Why are there eight gluon states and not nine?

During A-Level Physics, students learn about the strong nuclear force and very keen students may read about the eight different gluon states. It can be difficult for students to understand why there are eight states and not nine. Indeed, I’m not sure I understand it myself!

Nevertheless, in this video I try to explain it to A-Level students. I’m not sure I made quantum-chromodynamics any clearer though.