MathDB

Twelve balls are numbered by the numbers

1,2,3,\cdots,12

. Each ball is colored either red or green, so that the following two conditions are satisfied:
(i) If two balls marked by different numbers

a

and

b

are colored red and

a+b<13

, then the ball marked by the number

a+b

is colored red, too.
(ii) If two balls marked by different numbers

a

and

b

are colored green and

a+b<13

, then the ball marked by the number

a+b

is also colored green.
How many ways are there of coloring the balls?
Please remember to hide your solution. (by using the hide tags of course.. I don't literally mean that you should hide it :ninja: )

Problem Statement