Korean Chess), our featured variant for December, 2024.
Check out Janggi (Korean Chess), our featured variant for December, 2024.
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.