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Hmm that's a tough one, I don't know how to judge that. I guess it's either white, black and then all shades of grey cover 3 colors or just 1. I don't know if it's "correct" but I would lean towards counting them all as 1, otherwise 4 colors would be quite limiting when using white/black/grey as part of it.

If anyone else has any feedback, please let me know!

What about red and orange? Do these count as two? Is orange a shade of red or is it separate because yellow is mixed in?

I think you're taking it to another degree. That would be like saying, Red, Yellow and Blue are colours and everything else is a shade because they make up from the three primary colours being mixed. The definition of shade is not what you've defined so I'm not sure how you arrived at orange being a shade of red. I don't think the definition of colours is in dispute. As Mana said, Red and shades of red, ie; dark red, or light red are considered shades of red.

Ah, alright. I am not an expert.  I've just seen some artists use color palettes with red going into yellow  instead of into white to make it brighter,  so I was confused about what shade meant in art terms. Thanks for the info!