No combination of other colors can be used to make white paint because any other color of paint absorbs some of at least one particular wavelength. Combining paints or filters to form other colors is known as subtractive color mixing.
For example, cyan paint, no matter what its shade, absorbs some red-wavelength light. Yellow paint absorbs some blue-wavelength light. When these colors are combined, the mixture partially absorbs both red and blue wavelengths, resulting in a green color. Magenta pigments absorb some green light, so mixing equal amounts of equally bright cyan, yellow and magenta paint results in gray. Even if all three pigments are in very light shades, the only result can be a very light gray because not all of the wavelengths are reflected instead of absorbed. Therefore, the only method of making purely white paint is to use a single compound that reflects red, green and blue light, which appears white to the human eye.
However, in additive color mixing, in which wavelengths are emitted rather than absorbed, the opposite is true. If red, green and blue spotlights converge on the same spot, their combination is white. This principle is used in televisions, fluorescent lamps and computer monitors.