Three Kinds of Juice

Difficulty: Hard · Topics: Discrete Mathematics, Sets, Word Problems

For each of the 25 guests at an opening, one glass of tangerine juice, one glass of pomegranate juice and one glass of orange juice was prepared and offered. About these drinks it is known that:

- every guest took at least one kind of drink; - no guest took more than one glass of the same kind; - no guest took exactly two kinds.

At the end 7 glasses of tangerine juice, 8 glasses of pomegranate juice and 9 glasses of orange juice had not been taken.

How many guests took all three kinds of drink?