Fewest Who Play Nothing

Difficulty: Hard · Topics: Discrete Mathematics, Sets, Venn Diagrams

In a group of 40 people, 17 play football, 12 play basketball and 14 play volleyball. 5 people play both football and basketball, 6 play both basketball and volleyball, and 4 play both football and volleyball (these counts include anyone who plays all three).

What is the smallest possible number of people who play none of the three sports?