Overlapping groups without a Venn diagram drawn for you
An overlapping-groups problem solved without a Venn diagram already drawn.
The Question
In a class of 30 pupils, 18 play football, 14 play cricket and 5 play neither. How many play both?
The Answer
Reveal the Answer
25 pupils play at least one sport. If 18 + 14 = 32 counts everyone once too often for the overlap, then the overlap is 32 − 25 = 7. Draw the two circles and fill the middle first, not last.
Now watch the solution
Practice Sheet + Marked Answers
The four-question practice sheet, the solutions in our teaching voice and a self-marking quiz for this question are part of The Question Desk course — every school day of the term, with progress you can see. Enrolled group students get it included.
Want a Plan Built Around Your Child, Not Just This Week’s Question?
Small groups of around 4–5 (max 8), matched to your child’s year group and pace. Start with the free baseline assessment and we’ll tell you exactly where they are.
