2008 iTest Problems/Problem 88

Problem

A six dimensional "cube" (a $6$ -cube) has $64$ vertices at the points $(\pm 3,\pm 3,\pm 3,\pm 3,\pm 3,\pm 3)$ . This $6$ -cube has $192\text{ 1-D}$ edges and $240\text{ 2-D}$ edges. This $6$ -cube gets cut into $6^6=46656$ smaller congruent "unit" $6$ -cubes that are kept together in the tightly packaged form of the original $6$ -cube so that the $46656$ smaller $6$ -cubes share $2-D$ square faces with neighbors ( $\textit{one}$ $2$ -D square face shared by $\textit{several}$ unit $6$ -cube neighbors). How many $2$ -D squares are faces of one or more of the unit $6$ -cubes?

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2008 iTest Problems/Problem 88

Problem