Find Maximum in Venn Diagram In a class of 50 students, 34 students like Football, 26 students like Cricket and 16 students like Hockey. It is known that at least one student likes only Football, only Cricket and only Hockey. Similarly, at least one student likes both Football and Cricket (but not Hockey), both Football and Hockey (but not Cricket) and both Cricket and Hockey (but not Football). Further, at least one student likes all the three sports. Each student likes at least one sport. What can be the maximum number of students who like all three sports? My Solution through Venn Diagram was: ![Set Theory](

As an alternative, you could solve the problem using logical rules

h = |hockey| = 16

a = |football & !cricket & ! hockey| >= 1 b = |!football & cricket & ! hockey| >= 1 c = | football & cricket & ! hockey| >= 1

allSports = h - (min(a) + min(b) + min(c)) = 16 - 3 = 13