Chapter 4.7, Problem 31MS

Here we celebrate the power of algebra as a powerful way of finding unknown quantities by naming them, of expressing infinitely many relationships and connect ions clearly and succinctly, and of uncovering pattern and structure.

Summing square. After the Math Club built their 6-dimensional hypercube model, club president Edwinna decided to calculate how many square faces (2-dimensional faces) this monster model had. If a cube in n dimensions has $\left(n\right)\left(n-1\right)2^{n-3}2-dimensionalfaces,$ how many such faces does the Math Club’s model have?