The term "brightness" is a very unlucky term as it is often used incorrectly, especially in computer-related color space issues, mostly due to poor understanding of physics by the people who introduced the terms. Please see:
http://en.wikipedia.org/wiki/Brightness[
^].
I would prefer to call it "value", as in the name of the color space "HSV". Please see:
http://en.wikipedia.org/wiki/HSV_color_space[
^].
This article explains some controversies in "brightness" or "lightness".
For more general understanding of color spaces, please see:
http://en.wikipedia.org/wiki/Color_space[
^].
[EDIT]
Please also see my notes to Solution 1.
—SA