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'Cube Drilling' printed from http://nrich.maths.org/

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This activity is all about imagining, like you might when you listen to a story or poem.

There is no need to write or draw anything

BUT
talking about it could be good!


imagine!



Imagine a 4 by 4 by 4 cube hanging in front of you with just the front face facing you.
The cube is made up of 4x4x4, 64 cubes.
You drill a hole through the four corner cubes, that are facing you, all the way through to the back.

Drilling



A friend looks down on the cube, from above, and they also drill four holes through their four corner cubes all the way through to the bottom.
You and your friend examine all the 64 small cubes.

How many will not have holes drilled through them?

What if the same kind of activity happened with a new 4 by 4 by 4 cube but, this time, you drill holes through the four centre cubes that are facing you and your friend drills holes through the four centre cubes that are facing them.
You and your friend examine all the 64 small cubes.
How many will not have holes drilled through them?

Please do send in your solutions, describing how you worked them out.