I have an example that I think demonstrates Ni.
(From a first year biology lecture, with 2 friends ENFP and ESFP).
Lecturer: So, in this isolated population on the mountains, geneticists discovered that there was a higher proportion of the albino gene than in other general populations. They were very puzzled, as they thought that the healthier, stronger males with more exposure to the sun would represent a better mating choice. In this population, the sexes have very defined roles. The males would go out into the field during the day and work on their crops, the females would stay indoors and take care of the household.
At this point, I started chuckling and ENFP and ESFP both looked at me like I was crazy.
It took them till the lecturer finished the story to "get it".
I think it illustrated the Ni - all the relevant facts clicked together, and the result (to me) was very obvious.