All ten red-eyed inhabitants kill themselves on the tenth night after the missionary has left. To see why, consider two red-eyed among 28 green-eyed instead: Each one will see one other red-eyed inhabitant and 28 green-eyed ones, but will not know the own eye colour. If, after the first night, each of the red-eyed inhabitants sees that the other one has not killed themselves, following the missionary's statement, the only conclusion left is that their own eye colour must be red too, since the other must be seeing at least one red-eyed person in to not have killed themselves on the first night. Thus they both kill themselves on the second night. If there are three red-eyed inhabitants, each of them waits for two nights to see whether the other two red-eyed people kill themselves. As they don't, all three kill themselves on the third night. This argument can be extended very straightforwardly to ten inhabitants, who kill themselves on the tenth night.