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Inclusion Exclusion
How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?
One or Both
Problem one was solved by 70% of the pupils. Problem 2 was solved by 60% of them. Every pupil solved at least one of the problems. Nine pupils solved both problems. How many pupils took the exam?
Takeaway Time
Pizza, Indian or Chinese takeaway? If everyone liked at least one, how many only liked Indian?
Age 11 to 14 Short Challenge Level:
On Aisha's holiday, $11$ days had some rain.
A morning rain was always followed by a clear afternoon.
An afternoon rain was always preceded by a clear morning.
A total of $9$ mornings and $12$ afternoons were clear.
How many days had no rain at all?
This problem is taken from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.