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King's Maths School

Challenge 460: Polyglots

How many people speak multiple languages in these scenarios?

(a)

There is a city with a population of exactly 5 million people.

In this city, 9 languages are spoken, and each language has exactly 1 million speakers.

Find the least value of N such that there must exist a pair of languages with at least N speakers.

(b)

There is a city with a population of exactly 5 million people.

In this city, 16 languages are spoken, and each language has exactly 1 million speakers.

Find the least value of N such that there must exist a trio of languages with at least N speakers.

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