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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?

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Takeaway Time

Pizza, Indian or Chinese takeaway. Each teenager from a class only likes two of these, but can you work which two?

One or Both

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

An ideal opportunity to discuss different approaches to a solution which might result from students working on the first part of the problem.

Out of the methods adopted by the students might emerge the idea that the pupils in the problem who got both questions correct have been counted twice so 9 must represent any percentage over 100. This might be a useful idea when trying to tackle the second part of the problem.

The third part of the problem aims at encouraging greater generalisation and therefore reinforce some of the ideas developed in the first part of the problem.