Is this intuitively obvious?
Suppose that you are looking at information about 21 people on your computer screen. It is currently displaying the first 20. You look through the information and notice that everyone is from a different city. You scroll the list down and notice that the second to twenty-first people are from different cities. Is it obvious that everyone would be from a different city provided that the first and twenty-first were? How would you convince someone who was uncertain?
This is the best that I could do. Saying everyone is from a different city is the same as saying every pair is from a different city. From the first view we can conclude that every pair of people, not including the 21st person, is from a different city. From the second view, we can add every pair that includes the 21st person, except for the first person. The only pair that is missing is the 1st and 21st. If they are from different cities then everyone is.
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