More advanced techniques are required to show that 73 is the most random number between 1 and 100.
Some numbers are more random than others. Ask a large group of people for a random number between 1 and 20 and there will be many 17s (sometimes half of one of my classes will say 17). Asking them for the “most random number” is enjoyable too because it makes no sense.
Look around on the web—this is not a new observation.
I first saw this argument, which is intended to be both amusing and serious, in a class on Chaos in the early 1990s at the University of Melbourne.