A company that ships boxes to a total of 12 distribution centres uses colour coding to identify each centre. If either a single colour or a pair of two different colours is chosen to represent each centre and if each cenre is uniquely represented by that choice of one or two colours, what is the minimum number of colours needed for that coding, assuming that the order of the colours in a pair do not matter?
(A)4
(B)5
(C)6
(D)12
(E)24
OA is B
The method I followed was to look at the answer choices directly i.e. (A) 4 colours will cover 4 distribution centres and 4C2=6 so 6 more centres will be covered. 6+4=10 so two centres will still be left so incorrect.
(B)5 colours will cover 5 centres. Then 5C2=10 and 5+10=15 so this will cover all the twelve centres with a few combinations left over. So B
However, I'm hoping to figure out a direct method to solve this one. Hoping to get responses on an alternate method that is more direct. Detailed explanations would be highly appreciated.
(A)4
(B)5
(C)6
(D)12
(E)24
OA is B
The method I followed was to look at the answer choices directly i.e. (A) 4 colours will cover 4 distribution centres and 4C2=6 so 6 more centres will be covered. 6+4=10 so two centres will still be left so incorrect.
(B)5 colours will cover 5 centres. Then 5C2=10 and 5+10=15 so this will cover all the twelve centres with a few combinations left over. So B
However, I'm hoping to figure out a direct method to solve this one. Hoping to get responses on an alternate method that is more direct. Detailed explanations would be highly appreciated.
