What kind of math problem is this?

a list of bag (e.g. from 1 to 10), you can not change the order, you
can put 1 of 3 color ball (red, green and blue). a rule you have to
follow, you can not put more than 3 same color of ball side by side.
e.g. you put a red ball in bag No 4 first, and then bag No 5, Once you
put red ball to bag No 6, for bag No 3 and 7 can only place green and
blue ball.
Also, once you remove any one ball from bag 4, 5, and 6. the red ball
option will be back for bag 3 and 7.
Also, if there are red ball in bag 4, 5, and 7, then you can not put
red ball to bag 6 either.
Also,
Now the biggest problem I have, how to handle the remove part. I use
database, in this case, I store any change relate to bag 6, now I need
associate them to bag 4 and 5 as well.
What kind of math problem is this so I can research further, what's
the solution, where is the best place to find the answer.
.

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