Combinatorics and permutations of rankings

Question

In a country there are 2016 cities. We can draw 4 rankings A1. . . , A4, each order totally all the cities of this nation. Every tourist who comes will choose a ranking Ai and a c town and visit all the cities that, according to Ai, are better than c, eventually deciding whether to go also in c. In the end we want, for every two different cities c and c0, that the number of all the tourists who have visited c is different from the number of all those who have visited c0. What is the minimum number k of tourists with which it is possible to satisfy this condition?

Answer 1

Hint: if there are $n$ cities, you need $n$ different numbers of tourists visiting cities. How many tourists does it take to satisfy that, ignoring the fluff about how they decide which cities to visit? Now convince yourself that you can get all those numbers with the process described. In fact, you can do it with all the tourists using the same ranking.