2002 AMC 10P Problem 15

What is the smallest integer n for which any subset of \{ 1, 2, 3, \; \ldots \; , 20 \} of size n must contain two numbers that differ by 8?

\text{(A) }2 \qquad \text{(B) }8 \qquad \text{(C) }12 \qquad \text{(D) }13 \qquad \text{(E) }15

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.