We can create three drawers:  $(1, 4, 7, 10, 13, 16)$.  $(2, 5, 8, 11, 14, 17)$.  $(3, 6, 9, 12, 15)$.  At least $3\times3+1=10$ numbers should be chosen. 
There are $$17$$ balls in a bag. Each ball has a number from $$1$$ to $$17$$ on it. We randomly pick a ball from the bag. What is the smallest number of balls we have to pick in order to be sure that we have at least one pair of balls with a difference equal to $$3$$? (adapted from $$2005$$ Math Kangaroo Problem, Level $$9-10$$, Question \#$$15$$) 

A) $$7$$ 
B) $$8$$ 
C) $$10$$ 
D) $$11$$ 
E) $$16$$ 