255. Given the following statements:
1) Joe is a trickster;
2) Joe is unlucky;
3) Joe is lucky, but he is not a trickster;
4) if Joe is a trickster, then he is unlucky;
5) Joe is a trickster if and only if he is lucky;
6) either Joe is a trickster or he is lucky, but not both at the same time.

What is the maximum number of these six statements that can be true simultaneously?
$\triangle$ The third statement is incompatible with the first and the second. Therefore, among the first three statements, there is a false one. Since the number of true statements out of the given six should be the largest possible, the number of false statements should be the smallest. In this case, to have only one false statement among the first three, it is sufficient to consider the third statement as false.

The fifth statement is incompatible with the third, fourth, and sixth. For similar reasons, it should be considered false.

Thus, we have two false statements - the third and the fifth. The remaining statements are the first, second, fourth, and sixth. It is not difficult to verify that they are pairwise compatible with each other.

Answer: four - the first, second, fourth, and sixth.