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Omni-MATH / Consider the cube whose vertices are the eight points (x,y,z) for which each of x,y, and z is either 0 or 1 . How many ways are there to color its vertices black or white such that…

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problem

Consider the cube whose vertices are the eight points (x,y,z)(x, y, z) for which each of x,yx, y, and zz is either 0 or 1 . How many ways are there to color its vertices black or white such that, for any vertex, if all of its neighbors are the same color then it is also that color? Two vertices are neighbors if they are the two endpoints of some edge of the cube.
Plain-text mathematical notation (without MathML)
Consider the cube whose vertices are the eight points (x,y,z) for which each of x,y, and z is either 0 or 1 . How many ways are there to color its vertices black or white such that, for any vertex, if all of its neighbors are the same color then it is also that color? Two vertices are neighbors if they are the two endpoints of some edge of the cube.
Original LaTeX notation
Consider the cube whose vertices are the eight points $(x, y, z)$ for which each of $x, y$, and $z$ is either 0 or 1 . How many ways are there to color its vertices black or white such that, for any vertex, if all of its neighbors are the same color then it is also that color? Two vertices are neighbors if they are the two endpoints of some edge of the cube.

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Source and history

task_id
a43eb782-2d49-54da-a6fc-d6cab904a409
task_key
test--a43eb782-2d49-54da-a6fc-d6cab904a409
task_revision_id
1
config / split
/ test

Official source

initial import