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BMAT 2021 · Question 30 · Optimisation

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The students in year 8 at a school can choose between sports. They are divided into two equal groups. The first group chose between cricket and rounders in the first week, and between basketball and hockey in the second week. The second group chose between basketball and hockey in the first week, and between cricket and rounders in the second week. Numbers doing each sport are shown below:

Question diagram

What is the maximum number of pupils who chose both cricket and basketball?