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# Snatoms and Possible Combinations

I recently came across Snatoms by Derek Muller (Famous Veritasium guy).

Let's say we have a 'C' shape which can have 4 attachments to it

'O' shape that can have 2 attachments to it

and 'H' shape that can have only 1 attachment

How many possible valid combinations can be made out of 6 'C', 6 'O' shapes and 12 'H' shapes? Is there any way to generalize this? (Don't think about chemistry concepts while solving this problem, and by "valid" combinations I mean to exclude combinations that are not possible for instance CH5 to CH12)

Note by Vikram Pandya
10 months, 3 weeks ago

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Oh yes! That starts to delve into graph theory. You are basically asking for the number of graphs (up to isomorphism) where the vertices of degree 4, 2, 1 occur at most 6, 6, 12 times.

There are 2 ways to interpret the question
- We care about the positioning of the graph. E.g. $$O = O, O = O$$ is considered different from $$O - O - O - O$$ (with the last linked back to the first)
- We only care about the vertices that are used. Staff · 10 months, 2 weeks ago

Can you take a stab at generalization of this number theory problem over here · 9 months, 3 weeks ago