The 8-buffalo sentence is a valid sentence, but for a long time I thought "This is just wishful thinking. This is only valid if you phrase it right or add linking phrases in between." It eventually clicked for me that it was totally right. Anyway...
You could use induction to show that buffalo of any length is right. This would take a while, so I'll just do a high-level overview of the logic.
The meaning of the full sentence is, substituting different words for buffalo, is...
"Chicago bison Chicago bison bully bully Chicago bison."
i.e. "Chicago bison that Chicago bison bully themselves bully other Chicago bison."
But it's easy to add even more to this, say...
"[bison bully] Chicago bison Chicago bison bully bully Chicago bison" to get to n=10...
"[bison bully] Chicago bison Chicago bison bully bully bison" to get to n = 9...
"[Chicago bison bully] Chicago bison Chicago bison bully Chicago bison" to get to n = 11...
And you can keep doing this inductively to add more and more clauses. This is the grammatical equivalent of something like...
"The man walked with his friend, who walked with his friend, who walked with his friend, who walked with his friend..."
That is, it's syntactically valid by the rules of our grammar, even if it would be considered invalid in any kind of writing or even spoken conversation.
