Actually there is a way of proving that no answer other than C exists
After checking A,B,C only B can be blue ,other cases only exist when B is not blue
This implies,none of the A,B,C cannot be blue.
So, A,B,C are either white or pink.
This further implies first and last statements of the A,B,C are false.
B-> C->Pink A->Pink B->Blue
A-> B->White C->Pink A->Blue
C-> A->White B->Blue C->Blue
negating first statements of B,A,C we get
which are to be considered true.
now if A->Pink is a true statement then second statement of A must be true which says C->Pink but from above we can infer C->White which is a contradiction.
Hence ,C) is the answer