# 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
2 years, 8 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

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 - 2 years, 8 months ago

Can you take a stab at generalization of this number theory problem over here

- 2 years, 7 months ago

Hey Calvin, thanks for stopping by. I was travelling so could not reply in time. When I posed the question I had only vertices in my mind :)

- 2 years, 7 months ago