This is definitely one of those tricky visualization problems

Imagine just one face of the 5x5 cube. (I'm imagining this massive Rubik's cube

)

Which of the 1x1 cubes will have paint on only one face? Only those which are not on the

edges - these will share a painted face with another side. The cubes that are not part of the

edge form a 3x3 grouping of 1cm cubes.

Therefore each face has 9 cubes that are painted one color.

Since there are 6 faces we get 6x9 = 54.

Hope that helps!

_________________

Christopher Lele

Magoosh Test Prep