Chain Theory (I Feel Like A Scientist)

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Lavair

3:19

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Regardless on whether the grid has an even or odd amount of shaded cells
We can show the unshaded cells directly gained from the shaded 
(Before regarding connectivity) will always be an even total
It will be...
Maths aside, important part is that this will always be even
Now let's calculate how much borders in the grid will be passed through

The total amount of borders passed through will be...
Hmmm, how do we find the total of shadeds against a border though
This is actually known
Penalty shows us that it will always be...

You may recognise the end of that equation there
We can now ram these equations up against each other and simplify it all
I'm no maths whiz so ill just spit out Agnomy's result

Times 2
A.k.a "blah blah blah times 2"
So it's even
So what does this mean exactly
It means we can't have a situation in the grid where we make a chain link 
(Area where the dominos of located cells overlap) shaded
Because even though we may situationally be able to avoid a contradiction there
It will axiomatically lead to an impossibility later on somewhere
Or would imply that the grid does not contain symmetric regions
When I read this, it kinda blew my mind

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