The symbols $\odot$ and $\nabla$ represent different positive integers less than 20 . If $\nabla \times \nabla \times \nabla=\nabla$, what is the value of $\nabla \times \nabla$ ?
(A) 12
(B) 16
(C) 36
(D) 64
(E) 81
If $\odot=1$, then $\nabla=\varnothing \times \odot \times \odot=1 \times 1 \times 1=1$, which is not possible since $\nabla$ and $\odot$ must be different positive integers.

If $\odot=2$, then $\nabla=\odot \times \odot \times \odot=2 \times 2 \times 2=8$, which is possible.

If $\odot=3$, then $\nabla=\odot \times \odot \times \odot=3 \times 3 \times 3=27$, which is not possible since $\nabla$ is less than 20 . If $\odot$ is greater than 3 , then $\nabla$ will be greater than 27 and so $\odot$ cannot be greater than 3 .

Thus, $\odot=2$ and so $\nabla=8$.

This means that $\nabla \times \nabla=8 \times 8=64$.

ANSWER: (D)