According to the Wikipedia entry, a Latin Square is an NxN matrix filled with N different symbols such that no symbol appears more than once in any row or column.
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In signature order, they are: CD, BD, BC, AD, AC, and.
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If replacing each number by its square also results in a magic square, the square is bimagic.
Each cube results in three labeled edges on the graph (for twelve edges altogether) - an edge connecting two nodes (or a node with itself) when those two colors appear on opposite faces of the cube, labeled with an identifier for that cube.
Sometimes the additional restriction of disallowing a repeated symbol along either main diagonal is also added.
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