Combinatoric problem

One thousand unit cubes are fastened together to form a large cube with edge length 10 units; this is painted and then separated into the original cubes. What is the number of these unit cubes which have at least one face painted?

Solution

The unpainted cubes form the 8 \times 8 \times 8 cube of interior cubes. Therefore,  10^3-8^3=488 cubes have at least one face painted.

ចំលង​សំនួរ​និង​ចំលើយ​ជា​ភាសា​ខ្មែរ​ទុក.

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3 Responses

11.05.09

It’s nice to be at your new home!

All the best :)

11.05.09

Many thanks.
It’s still under-construction ;-)

Have a nice day

11.05.09

Thanks for your sharing, It is good!

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