There have been many attempts to answer the question of how many distinct colors there are, with widely varying answers. Here we present an analysis of what it would take to arrive at a reliable answer and show how currently available models fail to make predictions under the wide range of conditions that needs to be considered. Gamut volumes are reported for a number of light sources and viewing modes and the conclusion is drawn that the only reliable data we have comes from psychophysical work. The color gamut of the LUTCHI data in CIECAM02 is therefore shown as an alternative to the gamut of all possible colors.