Here's the surprising thing about light: it doesn't mix the same way paint does.

When you mix red and blue PAINT, you get purple — and it gets darker. But when you mix red and blue LIGHT, you get magenta — and it gets BRIGHTER. Scientists call this additive colour mixing, and it's the complete opposite of what happens with paint or dye.

Your three phone screens are sending red, green, and blue light at the same spot on the wall. Where all three overlap, you get WHITE 

— because red + green + blue light = white light. 

That's actually how sunlight works. White light contains all colours mixed together.

Now the shadow trick: when you put your hand in front, it blocks some of the light — but not all three colours. The wall behind your hand still gets lit by whichever phones your hand didn't block. So instead of a black shadow, you see whatever colours made it through.

• Block the red phone → green + blue light hits the wall → CYAN shadow

• Block the green phone → red + blue light hits the wall → MAGENTA shadow

• Block the blue phone → red + green light hits the wall → YELLOW shadow

Seven different shadow colours are possible. None of them have to be black — black only appears when all three lights are blocked at once.

Screens add light together from darkness. Paint and dye do the opposite — they subtract colours from white light by absorbing them. 

You can see the subtractive system in action in [Colour Smashers], where coloured paddles remove light rather than add it, and watch it happening inside real leaves in [Sneaky Light Absorbers].