# Chessboard Question

In a chessboard colouring of the " 2-D plane", every black square has an equal number of white and black squares as neighbours-4 (even sharing a single vertex is counted as a neighbour) . If one did a chessboard colouring of the 3-D space, such that it (the 3-D space) is divided into cubes, and for the 2 planes "vertical" and "horizontal" that every cube belongs to , has a chessboard colouring , what is the number of black neighbouring cubes a black cube has?

Note by Anshul Agarwal
5 years, 1 month ago

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Pls elaborate on the question.. its nt clear that which horizontal and vertical planes u are talking of...

- 5 years, 1 month ago

For consistency, please don't use all-caps and that many exclamation points.

- 5 years, 1 month ago

2

- 5 years ago

8 neighbours of the same color, if you mean that cubes sharing a vertex are neighbours....and 6 of the opposite color (right, left, up, down, front and back).

- 5 years, 1 month ago

- 5 years, 1 month ago

Think of a Rubik's cube in a checkerboard pattern. The (invisible) center cube is the black cube whose neighbors we are counting.

There are 26 small cubes "touching" the center cube in this 3x3x3 arrangement. All the middle edge cubes are black. All the corner (8) and center (6) cubes are white. There are 12 black cubes "touching" the center cube at their edges.

- 2 years, 8 months ago