Problem:
In a group of people, there are who like apples, who like blueberries, who like cantaloupe, and who like dates. (A person can like more than kind of fruit.) Each person who likes blueberries also likes exactly one of apples and cantaloupe. Each person who likes cantaloupe also likes exactly one of blueberries and dates. Find the minimum possible number of people in the group.
Solution:
Answer:
Everyone who likes cantaloupe likes exactly one of blueberries and dates. However, there are people who like cantaloupe, who like blueberries, and who like dates. Thus, everyone who likes blueberries or dates must also like cantaloupes (because if any of them didn't, we would end up with less than people who like cantaloupe).
Since everyone who likes blueberries likes cantaloupes, none of them can like apples. However, the people who like both cantaloupe and dates can also like apples. So, we could have a group where people like apples alone, like blueberries and cantaloupe, and like apples, cantaloupe, and dates. This gives people in the group, which is optimal.