In a college consisting of 200 students, 112 students took the Maths Olympiad, 160 students took the Physics Olympiad and 128 students took the Chemistry Olympiad. If each student in the college takes at least one of the three exams, what is the minimum number of students who took all the three exams?

Let the number of students who took exactly one exam be ‘x’.
The number of students who took exactly two exams be ‘y’ and the number of students who took exactly three exams be ‘z’.
So, x + y + z = 200
x + 2y + 3z = 112 + 160 + 128 = 400
From these two equations, we get, y + 2z = 200
To minimize ‘z’, we have to maximize ‘y’. If z = 0, y = 200. In this case, x = 0
So, the minimum number of students who took all the three tests is 0.