A company that ships boxes to a total of 12 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (assume that the order of the colors in a pair does not matter)  Choose the correct choice from the following answers:
A) 4
B) 5
C) 6
D) 12
E) 24

Rationale: "back - solving is the best way to solve this problem . you basically need 12 combinations ( including single colors ) if we start from option 1 - > 1 = > 4 c 2 + 4 = 10 ( not enough ) 2 = > 5 c 2 + 5 = 15 ( enough ) since the minimum number is asked . it should be 5 . answer - b"
Answer: B