# Rubik's Cube!

Discrete Mathematics Level 1

Find the smallest positive integer $$k$$, such that for all positive integers $$n$$, a $$kn \times kn \times kn$$ Rubik's cube can be used as a Rubik's cube of any size that is smaller than itself.

• An example of such a cube is a $$4 \times 4 \times 4$$ cube, because we can use it as a $$3 \times 3 \times 3$$ cube, a $$2 \times 2 \times 2$$ cube and a $$1 \times 1 \times 1$$ cube as shown. The 4 by 4 cube uses all 4 center pieces as one to function like a single center piece on a 3 by 3 cube.
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