Both quarks and gluons carry a type of charge called color. Like electric charge, color charge is always conserved. But unlike the electric charge, the color charge comes in six varieties, three colors and three anti-colors. The colors are usually called red, green, and blue. The idea is that we know that protons and neutrons as well as hadrons are made up of quarks. Yet we never see color charge even if we try to break up protons and neutrons into their constituent parts (colored quarks). So the objects that we observe, and therefore construct, must be colorless or color neutral; which is why we cannot see individual quarks. When each quark in a hadron has a different color:

the result is a color neutral object. This also allows the quark theory to describe another class of particles: mesons which have a quark and an anti-quark

color + anti-color = white

Gluons carry color/anti-color pairs that do not have to be the same color. There are 8 gluons as they each have one of the eight possible color/anti-color combinations.
See Quantum Chromodynamics

Oddly enough, if you count all possible color/anti-color pairs, you will get the number 9. But brainwave is still right, there are only 8 gluons. The reason for this is somewhat obscure, buried as it is in the intricacies of group theory, and it ends up sounding like a rather Tolkeinesque myth. It turns out that if all nine gluons existed then quarks would not be subject to confinement, and free color charge would be everywhere and the world would be completely dominated by the strong nuclear force, rather than the electromagnetic force as it is now. The absence of one combination forces quarks to be confined, and hence the strong force to have a very limited range.

Unfortunately, explaining which one is missing is kind of complicated. It is easiest to talk about gluons as if they were straight color/anti-color pairs like rb* (red/anti-blue) or gg* (green/anti-green). But it seems that the physical gluons are actually combinations of these such as (rb* + br*)/sqrt(2). The ninth, "missing", gluon is (rr* + bb* + gg*)/sqrt(3).

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