Question

I've decided I want to create my own new type of Colour representation!

I call it ROYGBIVT: Red, Orange, Yellow, Green, Blue, Indigo, Violet, Tartan.

Each of those eight colours will be treated as an individual colour channel for each pixel. Each channel will be represented by a 2-bit value.

What is the maximum possible number of colours representable for each pixel?

And... prove it!

Answer 1

ROYGBIVT: Red, Orange, Yellow, Green, Blue, Indigo, Violet, Tartan

They are 8 channels for a pixel and every channel represents two bits means 4 Values

Min - (00, 01, 10, 11) - Max

So the combination of these 8 channels can represented in
4 X 4 X 4 X 4 X 4 X 4 X 4 X 4 = 4⁸ = 65536 Colors

But the problem is that these colors are overlapping.
For example let your pixel has only for channel Red, Orange, Yellow, Green
And We use all Red(10), Orange(10), Yellow(10), Green(10)

So, in this case, Red + Yellow is already Orange,
So it will be like Orange + Orange + Green
But still, it will be a different color because orange and green are in 2:1

So there will be 65536 Colors and some will have more shades than others due to having the advantage of more representations.