Venn diagram

Question

Dave's sister baked 3 dozen pies of which half contained chocolate, two thirds contained marshmallows, three-fourths contained cayenne, and one-sixth contained salted soy nuts. What is the largest possible number of pies that had none of these ingredients?

Answer 1

The largest possible number of pies that had none of these ingredients is 6.

Answer 2

If 27 contained all three, then 9 could contain none.