12 Days of Christmas GMAT Competition - Day 1: Pablo wants to paint a

total faces are 6
we can have following cases
all faces Blue and 0 red - 1 way
all faces red and 0 blue ; 1 way
5 blue and 1 red ; 1 way
5 red and 1 blue ; 1 way
4 blue and 2 red ; 2 ways as red can be adjacent side
4 red and 2 blue ; 2 ways as blue can be adjacent side
3 red and 3 blue ; 2 ways
total ways ; 10
option B

chetan2u Bunuel KarishmaB GMATPill
Why is the solution not 2^6=64 (each of the 6 faces has 2 options)? How do we know when to use which approach?
Not able to understand why are we looking for pattern this way? Is this solution because of this part of the question- "if two cubes are considered different only when one cannot be reoriented to match the other"? Also is there any other easy way to visualize this? Not able to figure out this solution

We could use 2^6 if all faces were distinct, say in case of a die. Each face of the die has a number from 1 to 6 written on it. Now we could paint the 1 number face red or blue, the 2 number face red or blue etc. So here we can paint in 2^6 ways.
But a regular cube has all identical faces so we end up enumerating. With identical spots, often enumeration is required.

Yes, this part ("if two cubes are considered different only when one cannot be reoriented to match the other") tells us that say we paint the top face red and all other blue and in another case, we paint the bottom face red and all other blue - they are the same case and should be counted once only. The faces are to be considered identical because we can pick the first cube and put its top face down to give us the second case. So essentially, the faces are identical.