Poor knight in a dilemmatic situation

Nihar calls a situation in chess as dilemmatic if it consists of only a white knight and a black queen placed such that whatever first move the white knight plays it gets killed by the black queen in the next move. How many distinct arrangements of white knight and black queen can be made to achieve a dilemmatic situation?

As an explicit example,

The above figure shows red dots as all the places where the white knight can move. But since all red dots are in the attack range of the black queen, the white knight would be definitely killed and hence, this situation is dilemmatic.