MathDB

Twenty seven unit cubes are painted orange on a set of four faces so that two non-painted faces share an edge. The

27

cubes are randomly arranged to form a

3\times 3 \times 3

cube. Given the probability of the entire surface area of the larger cube is orange is

\frac{p^a}{q^br^c},

where

p

q

, and

r

are distinct primes and

a

b

, and

c

are positive integers, find

a+b+c+p+q+r

Problem Statement