A florist is filling three vases with flowers. She has carnations, geraniums, heather, jasmine, and roses. Each vase must contain exactly two or three flower types. Exactly one vase has both roses and heather. All three vases contain jasmine. If a vase contains geraniums, it does not contain carnations.
How many vases could contain geraniums?
Jasmine is in all three vases and one vase also contains roses and heather, so there are only two remaining vases with space to add more flowers. No vase can contain both geraniums and carnations, but we are not required to have any carnations at all. Thus, geraniums can go in both of the remaining vases.