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'Holes' printed from http://nrich.maths.org/
Here we have three solid cubes and
three cubes that have holes.
They're just the first three in a series that could go on and
I was wondering about the number of
cubes used in each ...
Then I thought about the difference
between those numbers.
So, for example, I found that the first cube, $3$ by $3$ by $3$,
used $27$ cubes.
The same cube with holes used $20$ cubes, a difference of
You can call these types of cubes
what you like but I called them "Solid" and "Frame".
How about exploring the numbers for the next few Solid and Frame
Do you notice any patterns?
Can you explain any of the