Six Desserts

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

At a party with 6 desserts, the number of people who tasted at least two of them is half the number of people who tasted at most three of them, and at the same time twice as large as 3 more than the number of people who tasted at least four of them.

There are people at this party who tasted all of the desserts. At least how many people tasted at most one dessert?