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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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School Dinners

Stage: 3 Short Challenge Level: Challenge Level:1

Every second meal I will have soup for my starter.
Every $5$th meal I will have meat for my main course.
Every $3$rd meal I will have crumble for my afters.

$2, 5$, and $3$ have no common factors, so I will have eaten $2\times5\times3=30$ school dinners before I sit down to the same combination.

This problem is taken from the UKMT Mathematical Challenges.
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