### 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 1 was solved by 70% of the pupils. Problem 2 was solved by 60% of them. Can you work out how many pupils took the exam?

### Takeaway Time

Pizza, Indian or Chinese takeaway? If everyone liked at least one, how many only liked Indian?

# Rain

##### 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.