Please try this activity:
Tell me if I have made mistakes or omissions, or any ideas for improvement.
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
There is only a single spelling error. Almost half way down the page "Amd."
To really investigate those stars would require a good sketcher type program. I quickly made a big mess with pen and paper.
What is the reason why for difference between the 6 and 7? Is it because they composite and prime?
In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.