Competition problem — Combinatorics

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Combinatorics Difficulty 2.2 Junior Find the answer

A wooden cube $n$ units on a side is painted red on all six faces and then cut into $n^3$ unit cubes. Exactly one-fourth of the total number of faces of the unit cubes are red. What is $n$ ?
$(\mathrm {A}) \ 3$ $(\mathrm {B}) \ 4$ $(\mathrm {C})\ 5$ $(\mathrm {D}) \ 6$ $(\mathrm {E})\ 7$

Your answer

Multiple choice: answer with the letter of the option you want.

Solution

There are $6n^3$ sides total on the unit cubes, and $6n^2$ are painted red.
$\dfrac{6n^2}{6n^3}=\dfrac{1}{4} \Rightarrow n=4 \rightarrow \mathrm {B}$

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.