Trying to solve this problem:

Mixtures are made from 18 different color paints.

Every mixture has 6 different colors.

Every combination of 3 different colors is contained in at least one mixture.

What is the minimum number of mixtures that can be formed?

Example:
If the problem was 6 different color paints, 3 different colors in each mixture
and every combination of 2 different colors is contained in at least one mixture,
then the answer would be 6:
(1-2-4), (1-3-6), (1-4-5), (2-3-5), (2-5-6), (3-4-6)

I get 52; can someone confirm? Thanks loads.