In a class of 40 students, 24 play cricket, 20 play football and 6 play neither game. How many students play both games?

First remove the 6 who play nothing: 40 − 6 = 34 students play at least one game. Adding the two groups gives 24 + 20 = 44, which counts every 'both' student twice, so the overlap is 44 − 34 = 10. The trap is 4, which comes from using the full 40 instead of 34 and so forgetting that 6 of the class are outside both circles.