[Dylan16807]

You've just expressed part of the problem with numbers, you haven't tied them into averages and minimums/maximums.

[phaemon]

Why is that required?

[Dylan16807]

The prompt you were responding to was "I have no idea what that explanation would look like in terms of maxes and averages, and I have to believe it would be much more difficult to understand."

Specifically, they were looking for how you write the can't-always-compress proof using formulation (1)

[phaemon]

Oh right. I read it as "how else could you explain it simply". I always thought the pigeon hole principal was a needless metaphor.