Geometry

[Fej]

A 5 cm cube is made up of 1 cm cubes glued together. How many of the 1 cm cubes are face to face with exactly 4 other cubes?

 

[Deleted member 4993]

A 5 cm cube is made up of 1 cm cubes glued together. How many of the 1 cm cubes are face to face with exactly 4 other cubes?

Does "5 cm cube" mean that each edge of the cube is 5 cm?

Is it a solid cube or hollow cube?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

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Please share your work/thoughts about this problem.

 

[Otis]

How many of the 1 cm cubes are face to face with exactly 4 other cubes?

Hi Fej. All cubes have six faces.

Hint: If a cube is face-to-face with only four other cubes, then two of its faces must be exposed to the air.

Did you draw any diagrams, to begin investigating?

Alternatively, you could experiment by stacking sugar cubes (or any type of available rectangular blocks).

You could also start by thinking about a 3×3×3 stack of cubes, to see what's happening, and then work up to a 5×5×5 stack.

Please share what you've tried or thought about.

?

 

[Otis]

Think about it.