Real numbers x, y, and z are chosen independently and at random from the interval [0, n] for some positive integer n. The probability that no two of x, y, and z are within 1 unit of each other is greater than \dfrac{1}{2}. What is the smallest possible value of n ?
Answer Choices
A. 7
B. 8
C. 9
D. 10
E. 11