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?

#HelpMe! #MathProblem #Math

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

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

Tim Vermeulen - 7 years, 11 months ago

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

Krishna Jha - 7 years, 11 months 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).

Luca Bernardelli - 7 years, 11 months ago

Daniel Leong - 7 years, 10 months ago

please answer this. it is very important for me.

ANSHUL AGARWAL - 7 years, 11 months 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.

Steven Perkins - 5 years, 6 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$