What Three Colours Cannot Be Made by Mixing Other Colours?

The three colours that cannot be made by mixing other colours are the primaries, and there are two correct sets. If you are mixing light, they are red, green and blue. If you are mixing ink, paint or any pigment, they are cyan, magenta and yellow. Red, yellow and blue, the set most of us learned at school, is an older approximation of the second set, and it is the reason you could never mix a clean bright cyan or magenta from a primary school paintbox. Nobody can. That is what makes them primary.

• For light, the three colours that cannot be mixed are red, green and blue.
• For ink and paint, they are cyan, magenta and yellow.
• Red, yellow and blue is an older approximation that cannot reach a clean cyan or magenta.
• Printers add black (the K in CMYK) as a shortcut, not as a fourth primary.

Here is why the answer depends on the question.

Because light and paint do opposite things. Light adds. Shine a red torch and a green torch on the same spot and you get yellow, brighter than either. Add blue and you get white. The three colours of light that cannot themselves be made from other lights are red, green and blue, which is why every screen you own is made of tiny red, green and blue dots.

Paint subtracts. A pigment looks coloured because it absorbs some wavelengths and reflects the rest. Mix two paints and you keep only the light that neither of them absorbs, so the result is always darker than what you started with. The three pigments that cannot be made from other pigments are the ones that each remove exactly one of the light primaries: cyan removes red, magenta removes green, yellow removes blue. Those are the subtractive primaries, and they are the ones printers use.

Because the tradition is centuries older than the science. Painters worked out by trial that red, yellow and blue gave them the widest range of mixes from three tubes, and that lore was taught long before anyone understood wavelengths. It works well enough for a paintbox. What it cannot do is reach the bright, clean cyan and magenta that the true subtractive primaries provide, because red and blue paint are already mixtures in disguise. Red is roughly magenta plus yellow; blue is roughly cyan plus magenta. You cannot un-mix them. The primary colours debate covers the history in detail.

Red, yellow and blue are not wrong. They are a good approximation that hits its limits exactly where cyan and magenta should be.

Because those three inks, overlapped in varying amounts on white paper, can reproduce more of the visible spectrum than any other trio. Cyan over yellow gives green. Magenta over yellow gives red. Cyan over magenta gives blue. Small dots of each, printed side by side and on top of one another, produce every photograph and every colour on every page you have ever read.

Printers add a fourth ink, black, for a practical reason: mixing all three colour inks to make black uses a lot of ink and gives a muddy dark brown rather than a crisp black. The K in CMYK stands for "key", the plate that carried the black detail. It is not a fourth primary. It is a shortcut.

With light, white. Red, green and blue together give back the full spectrum, which the eye reads as white. With pigment, near-black. Cyan, magenta and yellow together absorb red, green and blue, which leaves almost nothing to reflect. In practice paint and ink are imperfect, so you get a very dark brown or grey rather than true black, which is exactly why the printer keeps a black cartridge.

Not from pigments, no, and that is the whole point. If a colour can be mixed from others, it is not a primary. Cyan and magenta are unfamiliar to most people not because they are rare but because they were missing from the paintbox. They were there all along in every printed photograph and every inkjet cartridge. Once you learn to see them, they are everywhere: cyan in a swimming pool, magenta in a bougainvillea.

Like three cubes. The C Cube, M Cube and Y Cube are solid, optically clear acrylic cubes each sealed in one subtractive primary. Hold cyan over yellow at a window and green appears where they overlap. Swap cyan for magenta and red appears. Stack all three and the light goes almost dark. You have just watched a colour printer work, at a scale you can hold.

The CMY Pack puts the three together with the Original CMY Cube, which carries all three primaries on one object and mixes them as you turn it. For the same physics with a bit of chance in it, the Septem Aleae is a seven-piece set of translucent CMY dice, currently on pre-order, that turns every roll into an overlap experiment.

The science page explains the same thing wavelength by wavelength, if you want the long version.

Three colours cannot be mixed from others, and which three depends on what you are mixing. Red, green and blue for light. Cyan, magenta and yellow for ink and paint. Red, yellow and blue was a useful guess that predates the physics, and its one failing is that it cannot reach the two primaries most people have never been shown. Hold a cyan filter over a yellow one and you will have learned in a second what a paintbox could not teach in a decade.

See the three primaries as three cubes, and view life and light through a different lens.